./PaxHeaders.5293/geometry-2.1.10000644000000000000000000000013212676233417013120 xustar0030 mtime=1459173135.645054067 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/0000755000175000017500000000000012676233417014217 5ustar00juanpijuanpi00000000000000geometry-2.1.1/PaxHeaders.5293/INDEX0000644000000000000000000000013212676233416013631 xustar0030 mtime=1459173134.825445125 30 atime=1459173134.825445125 30 ctime=1459173135.645054067 geometry-2.1.1/INDEX0000644000175000017500000000752112676233416015015 0ustar00juanpijuanpi00000000000000geometry >> Computational Geometry 2D Descriptive geom2d_Contents points2d vectors2d angles2d edges2d rays2d lines2d boxes2d circles2d ellipses2d transforms2d polygons2d 2D Points centroid closed_path distancePoints drawPoint findClosestPoint isCounterClockwise isPointOnRay isPointInCircle isPointOnCircle isPointOnLine isPointInEllipse midPoint minDistancePoints polarPoint 2D Vectors createVector vectorNorm normalizeVector rotateVector 2D Angles angle2Points angle3Points angleAbsDiff angleDiff normalizeAngle vectorAngle angleSort lineAngle edgeAngle deg2rad rad2deg 2D Edges createEdge distancePointEdge drawCenteredEdge drawEdge edgeLength edgePosition edgeToLine intersectEdges intersectLineEdge reverseEdge transformEdge isPointOnEdge 2D Rays drawRay createRay 2D Lines cartesianLine createLine distancePointLine drawLine intersectLines isParallel isPerpendicular linePosition medianLine isLeftOriented orthogonalLine parallelLine pointOnLine projPointOnLine reverseLine 2D Polylines projPointOnPolyline 2D Boxes clipEdge clipLine clipPoints clipRay mergeBoxes intersectBoxes drawBox randomPointInBox drawRect drawOrientedBox 2D Circles createCircle createDirectedCircle circleArcAsCurve circleAsPolygon drawCircleArc drawCircle enclosingCircle intersectCircles intersectLineCircle radicalAxis 2D Ellipses cov2ellipse drawEllipseArc drawEllipse ellipseAsPolygon ellipse2cov inertiaEllipse 2D Transformations transformLine transformPoint transformVector createBasisTransform createHomothecy createLineReflection createRotation createScaling createTranslation fitAffineTransform2d 2D Cubic Bezier drawBezierCurve cbezier2poly 2D Polygons curvature distancePolygons distancePointPolygon distancePointPolyline drawPolygon drawPolyline expandPolygon fillPolygon medialAxisConvex parametrize polygonLoops polygonPoint polygonSubcurve polygonSelfIntersections polylineSelfIntersections rectAsPolygon reversePolyline reversePolygon simplifypolygon simplifypolyline splitPolygons supportFunction 2D Piecewise polynomial shapes polygon2shape shape2polygon shapecentroid shapeplot shapetransform curveval curve2polyline 2D Polynomial curves drawPolynomialCurve polynomialCurveCentroid polynomialCurveDerivative polynomialCurveFit polynomialCurvePoint polynomialCurveSetFit 2D Others beltproblem bisector crackPattern2 crackPattern drawArrow drawLabels drawParabola drawShape hexagonalGrid squareGrid triangleGrid 3D Descriptive geom3d_Contents meshes3d_Contents angles3d boxes3d circles3d lines3d planes3d points3d polygons3d spheres vectors3d 3D Points anglePoints3d angleSort3d distancePoints drawPoint3d projPointOnPlane 3D Lines distancePointLine3d 3D Edges drawEdge3d drawSphericalEdge 3D Planes createPlane intersectLinePlane intersectPlaneSphere normalizePlane planeNormal planePoint planePosition projPointOnPlane 3D Meshes createCubeOctahedron createCube drawCube drawMesh 3D Spheres circle3dOrigin circle3dPoint circle3dPosition drawCircle3d drawCircleArc3d drawSphere drawSphericalTriangle 3D Boxes boundingBox3d box3dVolume drawBox3d 3D Polygons drawPolygon3d drawPolyline3d drawSphericalPolygon polygonArea3d 3D Transformations createRotationOx createRotationOy createRotationOz createTranslation3d createScaling3d transformPoint3d 3D Others cart2cyl cart2sph2 cart2sph2d cyl2cart drawAxis3d drawCylinder drawTorus drawVector3d revolutionSurface sph2cart2 sph2cart2d vectorAngle3d Geometric graphs descriptive graphs_Contents Geometric graphs creation delaunayGraph knnGraph voronoi2d Geometric graphs visualization drawGraph Geometric graphs manipulation Input @svg/svg @svg/plot @svg/getpath @svg/path2polygon @svg/normalize @svg/pathid @svg/height @svg/width Output data2geo geometry-2.1.1/PaxHeaders.5293/NEWS0000644000000000000000000000013212676233416013536 xustar0030 mtime=1459173134.825445125 30 atime=1459173134.825445125 30 ctime=1459173135.645054067 geometry-2.1.1/NEWS0000644000175000017500000002631512676233416014724 0ustar00juanpijuanpi00000000000000Summary of important user-visible changes for releases of the geometry package =============================================================================== geometry-2.1.1 Release Date: 2016-03-24 Release Manager: Juan Pablo Carbajal =============================================================================== ** Added Functions fillPolygon rectAsPolygon ** Improved Functions drawShape was not working due to missing functions. they have all been added now. ============================================================================== geometry-2.1.0 Release Date: 2016-02-04 Release Manager: Juan Pablo Carbajal =============================================================================== ** Added Functions projPointOnPolyline: the function is added for compatibility, but it is just a wrapper of distancePointPolyline. findClosestPoint ** Improved Functions distancePointPolyline is now updated with a spee dup of 100x. It also calculates the projections, so projPointOnPolyline is obsolete. =============================================================================== geometry-2.0.0 Release Date: 2015-04-27 Release Manager: Juan Pablo Carbajal =============================================================================== ** Geometry 2.0.0 is not compatible with versions of octave older than 4.0. Thi si due to inputParser being used in the functions curve2polyline, cov2ellipse and simplifypolyline. If you do not need this functions you should no problems using octave > 3.6.0 ** Removed functions oc_polybol is not part of geomtry anymore. This function is part of the octclip package. ** Added Functions planePoint ** Bug Fixes: - polynomialCurveSetFit had debug entries, now removed. ** Other changes: - closed_path demo code was improved. =============================================================================== geometry-1.7.0 Release Date: 2013-04-07 Release Manager: Juan Pablo Carbajal =============================================================================== ** Added Functions box3dVolume cart2cyl circle3dPoint cyl2cart drawCircle3d drawPoint3d createScaling3d drawCube createCube drawSphericalTriangle drawTorus revolutionSurface drawVector3d spheres drawPolyline drawPolynomialCurve polynomialCurveCentroid polynomialCurveDerivative polynomialCurveFit polynomialCurvePoint polynomialCurveSetFit polygonPoint polygonSubcurve ** Bug Fixes: - cov2ellipse scale and orientation of axis. =============================================================================== geometry-1.6.0 Release Date: 2012-10-12 Release Manager: Juan Pablo Carbajal =============================================================================== ** geometry doesn't autoloads anymore ** Added Functions anglePoints3d angles3d boxes3d geom3d_Contents lines3d planes3d points3d polygons3d vectors3d graphs_Contents meshes3d_Contents angleSort3d createPlane intersectLinePlane normalizePlane planeNormal planePosition projPointOnPlane sph2cart2 vectorAngle3d distancePointLine3d cart2sph2d createRotationOx createRotationOy createRotationOz createTranslation3d drawAxis3d drawCylinder drawSphere polygonArea3d transformPoint3d drawBox3d drawEdge3d drawMesh createCubeOctahedron boundingBox3d cart2sph2 circle3dOrigin circle3dPosition drawCircleArc3d drawPolygon3d drawSphericalEdge drawSphericalPolygon intersectPlaneSphere sph2cart2d ** Updated functions distancePoints ** Bug Fixes: - drawArrow was not working due to porting errors. =============================================================================== geometry-1.5.0 Release Date: 2012-06-05 Release Manager: Juan Pablo Carbajal =============================================================================== * Added functions: - cov2ellipse & ellipse2cov: transform between ellipses and covariances matrices. - beltproblem : Finds the four lines tangent to two circles with given centers and radii. This is the solution to the belt problem in 2D. - curveval : Evaluates a polynomial curve defined as a 2-by-N matrix. - curve2polyline : Converts a polynomial curve into a polyline by the adaptive sampling method. - simplifypolyline : Ramer-Douglas-Peucker algorithm to simplify polylines. - parametrize : Estimate a parametrization of a polygon/line based on the distance between the points. - curvature : Estimation of the curvature of a polygon/line based on polynomial approximation. - reversePolygon and reversePolyline : reverse the orders of the points in of polygon/line. - supportFunction : Compute support function of a polygon. - distancePointPolygon , distancePointPolyline , distancePolygons , expandPolygon , medialAxisConvex , polygonLoops , polygonSelfIntersections polylineSelfIntersections , splitPolygons - close_path : given a set of points in the plane calculate a piecewise linear simple path that passes through all points. * Changed functions: - distancePointEdge : Now the function computes the distance between all points and all edges. A third optional argument provides backward compatibility. * Solved bugs: - simplifypolygon returned empty polygons when points are repeated, i.e when the polygon is not correctly formed. - Removed installation warnings. =============================================================================== geometry-1.4.1 Release Date: 2012-03-24 Release Manager: Juan Pablo Carbajal =============================================================================== * Renamed functions - Contents renamed to geom2d_Contents to avoid clashes. * Deprecated functions - svgload, svgnormalize, svgpath2polygon: Use the methods in class svg. * Bug fixes - @svg/path2polygon - Fix addpath/rmpath installation warnings - Fix octclip/src/Makefile - Fix shapecentriod for piece-wise polynomial shapes. * Known issues - simplifypolygon returns empty polygons when points are repeated, i.e when the polygon is not correctly formed. =============================================================================== geometry-1.4.0 Release Date: 2012-01-25 Release Manager: Juan Pablo Carbajal =============================================================================== * Added basic geometric graphs creation and manipulation. =============================================================================== geometry-1.3.0 Release Date: 2011-11-24 Release Manager: Juan Pablo Carbajal =============================================================================== * Geometry merged with octCLIP. * Geometry autoloads. =============================================================================== geometry-1.2.2 Release Date: 2011-11-04 Release Manager: Juan Pablo Carbajal =============================================================================== * Improved SVG interface. Thanks to jwe and carandraug. * Adding files to manipulate and convert 2D shapes defined with smooth polynomials. shape2polygon shapearea shapecentroid shapeplot shapetransform * Inverted the order in the NEWS file. New entries are on top. =============================================================================== geometry-1.2.1 Release Date: 2011-11-02 Release Manager: Juan Pablo Carbajal =============================================================================== * Adding SVG object and demo for data2geom (converting SVG to msh format) =============================================================================== geometry-1.2.0 Release Date: 2011-10-21 Release Manager: Juan Pablo Carbajal =============================================================================== * All geom2d added createCircle createDirectedCircle createEdge medianLine Contents bisector cartesianLine drawArrow edges2d lines2d orthogonalLine parallelLine projPointOnLine drawCenteredEdge drawCircle drawCircleArc drawEllipse drawEllipseArc drawLabels drawOrientedBox drawParabola drawRect drawShape circles2d ellipses2d createVector inertiaEllipse changelog.txt readme.txt hexagonalGrid squareGrid triangleGrid intersectCircles intersectEdges intersectLineCircle isLeftOriented isPointInCircle isPointInEllipse isPointOnCircle isPointOnLine edgeLength edgePosition edgeToLine circleArcAsCurve circleAsPolygon crackPattern crackPattern2 distancePointEdge distancePointLine ellipseAsPolygon enclosingCircle radicalAxis reverseEdge reverseLine =============================================================================== geometry-1.1.3 Release Date: 2011-10-13 Release Manager: Juan Pablo Carbajal =============================================================================== * Continue to add geom2d from matGeom (transforms and points2d) createBasisTransform createHomothecy createLineReflection createRotation createScaling createTranslation transformPoint transforms2d fitAffineTransform2d transformEdge transformLine centroid distancePoints midPoint polarPoint drawPoint isCounterClockwise minDistancePoints pointOnLine points2d intersectLineEdge isPointOnEdge =============================================================================== geometry-1.1.2 Release Date: 2011-10-09 Release Manager: Juan Pablo Carbajal =============================================================================== * Continue to add geom2d from matGeom (rays and vectors) createRay drawEdge drawRay isParallel isPerpendicular isPointOnRay normalizeVector rays2d rotateVector transformVector vectorNorm vectors2d =============================================================================== geometry-1.1.1 Release Date: 2011-10-06 Release Manager: Juan Pablo Carbajal =============================================================================== * Continue to add geom2d from matGeom (boxes and clips) cbezier2poly boxes2d clipEdge clipLine clipPoints drawBezierCurve drawBox clipRay intersectBoxes intersectLines linePosition mergeBoxes randomPointInBox drawLine =============================================================================== geometry-1.1.0 Release Date: 2011-10-04 Release Manager: Juan Pablo Carbajal =============================================================================== * Starting to add geom2d from matGeom angle2Points angle3Points angleAbsDiff angleDiff angles2d angleSort createLine deg2rad edgeAngle lineAngle normalizeAngle rad2deg vectorAngle =============================================================================== geometry-1.0.1 Release Date: 2011-09-27 Release Manager: Juan Pablo Carbajal =============================================================================== Improvements to the docstrings of all functions. =============================================================================== geometry-1.0.0 Release Date: 2011-09-26 Release Manager: Juan Pablo Carbajal =============================================================================== ** First official release. =============================================================================== geometry-2.1.1/PaxHeaders.5293/DESCRIPTION0000644000000000000000000000013212676233416014545 xustar0030 mtime=1459173134.825445125 30 atime=1459173134.825445125 30 ctime=1459173135.645054067 geometry-2.1.1/DESCRIPTION0000644000175000017500000000104012676233416015717 0ustar00juanpijuanpi00000000000000Name: Geometry Version: 2.1.1 Date: 2016-03-24 Author: Juan Pablo Carbajal , Simeon Simeonov , David Legland , Maintainer: Juan Pablo Carbajal Title: Computational Geometry Description: Library for geometric computing extending MatGeom functions. Useful to create, transform, manipulate and display geometric primitives. Depends: octave (>= 4.0.0) Autoload: no License: GPLv3+, FreeBSD Url: http://octave.sf.net, https://github.com/dlegland/matGeom geometry-2.1.1/PaxHeaders.5293/COPYING0000644000000000000000000000013212676233416014072 xustar0030 mtime=1459173134.825445125 30 atime=1459173134.825445125 30 ctime=1459173135.645054067 geometry-2.1.1/COPYING0000644000175000017500000010451312676233416015255 0ustar00juanpijuanpi00000000000000 GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. 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But first, please read . geometry-2.1.1/PaxHeaders.5293/inst0000644000000000000000000000013212676233417013740 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/0000755000175000017500000000000012676233417015174 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/PaxHeaders.5293/geom3d0000644000000000000000000000013212676233417015116 xustar0030 mtime=1459173135.541103626 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/0000755000175000017500000000000012676233417016352 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/geom3d/PaxHeaders.5293/angles3d.m0000644000000000000000000000013212676233417017051 xustar0030 mtime=1459173135.497124593 30 atime=1459173135.497124593 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/angles3d.m0000644000175000017500000000614012676233417020231 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} angles3d () ##ANGLES3D Conventions for manipulating angles in 3D ## ## Contrary to the plane, there are no oriented angles in 3D. Angles ## between lines or between planes are comprised between 0 and PI. ## ## Spherical angles ## Spherical angles are defined by 2 angles: ## * THETA, the colatitude, representing angle with Oz axis (between 0 and ## PI) ## * PHI, the azimut, representing angle with Ox axis of horizontal ## projection of the direction (between 0 and 2*PI) ## ## Spherical coordinates can be represented by THETA, PHI, and the ## distance RHO to the origin. ## ## Euler angles ## Some functions for creating rotations use Euler angles. They follow the ## ZYX convention in the global reference system, that is eqivalent to the ## XYZ convention ine a local reference system. ## Euler angles are given by a triplet of angles [PHI THETA PSI] that ## represents the succession of 3 rotations: ## * rotation around X by angle PSI ("roll") ## * rotation around Y by angle THETA ("pitch") ## * rotation around Z by angle PHI ("yaw") ## ## In this library, euler angles are given in degrees. The functions that ## use euler angles use the keyword 'Euler' in their name. ## ## ## @seealso{cart2sph2, sph2cart2, cart2sph2d, sph2cart2d ## anglePoints3d, angleSort3d, sphericalAngle, randomAngle3d ## dihedralAngle, polygon3dNormalAngle, eulerAnglesToRotation3d ## rotation3dAxisAndAngle, rotation3dToEulerAngles} ## @end deftypefn function angles3d() help angles3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/intersectLinePlane.m0000644000000000000000000000013012676233417021137 xustar0029 mtime=1459173135.52511125 29 atime=1459173135.52511125 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/intersectLinePlane.m0000644000175000017500000000764312676233417022332 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pt} =} intersectLinePlane (@var{line}, @var{plane}) ## @deftypefnx {Function File} {@var{pt} =} intersectLinePlane (@dots{}, @var{tol}) ## Intersection point between a 3D line and a plane ## ## PT = intersectLinePlane(LINE, PLANE) ## Returns the intersection point of the given line and the given plane. ## LINE: [x0 y0 z0 dx dy dz] ## PLANE: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] ## PT: [xi yi zi] ## If LINE and PLANE are parallel, return [NaN NaN NaN]. ## If LINE (or PLANE) is a matrix with 6 (or 9) columns and N rows, result ## is an array of points with N rows and 3 columns. ## ## PT = intersectLinePlane(LINE, PLANE, TOL) ## Specifies the tolerance factor to test if a line is parallel to a ## plane. Default is 1e-14. ## ## Example ## @example ## # define horizontal plane through origin ## plane = [0 0 0 1 0 0 0 1 0]; ## # intersection with a vertical line ## line = [2 3 4 0 0 1]; ## intersectLinePlane(line, plane) ## ans = ## 2 3 0 ## # intersection with a line "parallel" to plane ## line = [2 3 4 1 2 0]; ## intersectLinePlane(line, plane) ## ans = ## NaN NaN NaN ## @end example ## ## @seealso{lines3d, planes3d, points3d, clipLine3d} ## @end deftypefn function point = intersectLinePlane (line, plane, varargin) # extract tolerance if needed tol = 1e-14; if nargin > 2 tol = varargin{1}; end # unify sizes of data nLines = size (line, 1); nPlanes = size (plane, 1); # N planes and M lines not allowed if nLines ~= nPlanes && min (nLines, nPlanes) > 1 error ('geometry:geom3d:intersectLinePlane', ... 'Input must have same number of rows, or one must be 1'); end # plane normal n = cross (plane(:,4:6), plane(:,7:9)); # difference between origins of plane and line dp = bsxfun (@minus, plane(:, 1:3), line(:, 1:3)); # dot product of line direction with plane normal denom = sum (bsxfun (@times, n, line(:,4:6)), 2); # relative position of intersection point on line (can be inf in case of a # line parallel to the plane) t = sum (bsxfun (@times, n, dp),2) ./ denom; # compute coord of intersection point point = bsxfun (@plus, line(:,1:3), bsxfun (@times, [t t t], line(:,4:6))); # set indices of line and plane which are parallel to NaN par = abs (denom) < tol; point(par,:) = NaN; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/boundingBox3d.m0000644000000000000000000000013212676233417020056 xustar0030 mtime=1459173135.497124593 30 atime=1459173135.497124593 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/boundingBox3d.m0000644000175000017500000000545312676233417021244 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{box} =} boundingBox3d (@var{points}) ## Bounding box of a set of 3D points ## ## Returns the bounding box of the set of points POINTS. POINTS is a ## N-by-3 array containing points coordinates. The result BOX is a 1-by-6 ## array, containing: ## [XMIN XMAX YMIN YMAX ZMIN ZMAX] ## ## Example ## @group ## # Draw bounding box of a cubeoctehedron ## [v e f] = createCubeOctahedron; ## box3d = boundingBox3d(v); ## figure; hold on; ## drawMesh(v, f); ## drawBox3d(box3d); ## axis([-2 2 -2 2 -2 2]); ## view(3) ## @end group ## ## @seealso{boxes3d, drawBox3d} ## @end deftypefn function box = boundingBox3d(points) # compute extreme x and y values xmin = min(points(:,1)); xmax = max(points(:,1)); ymin = min(points(:,2)); ymax = max(points(:,2)); box = [xmin xmax ymin ymax]; # process case of 3D points if size(points, 2) > 2 zmin = min(points(:,3)); zmax = max(points(:,3)); box = [xmin xmax ymin ymax zmin zmax]; end endfunction %!demo %! # Draw bounding box of a cubeoctehedron %! [v e f] = createCubeOctahedron; %! box3d = boundingBox3d(v); %! figure; hold on; %! drawMesh(v, f); %! drawBox3d(box3d); %! axis([-2 2 -2 2 -2 2]); %! view(3) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawAxis3d.m0000644000000000000000000000013212676233417017362 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.513116969 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawAxis3d.m0000644000175000017500000000540612676233417020546 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawAxis3d () ## @deftypefnx {Function File} drawAxis3d (@var{l},@var{r}) ## Draw a coordinate system and an origin ## ## Adds 3 cylinders to the current axis, corresponding to the directions ## of the 3 basis vectors Ox, Oy and Oz. ## Ox vector is red, Oy vector is green, and Oz vector is blue. ## ## @var{l} specifies the length and @var{r} the radius of the cylinders ## representing the different axes. ## ## WARNING: This function doesn't work in gnuplot (as of version 4.2). ## ## @seealso{drawAxisCube} ## @end deftypefn function drawAxis3d(L=1,r=1/10) # geometrical data origin = [0 0 0]; v1 = [1 0 0]; v2 = [0 1 0]; v3 = [0 0 1]; # draw 3 cylinders and a ball holded = false; if ~ishold(gca) hold on; holded = true; endif drawCylinder([origin origin+v1*L r], 16, 'facecolor', 'r', 'edgecolor', 'none'); drawCylinder([origin origin+v2*L r], 16, 'facecolor', 'g', 'edgecolor', 'none'); drawCylinder([origin origin+v3*L r], 16, 'facecolor', 'b', 'edgecolor', 'none'); drawSphere([origin 2*r], 'faceColor', 'black'); if holded hold off endif endfunction %!demo %! scatter3(5*randn(100,1),5*randn(100,1),5*randn(100,1)); %! drawAxis3d() %! axis tight geometry-2.1.1/inst/geom3d/PaxHeaders.5293/transformPoint3d.m0000644000000000000000000000013212676233417020625 xustar0030 mtime=1459173135.537105532 30 atime=1459173135.537105532 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/transformPoint3d.m0000644000175000017500000001211612676233417022005 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pt2} =} transformPoint3d (@var{pt1}, @var{trans}) ## @deftypefnx {Function File} {@var{pt2} =} transformPoint3d (@var{x1},@var{y1},@var{z1}, @var{trans}) ## @deftypefnx {Function File} {[@var{x2},@var{y2},@var{z2}] =} transformPoint3d (@dots{}) ## Transform a point with a 3D affine transform ## ## PT2 = transformPoint3d(PT1, TRANS); ## PT2 = transformPoint3d(X1, Y1, Z1, TRANS); ## where PT1 has the form [xp yp zp], and TRANS is a [3x3], [3x4], [4x4] ## matrix, return the point transformed according to the affine transform ## specified by TRANS. ## ## Format of TRANS is a 4-by-4 matrix. ## ## The function accepts transforms given using the following formats: ## [a b c] , [a b c j] , or [a b c j] ## [d e f] [d e f k] [d e f k] ## [g h i] [g h i l] [g h i l] ## [0 0 0 1] ## ## PT2 = transformPoint3d(PT1, TRANS) ## also work when PT1 is a [Nx3xMxPxETC] array of double. In this case, ## PT2 has the same size as PT1. ## ## PT2 = transformPoint3d(X1, Y1, Z1, TRANS); ## also work when X1, Y1 and Z1 are 3 arrays with the same size. In this ## case, PT2 will be a 1-by-3 cell containing @{X Y Z@} outputs of size(X1). ## ## [X2 Y2 Z2] = transformPoint3d(@dots{}); ## returns the result in 3 different arrays the same size as the input. ## This form can be useful when used with functions like meshgrid or warp. ## ## @seealso{points3d, transforms3d, translation3d,meshgrid} ## @end deftypefn function varargout = transformPoint3d(varargin) # process input arguments if length(varargin) == 2 # Point coordinates are given in a single N-by-3-by-M-by-etc argument. # Preallocate x, y, and z to size N-by-1-by-M-by-etc, then fill them in dim = size(varargin{1}); dim(2) = 1; [x,y,z] = deal(zeros(dim,class(varargin{1}))); x(:) = varargin{1}(:,1,:); y(:) = varargin{1}(:,2,:); z(:) = varargin{1}(:,3,:); trans = varargin{2}; elseif length(varargin) == 4 # Point coordinates are given in 3 different arrays x = varargin{1}; y = varargin{2}; z = varargin{3}; dim = size(x); trans = varargin{4}; end # eventually add null translation if size(trans, 2) == 3 trans = [trans zeros(size(trans, 1), 1)]; end # eventually add normalization if size(trans, 1) == 3 trans = [trans;0 0 0 1]; end # convert coordinates NP = numel(x); try # vectorial processing, if there is enough memory #res = (trans*[x(:) y(:) z(:) ones(NP, 1)]')'; #res = [x(:) y(:) z(:) ones(NP, 1)]*trans'; res = [x(:) y(:) z(:) ones(NP,1,class(x))] * trans'; # Back-fill x,y,z with new result (saves calling costly reshape()) x(:) = res(:,1); y(:) = res(:,2); z(:) = res(:,3); catch ME disp(ME.message) # process each point one by one, writing in existing array for i = 1:NP res = [x(i) y(i) z(i) 1] * trans'; x(i) = res(1); y(i) = res(2); z(i) = res(3); end end # process output arguments if nargout <= 1 # results are stored in a unique array if length(dim) > 2 && dim(2) > 1 warning('geom3d:shapeMismatch',... 'Shape mismatch: Non-vector xyz input should have multiple x,y,z output arguments. Cell {x,y,z} returned instead.') varargout{1} = {x,y,z}; else varargout{1} = [x y z]; end elseif nargout == 3 varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawTorus.m0000644000000000000000000000013212676233417017343 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawTorus.m0000644000175000017500000000545712676233417020535 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} drawTorus (@var{torus}) ## Draw a torus (3D ring) ## ## drawTorus(TORUS) ## Draws the torus on the current axis. TORUS is given by ## [XC YC ZY R1 R2 THETA PHI] ## where (XC YZ ZC) is the center of the torus, R1 is the main radius, R2 ## is the radius of the torus section, and (THETA PHI) is the angle of the ## torus normal vector (both in degrees). ## ## Example ## @example ## figure; ## drawTorus([50 50 50 30 10 30 45]); ## axis equal; ## @end example ## ## @seealso{drawEllipsoid, revolutionSurface} ## @end deftypefn function varargout = drawTorus(torus, varargin) center = torus(1:3); r1 = torus(4); r2 = torus(5); if size(torus, 2) >= 7 normal = torus(6:7); end # default drawing options varargin = [{'FaceColor', 'g'}, varargin]; # create base torus circle = circleAsPolygon ([r1 0 r2], 60); [x y z] = revolutionSurface (circle, linspace(0, 2*pi, 60)); # transform torus trans = localToGlobal3d ([center normal]); [x y z] = transformPoint3d (x, y, z, trans); # draw the surface hs = surf(x, y, z, varargin{:}); if nargout > 0 varargout = {hs}; end endfunction %!demo %! figure; %! drawTorus([50 50 50 30 10 30 45]); %! axis square equal; %! view(45,40); geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawPolyline3d.m0000644000000000000000000000013212676233417020251 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawPolyline3d.m0000644000175000017500000001067612676233417021442 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawPolyline3d (@var{poly}) ## @deftypefnx {Function File} {@var{h} =} drawPolyline3d (@var{px},@var{py},@var{pz}) ## @deftypefnx {Function File} {@var{h} =} drawPolyline3d (@dots{},@var{closed}) ## @deftypefnx {Function File} {@var{h} =} drawPolyline3d (@dots{},@var{param},@var{value}) ## Draw a 3D polyline specified by a list of vertices ## ## drawPolyline3d(POLY); ## packs coordinates in a single N-by-3 array. ## ## drawPolyline3d(PX, PY, PZ); ## specify coordinates in separate arrays. ## ## drawPolyline3d(..., CLOSED); ## Specifies if the polyline is closed or open. CLOSED can be one of: ## - 'closed' ## - 'open' (the default) ## - a boolean variable with value TRUE for closed polylines. ## ## drawPolyline3d(..., PARAM, VALUE); ## Specifies style options to draw the polyline, see plot for details. ## ## H = drawPolyline3d(...); ## also return a handle to the list of line objects. ## ## @seealso{polygons3d, drawPolygon3d, fillPolygon3d} ## @end deftypefn function varargout = drawPolyline3d(varargin) ## Process input arguments # check case we want to draw several curves, stored in a cell array var = varargin{1}; if iscell(var) holded = false; if ~ishold(gca) hold on; holded = true; end h = []; for i = 1:length(var(:)) h = [h; drawPolyline3d(var{i}, varargin{2:end})]; ##ok end if holded hold off end if nargout > 0 varargout = {h}; end return; end # extract curve coordinates if size(var, 2) == 1 # first argument contains x coord, second argument contains y coord # and third one the z coord px = var; if length(varargin) < 3 error('Wrong number of arguments in drawPolyline3d'); end py = varargin{2}; pz = varargin{3}; varargin = varargin(4:end); else # all coordinates are grouped in the first argument px = var(:, 1); py = var(:, 2); pz = var(:, 3); varargin = varargin(2:end); end # check if curve is closed or open (default is open) closed = false; if ~isempty(varargin) var = varargin{1}; if islogical(var) # check boolean flag closed = var; varargin = varargin(2:end); elseif ischar(var) # check string indicating close or open if strncmpi(var, 'close', 5) closed = true; varargin = varargin(2:end); elseif strncmpi(var, 'open', 4) closed = false; varargin = varargin(2:end); end end end ## draw the curve # for closed curve, add the first point at the end to close curve if closed px = [px; px(1)]; py = [py; py(1)]; pz = [pz; pz(1)]; end h = plot3(px, py, pz, varargin{:}); if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/cart2sph2d.m0000644000000000000000000000013212676233417017325 xustar0030 mtime=1459173135.501122687 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/cart2sph2d.m0000644000175000017500000000641012676233417020505 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{theta} @var{phi} @var{rho}] =} cart2sph2d (@var{coord}) ## @deftypefnx {Function File} {[@dots{}] =} cart2sph2d (@var{x},@var{y},@var{z}) ## Convert cartesian coordinates to spherical coordinates in degrees ## ## The following convention is used: ## THETA is the colatitude, in degrees, 0 for north pole, 180 degrees for ## south pole, 90 degrees for points with z=0. ## PHI is the azimuth, in degrees, defined as matlab cart2sph: angle from ## Ox axis, counted counter-clockwise. ## RHO is the distance of the point to the origin. ## Discussion on choice for convention can be found at: ## @url{http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf} ## ## Example: ## @example ## cart2sph2d([1 0 0]) ## ans = ## 90 0 1 ## ## cart2sph2d([1 1 0]) ## ans = ## 90 45 1.4142 ## ## cart2sph2d([0 0 1]) ## ans = ## 0 0 1 ## @end example ## ## @seealso{angles3d, sph2cart2d, cart2sph, cart2sph2} ## @end deftypefn function varargout = cart2sph2d(x, y, z) # if data are grouped, extract each coordinate if nargin == 1 y = x(:, 2); z = x(:, 3); x = x(:, 1); end # cartesian to spherical conversion hxy = hypot(x, y); rho = hypot(hxy, z); theta = 90 - atan2(z, hxy) * 180 / pi; phi = atan2(y, x) * 180 / pi; # # convert to degrees and theta to colatitude # theta = 90 - rad2deg(theta); # phi = rad2deg(phi); # format output if nargout <= 1 varargout{1} = [theta phi rho]; elseif nargout == 2 varargout{1} = theta; varargout{2} = phi; else varargout{1} = theta; varargout{2} = phi; varargout{3} = rho; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/points3d.m0000644000000000000000000000013212676233417017114 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/points3d.m0000644000175000017500000000403212676233417020272 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} points3d () ##POINTS3D Description of functions operating on 3D points ## ## Points are represented by their 3 Cartesian coordinates: ## P = [X Y Z]; ## ## Arrays of points consist in N*3 arrays, each row being a point. ## ## @seealso{isCoplanar, distancePoints, anglePoints3d, angleSort3d, sphericalAngle, ## sph2cart2, cart2sph2, cart2cyl, cyl2cart, transformPoint3d, clipPoints3d} ## @end deftypefn function points3d() help points3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/box3dVolume.m0000644000000000000000000000013212676233417017560 xustar0030 mtime=1459173135.501122687 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/box3dVolume.m0000644000175000017500000000407112676233417020741 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{v} =} box3dVolume (@var{box}) ## Volume of a 3-dimensional box ## ## A box is represented as a set of limits in each direction: ## BOX = [XMIN XMAX YMIN YMAX ZMIN ZMAX]. ## ## Example ## @example ## [n e f] = createCubeOctahedron; ## box = boundingBox3d(n); ## vol = box3dVolume(box) ## vol = ## 8 ## @end example ## ## @seealso{boxes3d, boundingBox3d} ## @end deftypefn function vol = box3dVolume(box) vol = prod(box(:, 2:2:end) - box(:, 1:2:end), 2); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/angleSort3d.m0000644000000000000000000000013212676233417017536 xustar0030 mtime=1459173135.497124593 30 atime=1459173135.497124593 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/angleSort3d.m0000644000175000017500000000742712676233417020727 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts2} =} angleSort3d (@var{pts}) ## @deftypefnx {Function File} {@var{pts2} =} angleSort3d (@var{pts},@var{pts0}) ## @deftypefnx {Function File} {@var{pts2} =} angleSort3d (@var{pts},@var{pts0},@var{pts1}) ## @deftypefnx {Function File} {[@var{pts2} @var{i}]=} angleSort3d (@dots{}) ## Sort 3D coplanar points according to their angles in plane ## ## @var{pts2} = angleSort3d(@var{pts}); ## Considers all points are located on the same plane, and sort them ## according to the angle on plane. @var{pts} is a [Nx2] array. Note that the ## result depend on plane orientation: points can be in reverse order ## compared to expected. The reference plane is computed besed on the 3 ## first points. ## ## @var{pts2} = angleSort3d(@var{pts}, @var{pts0}); ## Computes angles between each point of @var{pts} and PT0. By default, uses ## centroid of points. ## ## @var{pts2} = angleSort3d(@var{pts}, @var{pts0}, @var{pts1}); ## Specifies the point which will be used as a start. ## ## [@var{pts2}, @var{i}] = angleSort3d(...); ## Also return in @var{i} the indices of @var{pts}, such that @var{pts2} = @var{pts}(I, :); ## ## @seealso{points3d, angles3d, angleSort} ## @end deftypefn function varargout = angleSort3d(pts, varargin) # default values pt0 = mean (pts, 1); pt1 = pts(1,:); if length (varargin)==1 pt0 = varargin{1}; elseif length (varargin)==2 pt0 = varargin{1}; pt1 = varargin{2}; end # create support plane plane = createPlane (pts(1:3, :)); # project points onto the plane pts2d = planePosition (pts, plane); pt0 = planePosition (pt0, plane); pt1 = planePosition (pt1, plane); # compute origin angle theta0 = atan2 (pt1(2)-pt0(2), pt1(1)-pt0(1)); theta0 = mod (theta0 + 2*pi, 2*pi); # translate to reference point n = size (pts, 1); pts2d = pts2d - repmat (pt0, [n 1]); # compute angles angle = atan2 (pts2d(:,2), pts2d(:,1)); angle = mod (angle - theta0 + 4*pi, 2*pi); # sort points according to angles [angle, I] = sort (angle); ##ok # format output if nargout<2 varargout{1} = pts(I, :); elseif nargout==2 varargout{1} = pts(I, :); varargout{2} = I; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createScaling3d.m0000644000000000000000000000013212676233417020344 xustar0030 mtime=1459173135.509118875 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createScaling3d.m0000644000175000017500000000657512676233417021540 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{trans} =} createScaling3d (@var{s}) ## @deftypefnx {Function File} {@var{trans} =} createScaling3d (@var{sx}, @var{sy}, @var{sz}) ## Create the 4x4 matrix of a 3D scaling ## ## TRANS = createScaling3d(S); ## returns the scaling transform corresponding to a scaling factor S in ## each direction. S can be a scalar, or a 1x3 vector containing the ## scaling factor in each direction. ## ## TRANS = createScaling3d(SX, SY, SZ); ## returns the scaling transform corresponding to a different scaling ## factor in each direction. ## ## The returned matrix has the form : ## @group ## [SX 0 0 0] ## [ 0 SY 0 0] ## [ 0 0 SZ 0] ## [ 0 0 0 0] ## @end group ## ## @seealso{transforms3d, transformPoint3d, transformVector3d, createTranslation3d, ## createRotationOx, createRotationOy, createRotationOz} ## @end deftypefn function trans = createScaling3d(varargin) # process input parameters if isempty(varargin) # assert uniform scaling in each direction sx = 1; sy = 1; sz = 1; elseif length(varargin)==1 # only one argument var = varargin{1}; if length(var)==1 # same scaling factor in each direction sx = var; sy = var; sz = var; elseif length(var)==3 # scaling is a vector, giving different scaling in each direction sx = var(1); sy = var(2); sz = var(3); else error('wrong size for first parameter of "createScaling3d"'); end elseif length(varargin)==3 # 3 arguments, giving scaling in each direction sx = varargin{1}; sy = varargin{2}; sz = varargin{3}; else error('wrong number of arguments for "createScaling3d"'); end # create the scaling matrix trans = [sx 0 0 0;0 sy 0 0;0 0 sz 0;0 0 0 1]; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawEdge3d.m0000644000000000000000000000013212676233417017322 xustar0030 mtime=1459173135.517115063 30 atime=1459173135.517115063 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawEdge3d.m0000644000175000017500000000535012676233417020504 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawEdge (@var{edge}) ## Draw 3D edge in the current Window ## ## draw the edge EDGE on the current axis. EDGE has the form: ## [x1 y1 z1 x2 y2 z2]. ## No clipping is performed. ## ## @end deftypefn function varargout = drawEdge3d(varargin) # extract edges from input arguments nCol = size(varargin{1}, 2); if nCol==6 # all parameters in a single array edges = varargin{1}; options = varargin(2:end); elseif nCol==3 # parameters are two points, or two arrays of points, of size N*3. edges = [varargin{1} varargin{2}]; options = varargin(3:end); elseif nCol==6 # parameters are 6 parameters of the edge : x1 y1 z1 x2 y2 and z2 edges = [varargin{1} varargin{2} varargin{3} varargin{4} varargin{5} varargin{6}]; options = varargin(7:end); end # draw edges h = line( [edges(:, 1) edges(:, 4)]', ... [edges(:, 2) edges(:, 5)]', ... [edges(:, 3) edges(:, 6)]', 'color', 'b'); # apply optional drawing style if ~isempty(options) set(h, options{:}); end # return handle to created Edges if nargout>0 varargout{1}=h; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/cart2sph2.m0000644000000000000000000000013212676233417017161 xustar0030 mtime=1459173135.501122687 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/cart2sph2.m0000644000175000017500000000604512676233417020345 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{theta} @var{phi} @var{rho}] =} cart2sph2([@var{x} @var{y} @var{z}]) ## @deftypefnx {Function File} {[@var{theta} @var{phi} @var{rho}] =} cart2sph2(@var{x}, @var{y}, @var{z}) ## Convert cartesian coordinates to spherical coordinates ## ## The following convention is used: ## @var{theta} is the colatitude, in radians, 0 for north pole, +pi for south ## pole, pi/2 for points with z=0. ## @var{phi} is the azimuth, in radians, defined as matlab cart2sph: angle from ## Ox axis, counted counter-clockwise. ## @var{rho} is the distance of the point to the origin. ## Discussion on choice for convention can be found at: ## @url{http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf} ## ## Example: ## @example ## cart2sph2([1 0 0]) returns [pi/2 0 1]; ## cart2sph2([1 1 0]) returns [pi/2 pi/4 sqrt(2)]; ## cart2sph2([0 0 1]) returns [0 0 1]; ## @end example ## ## @seealso{angles3d, sph2cart2, cart2sph, cart2sph2d} ## @end deftypefn function varargout = cart2sph2(varargin) if length(varargin)==1 var = varargin{1}; elseif length(varargin)==3 var = [varargin{1} varargin{2} varargin{3}]; end if size(var, 2)==2 var(:,3)=1; end [p t r] = cart2sph(var(:,1), var(:,2), var(:,3)); if nargout == 1 || nargout == 0 varargout{1} = [pi/2-t p r]; elseif nargout==2 varargout{1} = pi/2-t; varargout{2} = p; else varargout{1} = pi/2-t; varargout{2} = p; varargout{3} = r; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/circle3dPoint.m0000644000000000000000000000013212676233417020053 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.505120781 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/circle3dPoint.m0000644000175000017500000000632612676233417021241 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} =} circle3dPoint (@var{circle},@var{pos}) ## Coordinates of a point on a 3D circle from its position ## ## ## Example ## @example ## circle = [0 0 0 1 45 45 0]; ## # Draw some points on a 3D circle ## figure; hold on; ## # origin point ## pos1 = 0; ## drawPoint3d(circle3dPoint(circle, pos1), 'ro') ## # few points regularly spaced ## for i = 10:10:40 ## drawPoint3d(circle3dPoint(circle, i)) ## end ## # Draw point opposite to origin ## drawPoint3d(circle3dPoint(circle, 180), 'k*') ## @end example ## ## @seealso{circles3d, circle3dPosition} ## @end deftypefn function point = circle3dPoint(circle, pos) # extract circle coordinates xc = circle(1); yc = circle(2); zc = circle(3); r = circle(4); theta = circle(5); phi = circle(6); psi = circle(7); # convert position to angle t = pos * pi / 180; # compute position on base circle x = r * cos(t); y = r * sin(t); z = 0; pt0 = [x y z]; # compute transformation from local basis to world basis trans = localToGlobal3d (xc, yc, zc, theta, phi, psi); # compute points of transformed circle point = transformPoint3d (pt0, trans); endfunction %!demo %! # Draw some points on a 3D circle %! circle = [0 0 0 1 45 45 0]; %! figure; %! %! drawCircle3d(circle); %! hold on; %! %! # origin point %! pos1 = 0; %! drawPoint3d(circle3dPoint(circle, pos1), 'go') %! # few points regularly spaced %! for i = 10:10:90 %! drawPoint3d(circle3dPoint(circle, i)) %! end %! # Draw point opposite to origin %! drawPoint3d(circle3dPoint(circle, 180), 'k*') %! axis square equal; %! view(70,30) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/projPointOnPlane.m0000644000000000000000000000013212676233417020612 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.533107438 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/projPointOnPlane.m0000644000175000017500000000515112676233417021773 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pt2} =} projPointOnPlane (@var{pt1}, @var{plane}) ## Return the orthogonal projection of a point on a plane ## ## PT2 = projPointOnPlane(PT1, PLANE); ## Compute the (orthogonal) projection of point PT1 onto the line PLANE. ## ## Function works also for multiple points and planes. In this case, it ## returns multiple points. ## Point PT1 is a [N*3] array, and PLANE is a [N*9] array (see createPlane ## for details). Result PT2 is a [N*3] array, containing coordinates of ## orthogonal projections of PT1 onto planes PLANE. ## ## @seealso{planes3d, points3d, planePosition, intersectLinePlane} ## @end deftypefn function point = projPointOnPlane (point, plane) if size (point, 1)==1 point = repmat (point, [size(plane, 1) 1]); elseif size (plane, 1)==1 plane = repmat (plane, [size(point, 1) 1]); elseif size (plane, 1) ~= size (point, 1) error ('projPointOnPlane: size of inputs differ'); end n = planeNormal (plane); line = [point n]; point = intersectLinePlane (line, plane); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/circle3dPosition.m0000644000000000000000000000013212676233417020566 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.505120781 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/circle3dPosition.m0000644000175000017500000000546512676233417021757 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pos} =} circle3dPosition(@var{point}, @var{circle}) ## Return the angular position of a point on a 3D circle ## ## Returns angular position of point on the circle, in degrees, between 0 ## and 360. ## with @var{point}: [xp yp zp] ## and @var{circle}: [X0 Y0 Z0 R THETA PHI] or [X0 Y0 Z0 R THETA PHI PSI] ## (THETA being the colatitude, and PHI the azimut) ## ## @seealso{circles3d, circle3dOrigin, circle3dPoint} ## @end deftypefn function theta = circle3dPosition(point, circle) # get center and radius xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); # get angle of normal theta = circle(:,5); phi = circle(:,6); # find origin of the circle ori = circle3dOrigin(circle); # normal vector of the supporting plane (cartesian coords) vn = sph2cart2d([theta phi]); # create plane containing the circle plane = createPlane([xc yc zc], vn); # find position of point on the circle plane pp0 = planePosition(ori, plane); pp = planePosition(point, plane); # compute angles in the planes theta0 = mod(atan2(pp0(:,2), pp0(:,1)) + 2*pi, 2*pi); theta = mod(atan2(pp(:,2), pp(:,1)) + 2*pi - theta0, 2*pi); # convert to degrees theta = theta * 180 / pi; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/distancePoints.m0000644000000000000000000000013212676233417020340 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.513116969 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/distancePoints.m0000644000175000017500000001365112676233417021525 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{d} =} distancePoints(@var{p1}, @var{p2}) ## @deftypefnx {Function File} {@var{d} =} distancePoints(@var{p1}, @var{p2},@var{norm}) ## @deftypefnx {Function File} {@var{d} = } distancePoints (@dots{}, @asis{'diag'}) ## Compute euclidean distance between pairs of points in any dimension ## ## Return distance @var{d} between points @var{p1} and ## @var{p2}, given as [X Y Z @dots{} Wdim]. ## ## If @var{p1} and @var{p2} are two arrays of points, result is a N1-by-N2 array ## containing distance between each point of @var{p1} and each point of @var{p2}. ## ## ## @var{d} = distancePoints(@var{p1}, @var{p2}, @var{norm}) ## with @var{norm} being 1, 2, or Inf, corresponfing to the norm used. Default is ## 2 (euclidean norm). 1 correspond to manhattan (or taxi driver) distance ## and Inf to maximum difference in each coordinate. ## ## When 'diag' is given, computes only distances between @code{@var{p1}(i,:)} and @code{@var{p2}(i,:)}. ## In this case the numer of points in each array must be the same. ## ## @seealso{points3d, minDistancePoints} ## @end deftypefn function dist = distancePoints(p1, p2, varargin) norm = 2; diagonal = false; switch numel(varargin) case 0 1; case 1 if isnumeric (varargin{1}) norm = varargin{1}; else diagonal = true; end case 2 norm = varargin{1}; diagonal = true; otherwise print_usage; end # compute difference of coordinate for each all points [n1 dim] = size(p1); [n2 dim] = size(p2); if diagonal if n1 ~= n2 error ("geometry:InvalidArgument",... "When option diag is given the number of points must be equal.\n"); end ptsDiff = p2 - p1; else ptsDiff = zeros (n1,n2,dim); for i =1:dim ptsDiff(:,:,i) = p2(:,i)' - p1(:,i); end end # Return dist based on the type of measurement requested along_dim = length(size(ptsDiff)); switch(norm) case 1 dist = sum(abs(ptsDiff), along_dim); case 2 if ~diagonal dist = reshape(vectorNorm (reshape(ptsDiff,n1*n2,dim)),n1,n2); else dist = vectorNorm (ptsDiff); end case Inf dist = max(abs(ptsDiff), [], along_dim); otherwise dist = sum(ptsDiff.^norm, along_dim).^(1/norm); end endfunction %!shared pt1,pt2,pt3,pt4 %! pt1 = [10 10]; %! pt2 = [10 20]; %! pt3 = [20 20]; %! pt4 = [20 10]; %!assert (distancePoints(pt1, pt2), 10, 1e-6); %!assert (distancePoints(pt2, pt3), 10, 1e-6); %!assert (distancePoints(pt1, pt3), 10*sqrt(2), 1e-6); %!assert (distancePoints(pt1, pt2, 1), 10, 1e-6); %!assert (distancePoints(pt2, pt3, 1), 10, 1e-6); %!assert (distancePoints(pt1, pt3, 1), 20, 1e-6); %!assert (distancePoints(pt1, pt2, inf), 10, 1e-6); %!assert (distancePoints(pt2, pt3, inf), 10, 1e-6); %!assert (distancePoints(pt1, pt3, inf), 10, 1e-6); %!assert (distancePoints(pt1, [pt1; pt2; pt3]), [0 10 10*sqrt(2)], 1e-6); %!test %! array1 = [pt1;pt2;pt3]; %! array2 = [pt1;pt2;pt3;pt4]; %! res = [0 10 10*sqrt(2) 10; 10 0 10 10*sqrt(2); 10*sqrt(2) 10 0 10]; %! assert (distancePoints(array1, array2), res, 1e-6); %! assert (distancePoints(array2, array2, 'diag'), [0;0;0;0], 1e-6); %!test %! array1 = [pt1;pt2;pt3]; %! array2 = [pt2;pt3;pt1]; %! assert (distancePoints(array1, array2, inf, 'diag'), [10;10;10], 1e-6); %!shared pt1,pt2,pt3,pt4 %! pt1 = [10 10 10]; %! pt2 = [10 20 10]; %! pt3 = [20 20 10]; %! pt4 = [20 20 20]; %!assert (distancePoints(pt1, pt2), 10, 1e-6); %!assert (distancePoints(pt2, pt3), 10, 1e-6); %!assert (distancePoints(pt1, pt3), 10*sqrt(2), 1e-6); %!assert (distancePoints(pt1, pt4), 10*sqrt(3), 1e-6); %!assert (distancePoints(pt1, pt2, inf), 10, 1e-6); %!assert (distancePoints(pt2, pt3, inf), 10, 1e-6); %!assert (distancePoints(pt1, pt3, inf), 10, 1e-6); %!assert (distancePoints(pt1, pt4, inf), 10, 1e-6); %!shared pt1,pt2,pt3,pt4 %! pt1 = [10 10 30]; %! pt2 = [10 20 30]; %! pt3 = [20 20 30]; %! pt4 = [20 20 40]; %!assert (distancePoints(pt1, pt2, 1), 10, 1e-6); %!assert (distancePoints(pt2, pt3, 1), 10, 1e-6); %!assert (distancePoints(pt1, pt3, 1), 20, 1e-6); %!assert (distancePoints(pt1, pt4, 1), 30, 1e-6); %!test %! array1 = [pt1;pt2;pt3]; %! array2 = [pt2;pt3;pt1]; %! assert (distancePoints(array1, array2, 'diag'), [10;10;10*sqrt(2)], 1e-6); %! assert (distancePoints(array1, array2, 1, 'diag'), [10;10;20], 1e-6); geometry-2.1.1/inst/geom3d/PaxHeaders.5293/private0000644000000000000000000000013212676233417016570 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/private/0000755000175000017500000000000012676233417020024 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/geom3d/private/PaxHeaders.5293/localToGlobal3d.m0000644000000000000000000000013212676233417021770 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.533107438 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/private/localToGlobal3d.m0000644000175000017500000001027312676233417023152 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{} =} localToGlobal3d (@var{center}, @var{theta},@var{phi},@var{psi}) ## Transformation matrix from local to global coordinate system ## ## TRANS = localToGlobal3d(CENTER, THETA, PHI, PSI) ## Compute the transformation matrix from a local (or modelling) ## coordinate system to the global (or world) coordinate system. ## This is a low-level function, used by several drawing functions. ## ## The transform is defined by: ## - CENTER: the position of the local origin into the World coordinate ## system ## - THETA: colatitude, defined as the angle with the Oz axis (between 0 ## and 180 degrees), positive in the direction of the of Oy axis. ## - PHI: azimut, defined as the angle of the normal with the Ox axis, ## between 0 and 360 degrees ## - PSI: intrinsic rotation, corresponding to the rotation of the object ## around the direction vector, between 0 and 360 degrees ## ## The resulting transform is obtained by applying (in that order): ## - Rotation by PSI around he Z-axis ## - Rotation by THETA around the Y-axis ## - Rotation by PHI around the Z-axis ## - Translation by vector CENTER ## This corresponds to Euler ZYZ rotation, using angles PHI, THETA and ## PSI. ## ## The 'createEulerAnglesRotation' function may better suit your needs as ## it is more 'natural'. ## ## @seealso{transforms3d, createEulerAnglesRotation} ## @end deftypefn function trans = localToGlobal3d(varargin) ## extract the components of the transform if nargin == 1 ## all components are bundled in the first argument var = varargin{1}; center = var(1:3); theta = var(4); phi = var(5); psi = 0; if length(var) > 5 psi = var(6); end elseif nargin == 4 ## arguments = center, then the 3 angles center = varargin{1}; theta = varargin{2}; phi = varargin{3}; psi = varargin{4}; elseif nargin > 4 ## center is given in 3 arguments, then 3 angles center = [varargin{1} varargin{2} varargin{3}]; theta = varargin{4}; phi = varargin{5}; psi = 0; if nargin > 5 psi = varargin{6}; end end ## conversion from degrees to radians k = pi / 180; ## rotation around normal vector axis rot1 = createRotationOz(psi * k); ## colatitude rot2 = createRotationOy(theta * k); ## longitude rot3 = createRotationOz(phi * k); ## shift center tr = createTranslation3d(center); ## create final transform by concatenating transforms trans = tr * rot3 * rot2 * rot1; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawBox3d.m0000644000000000000000000000013212676233417017206 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.513116969 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawBox3d.m0000644000175000017500000000755212676233417020376 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawBox3d (@var{box}) ## @deftypefnx {Function File} drawBox3d (@dots{},@var{opt}) ## Draw a 3D box defined by coordinate extents ## ## Draw a box defined by its coordinate extents: ## BOX = [XMIN XMAX YMIN YMAX ZMIN ZMAX]. ## The function draws only the outline edges of the box. ## Extra options @var{opt} are passed to the function @code{drawEdges3d}. ## ## Example ## @example ## # Draw bounding box of a cubeoctehedron ## [v e f] = createCubeOctahedron; ## box3d = boundingBox3d(v); ## figure; hold on; ## drawMesh(v, f); ## drawBox3d(box3d); ## axis([-2 2 -2 2 -2 2]); ## view(3) ## @end example ## ## @seealso{boxes3d, boundingBox3d} ## @end deftypefn function drawBox3d(box, varargin) # default values xmin = box(:,1); xmax = box(:,2); ymin = box(:,3); ymax = box(:,4); zmin = box(:,5); zmax = box(:,6); nBoxes = size(box, 1); for i=1:length(nBoxes) # lower face (z=zmin) drawEdge3d([xmin(i) ymin(i) zmin(i) xmax(i) ymin(i) zmin(i)], varargin{:}); drawEdge3d([xmin(i) ymin(i) zmin(i) xmin(i) ymax(i) zmin(i)], varargin{:}); drawEdge3d([xmax(i) ymin(i) zmin(i) xmax(i) ymax(i) zmin(i)], varargin{:}); drawEdge3d([xmin(i) ymax(i) zmin(i) xmax(i) ymax(i) zmin(i)], varargin{:}); # front face (y=ymin) drawEdge3d([xmin(i) ymin(i) zmin(i) xmin(i) ymin(i) zmax(i)], varargin{:}); drawEdge3d([xmax(i) ymin(i) zmin(i) xmax(i) ymin(i) zmax(i)], varargin{:}); drawEdge3d([xmin(i) ymin(i) zmax(i) xmax(i) ymin(i) zmax(i)], varargin{:}); # left face (x=xmin) drawEdge3d([xmin(i) ymax(i) zmin(i) xmin(i) ymax(i) zmax(i)], varargin{:}); drawEdge3d([xmin(i) ymin(i) zmax(i) xmin(i) ymax(i) zmax(i)], varargin{:}); # the last 3 remaining edges drawEdge3d([xmin(i) ymax(i) zmax(i) xmax(i) ymax(i) zmax(i)], varargin{:}); drawEdge3d([xmax(i) ymax(i) zmin(i) xmax(i) ymax(i) zmax(i)], varargin{:}); drawEdge3d([xmax(i) ymin(i) zmax(i) xmax(i) ymax(i) zmax(i)], varargin{:}); end endfunction %!demo %! close all %! # Draw bounding box of a cubeoctehedron %! [v e f] = createCubeOctahedron; %! box3d = boundingBox3d(v); %! figure; %! hold on; %! drawMesh(v, f); %! drawBox3d(box3d); %! axis([-2 2 -2 2 -2 2]); %! view(3) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/distancePointLine3d.m0000644000000000000000000000013212676233417021214 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/distancePointLine3d.m0000644000175000017500000000765112676233417022404 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{d} =} distancePointLine3d (@var{point}, @var{line}) ## Euclidean distance between 3D point and line ## ## Returns the distance between point POINT and the line LINE, given as: ## POINT : [x0 y0 z0] ## LINE : [x0 y0 z0 dx dy dz] ## D : (positive) scalar ## ## Run @command{demo distancePointLine3d} to see examples. ## ## References ## http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html ## ## @seealso{lines3d, distancePointLine, distancePointEdge3d, projPointOnLine3d} ## @end deftypefn function d = distancePointLine3d(point, lin) [np nd] = size (point); [nl ndl] = size (lin); if ndl < 4 error("geometry:InvalidInput","second argument must be a line. See lines3d."); end # Compare everything to everything if np != nl # Order the lines such that all points are compared against 1st line, then # secoind and so on. --JPi idx = reshape (1:np*nl,nl,np)'(:); lin = repmat (lin, np, 1)(idx,:); point = repmat (point, nl, 1); end d = vectorNorm ( cross ( lin(:,4:6), lin(:,1:3)-point, 2)) ./ ... vectorNorm (lin(:,4:6)); endfunction %!demo %! point = [0 0 1]; %! lin = [0 0 0 1 1 1]; %! d = distancePointLine3d (point,lin); %! %! # Orthogonal and Parallel projectors %! dl = normalizeVector (lin(4:end))'; %! V = dl*dl'; %! P = eye(3) - dl*dl'; %! pv = P*point'; %! vv = V*point'; %! %! # Compare %! disp([d vectorNorm(pv)]) %! %! figure(1); %! clf %! plot3 (point(1),point(2),point(3),'.k'); %! line ([0 point(1)],[0 point(2)],[0 point(3)],'color','k'); %! line (dl(1)*[-2 2],dl(2)*[-2 2],dl(3)*[-2 2],'color','r'); %! line ([0 vv(1)],[0 vv(2)],[0 vv(3)],'color','g'); %! line (vv(1)+[0 pv(1)],vv(2)+[0 pv(2)],vv(3)+[0 pv(3)],'color','b'); %! axis square equal %! %! # ------------------------------------------------------------------------- %! # Distance between a line and a point, the distance is verified against the %! # vector form the point to the line, orthogonal to the line. %!demo %! point = 2*rand(4,3)-1; %! lin = [0 0 0 1 1 1; 0 0 0 1 1 0]; %! d = distancePointLine3d (point,lin) %! %! # Organize as matrix point vs lines %! reshape (d,4,2) %! %! # ------------------------------------------------------------------------- %! # Distance between 4 points and two lines. The result can be arrange as a %! # distance matrix. geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawSphericalEdge.m0000644000000000000000000000013212676233417020726 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawSphericalEdge.m0000644000175000017500000000555612676233417022120 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawSphericalEdge (@var{sphere}, @var{edge}) ## Draw an edge on the surface of a sphere ## ## @var{edge} is given as a couple of 3D corodinates corresponding to edge ## extremities. The shortest spherical edge joining the two extremities is ## drawn on the current axes. ## ## @seealso{drawSphericalPolygon} ## @end deftypefn function varargout = drawSphericalEdge(sphere, edge, varargin) # extract data of the sphere origin = sphere(:, 1:3); # extremities of current edge point1 = edge(1:3); point2 = edge(4:6); # compute plane containing current edge plane = createPlane(origin, point1, point2); # intersection of the plane with unit sphere circle = intersectPlaneSphere(plane, sphere); # find the position (in degrees) of the 2 vertices on the circle angle1 = circle3dPosition(point1, circle); angle2 = circle3dPosition(point2, circle); # ensure angles are in right direction if mod(angle2 - angle1 + 360, 360) > 180 tmp = angle1; angle1 = angle2; angle2 = tmp; end # compute angle extent of the circle arc angleExtent = mod(angle2 - angle1 + 360, 360); # create circle arc arc = [circle angle1 angleExtent]; # draw the arc h = drawCircleArc3d(arc, varargin{:}); if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawSphere.m0000644000000000000000000000013212676233417017455 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawSphere.m0000644000175000017500000001323212676233417020635 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{} =} function_name (@var{}, @var{}) ## Draw a sphere as a mesh ## ## drawSphere(SPHERE) ## Where SPHERE = [XC YC ZC R], draw the sphere centered on the point with ## coordinates [XC YC ZC] and with radius R, using a quad mesh. ## ## drawSphere(CENTER, R) ## Where CENTER = [XC YC ZC], specifies the center and the radius with two ## arguments. ## ## drawSphere(XC, YC, ZC, R) ## Specifiy sphere center and radius as four arguments. ## ## drawSphere(..., NAME, VALUE); ## Specifies one or several options using parameter name-value pairs. ## Available options are usual drawing options, as well as: ## 'nPhi' the number of arcs used for drawing the meridians ## 'nTheta' the number of circles used for drawing the parallels ## ## H = drawSphere(...) ## Return a handle to the graphical object created by the function. ## ## [X Y Z] = drawSphere(...) ## Return the coordinates of the vertices used by the sphere. In this ## case, the sphere is not drawn. ## ## Run @code{demo drawSphere} to see several examples. ## ## @seealso{spheres, circles3d, sphere, drawEllipsoid} ## @end deftypefn function varargout = drawSphere(varargin) # process input options: when a string is found, assumes this is the # beginning of options options = {'FaceColor', 'g', 'linestyle', 'none'}; for i=1:length(varargin) if ischar(varargin{i}) options = [options(1:end) varargin(i:end)]; varargin = varargin(1:i-1); break; end end # Parse the input (try to extract center coordinates and radius) if isempty(varargin) # no input: assumes unit sphere xc = 0; yc = 0; zc = 0; r = 1; elseif length(varargin) == 1 # one argument: concatenates center and radius sphere = varargin{1}; xc = sphere(:,1); yc = sphere(:,2); zc = sphere(:,3); r = sphere(:,4); elseif length(varargin) == 2 # two arguments, corresponding to center and radius center = varargin{1}; xc = center(1); yc = center(2); zc = center(3); r = varargin{2}; elseif length(varargin) == 4 # four arguments, corresponding to XC, YX, ZC and R xc = varargin{1}; yc = varargin{2}; zc = varargin{3}; r = varargin{4}; else error('drawSphere: please specify center and radius'); end # number of meridians nPhi = 32; ind = strmatch('nphi', lower(options(1:2:end))); if ~isempty(ind) ind = ind(1); nPhi = options{2*ind}; options(2*ind-1:2*ind) = []; end # number of parallels nTheta = 16; ind = strmatch('ntheta', lower(options(1:2:end))); if ~isempty(ind) ind = ind(1); nTheta = options{2*ind}; options(2*ind-1:2*ind) = []; end # compute spherical coordinates theta = linspace(0, pi, nTheta+1); phi = linspace(0, 2*pi, nPhi+1); # convert to cartesian coordinates sintheta = sin(theta); x = xc + cos(phi')*sintheta*r; y = yc + sin(phi')*sintheta*r; z = zc + ones(length(phi),1)*cos(theta)*r; # Process output if nargout == 0 # no output: draw the sphere surf(x, y, z, options{:}); elseif nargout == 1 # one output: compute varargout{1} = surf(x, y, z, options{:}); elseif nargout == 3 varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction %!demo %! # Draw four spheres with different centers %! figure(1); clf; hold on; %! drawSphere([10 10 30 5]); %! drawSphere([20 30 10 5]); %! drawSphere([30 30 30 5]); %! drawSphere([30 20 10 5]); %! view([-30 20]); %! axis tight %! axis equal; %!demo %! # Draw sphere with different settings %! figure(1); clf; %! drawSphere([10 20 30 10], 'linestyle', ':', 'facecolor', 'r'); %! axis tight %! axis equal; %!demo %! # Draw sphere with different settings, but changes style using graphic handle %! figure(1); clf; %! h = drawSphere([10 20 30 10]); %! set(h, 'edgecolor', 'none'); %! set(h, 'facecolor', 'r'); %! axis tight %! axis equal; #%!demo #%! # Draw a sphere with high resolution #%! figure(1); clf; #%! h = drawSphere([10 20 30 10], 'nPhi', 360, 'nTheta', 180); #%! view(3); #%! axis equal; geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawPoint3d.m0000644000000000000000000000013212676233417017547 xustar0030 mtime=1459173135.517115063 30 atime=1459173135.517115063 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawPoint3d.m0000644000175000017500000000606612676233417020736 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawPoint3d (@var{x}, @var{y}, @var{z}) ## @deftypefnx {Function File} {@var{h} =} drawPoint3d (@var{coord}) ## @deftypefnx {Function File} {@var{h} =} drawPoint3d (@dots{}) ## Draw 3D point on the current axis. ## ## drawPoint3d(X, Y, Z) ## will draw points defined by coordinates X and Y. ## X and Y are N*1 array, with N being number of points to be drawn. ## ## drawPoint3d(COORD) ## packs coordinates in a single [N*3] array. ## ## drawPoint3d(..., OPT) ## will draw each point with given option. OPT is a string compatible with ## 'plot' model. ## ## H = drawPoint3d(...) ## Also return a handle to each of the drawn points. ## ## @seealso{points3d, clipPoints3d} ## @end deftypefn function varargout = drawPoint3d(varargin) var = varargin{1}; if size(var, 2)==3 # points are given as one single array with 3 columns px = var(:, 1); py = var(:, 2); pz = var(:, 3); varargin = varargin(2:end); elseif length(varargin)<3 error('wrong number of arguments in drawPoint3d'); else # points are given as 3 columns with equal length px = varargin{1}; py = varargin{2}; pz = varargin{3}; varargin = varargin(4:end); end # default draw style: no line, marker is 'o' if length(varargin)~=1 varargin = ['linestyle', 'none', 'marker', 'o', varargin]; end # plot only points inside the axis. h = plot3(px, py, pz, varargin{:}); if nargout>0 varargout{1} = h; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/geom3d_Contents.m0000644000000000000000000000013012676233417020402 xustar0029 mtime=1459173135.52511125 29 atime=1459173135.52511125 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/geom3d_Contents.m0000644000175000017500000003154412676233417021572 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} geom3d_Contents () ## GEOM3D Geometry 3D Toolbox ## Version 1.0 21-Mar-2011 . ## ## Creation, transformations, algorithms and visualization of geometrical ## 3D primitives, such as points, lines, planes, polyhedra, circles and ## spheres. ## ## Euler Angles are defined as follow: ## PHI is the azimut, i.e. the angle of the projection on horizontal plane ## with the Ox axis, with value beween 0 and 180 degrees. ## THETA is the latitude, i.e. the angle with the Oz axis, with value ## between -90 and +90 degrees. ## PSI is the 'roll', i.e. the rotation around the (PHI, THETA) direction, ## with value in degrees ## See also the 'angles3d' page. ## ## Base format for primitives: ## Point: [x0 y0 z0] ## Vector: [dx dy dz] ## Line: [x0 y0 z0 dx dy dz] ## Edge: [x1 y1 z1 x2 y2 z2] ## Plane: [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] ## Sphere: [x0 y0 z0 R] ## Circle: [x0 y0 z0 R PHI THETA PSI] (origin+center+normal+'roll'). ## Cylinder: [X1 Y1 Z1 X2 Y2 Z2 R] ## Box: [xmin xmax ymin ymax zmin zmax]. Used for clipping shapes. ## ## Polygons are represented by N-by-3 array of points, the last point is ## not necessarily the same as the first one. Points must be coplanar. ## ## Meshes and Polyhedra are represented by a couple of variables @{V, F@}: ## V: N-by-3 array of vetrtices: [x1 y1 z1; ... ;xn yn zn]; ## F: is either a [Nf*3] or [Nf*4] array containing reference for vertices ## of each face, or a [Nf*1] cell array, where each cell is an array ## containing a variable number of node indices. ## For some functions, the array E of edges is needed. It consists in a ## Ne-by-2 array containing indices of source and target vertices. ## ## ## 3D Points ## points3d - Description of functions operating on 3D points ## midPoint3d - Middle point of two 3D points or of a 3D edge ## isCoplanar - Tests input points for coplanarity in 3-space. ## transformPoint3d - Transform a point with a 3D affine transform ## distancePoints - Compute euclidean distance between pairs of 3D Points ## clipPoints3d - Clip a set of points by a box ## drawPoint3d - Draw 3D point on the current axis. ## ## 3D Vectors ## vectors3d - Description of functions operating on 3D vectors ## transformVector3d - Transform a vector with a 3D affine transform ## normalizeVector3d - Normalize a 3D vector to have norm equal to 1 ## vectorNorm3d - Norm of a 3D vector or of set of 3D vectors ## vectorAngle3d - Angle between two 3D vectors ## isParallel3d - Check parallelism of two 3D vectors ## isPerpendicular3d - Check orthogonality of two 3D vectors ## ## Angles ## angles3d - Conventions for manipulating angles in 3D ## anglePoints3d - Compute angle between three 3D points ## sphericalAngle - Compute angle between points on the sphere ## angleSort3d - Sort 3D coplanar points according to their angles in plane ## randomAngle3d - Return a 3D angle uniformly distributed on unit sphere ## ## Coordinate transforms ## sph2cart2 - Convert spherical coordinates to cartesian coordinates ## cart2sph2 - Convert cartesian coordinates to spherical coordinates ## cart2sph2d - Convert cartesian coordinates to spherical coordinates in degrees ## sph2cart2d - Convert spherical coordinates to cartesian coordinates in degrees ## cart2cyl - Convert cartesian to cylindrical coordinates ## cyl2cart - Convert cylindrical to cartesian coordinates ## ## 3D Lines and Edges ## lines3d - Description of functions operating on 3D lines ## createLine3d - Create a line with various inputs. ## transformLine3d - Transform a 3D line with a 3D affine transform ## clipLine3d - Clip a line with a box and return an edge ## midPoint3d - Middle point of two 3D points or of a 3D edge ## distancePointLine3d - Euclidean distance between 3D point and line ## distanceLines3d - Minimal distance between two 3D lines ## linePosition3d - Return the position of a 3D point on a 3D line ## drawEdge3d - Draw 3D edge in the current Window ## drawLine3d - Draw a 3D line on the current axis ## ## Planes ## planes3d - Description of functions operating on 3D planes ## createPlane - Create a plane in parametrized form ## normalizePlane - Normalize parametric representation of a plane ## intersectPlanes - Return intersection line between 2 planes in space ## intersectLinePlane - Return intersection point between a plane and a line ## intersectEdgePlane - Return intersection point between a plane and a edge ## distancePointPlane - Signed distance betwen 3D point and plane ## projPointOnPlane - Return the orthogonal projection of a point on a plane ## isBelowPlane - Test whether a point is below or above a plane ## medianPlane - Create a plane in the middle of 2 points ## planeNormal - Compute the normal to a plane ## planePosition - Compute position of a point on a plane ## planePoint - Compute 3D position of a point in a plane ## dihedralAngle - Compute dihedral angle between 2 planes ## drawPlane3d - Draw a plane clipped in the current window ## ## 3D Polygons and curves ## polygons3d - Description of functions operating on 3D polygons ## polygonCentroid3d - Centroid (or center of mass) of a polygon ## triangleArea3d - Area of a 3D triangle ## polygon3dNormalAngle - Normal angle at a vertex of the 3D polygon ## intersectLinePolygon3d - Intersection point of a 3D line and a 3D polygon ## intersectLineTriangle3d - Intersection point of a 3D line and a 3D triangle ## intersectRayPolygon3d - Intersection point of a 3D ray and a 3D polygon ## clipConvexPolygon3dHP - Clip a convex 3D polygon with Half-space ## drawPolygon3d - Draw a 3D polygon specified by a list of vertices ## drawPolyline3d - Draw a 3D polyline specified by a list of vertices ## fillPolygon3d - Fill a 3D polygon specified by a list of points ## ## 3D circles and ellipses ## circles3d - Description of functions operating on 3D circles ## circle3dPosition - Return the angular position of a point on a 3D circle ## circle3dPoint - Coordinates of a point on a 3D circle from its position ## circle3dOrigin - Return the first point of a 3D circle ## drawCircle3d - Draw a 3D circle ## drawCircleArc3d - Draw a 3D circle arc ## drawEllipse3d - Draw a 3D ellipse ## ## Spheres ## spheres - Description of functions operating on 3D spheres ## createSphere - Create a sphere containing 4 points ## intersectLineSphere - Return intersection points between a line and a sphere ## intersectPlaneSphere - Return intersection circle between a plane and a sphere ## drawSphere - Draw a sphere as a mesh ## drawSphericalTriangle - Draw a triangle on a sphere ## ## Smooth surfaces ## inertiaEllipsoid - Inertia ellipsoid of a set of 3D points ## intersectLineCylinder - Compute intersection points between a line and a cylinder ## revolutionSurface - Create a surface of revolution from a planar curve ## surfaceCurvature - Curvature on a surface from angle and principal curvatures ## drawEllipsoid - Draw a 3D ellipsoid ## drawTorus - Draw a torus (3D ring) ## drawCylinder - Draw a cylinder ## drawSurfPatch - Draw a 3D surface patch, with 2 parametrized surfaces ## ## Bounding boxes management ## boxes3d - Description of functions operating on 3D boxes ## point3dBounds - Bounding box of a set of 3D points ## intersectBoxes3d - Intersection of two 3D bounding boxes ## mergeBoxes3d - Merge 3D boxes, by computing their greatest extent ## box3dVolume - Volume of a 3-dimensional box ## randomPointInBox3d - Generate random point(s) within a 3D box ## drawBox3d - Draw a 3D box defined by coordinate extents ## ## Geometric transforms ## transforms3d - Conventions for manipulating 3D affine transforms ## createTranslation3d - Create the 4x4 matrix of a 3D translation ## createScaling3d - Create the 4x4 matrix of a 3D scaling ## createRotationOx - Create the 4x4 matrix of a 3D rotation around x-axis ## createRotationOy - Create the 4x4 matrix of a 3D rotation around y-axis ## createRotationOz - Create the 4x4 matrix of a 3D rotation around z-axis ## createBasisTransform3d - Compute matrix for transforming a basis into another basis ## eulerAnglesToRotation3d - Convert 3D Euler angles to 3D rotation matrix ## rotation3dToEulerAngles - Extract Euler angles from a rotation matrix ## createRotation3dLineAngle - Create rotation around a line by an angle theta ## rotation3dAxisAndAngle - Determine axis and angle of a 3D rotation matrix ## recenterTransform3d - Change the fixed point of an affine 3D transform ## composeTransforms3d - Concatenate several space transformations ## ## Various drawing Functions ## drawGrid3d - Draw a 3D grid on the current axis ## drawAxis3d - Draw a coordinate system and an origin ## drawAxisCube - Draw a colored cube representing axis orientation ## drawCube - Draw a 3D centered cube, eventually rotated ## drawCuboid - Draw a 3D cuboid, eventually rotated ## ## ## Credits: ## * function isCoplanar was originally written by Brett Shoelson. ## * Songbai Ji enhanced file intersectPlaneLine (6/23/2006). ## ## @end deftypefn function geom3d_Contents () help('geom3d_Contents'); ## In development: ## clipPolygon3dHP - clip a 3D polygon with Half-space ## drawPartialPatch - draw surface patch, with 2 parametrized surfaces ## Deprecated: ## intersectPlaneLine - return intersection between a plane and a line ## translation3d - return 4x4 matrix of a 3D translation ## scale3d - return 4x4 matrix of a 3D scaling ## rotationOx - return 4x4 matrix of a rotation around x-axis ## rotationOy - return 4x4 matrix of a rotation around y-axis ## rotationOz - return 4x4 matrix of a rotation around z-axis ## scaling3d - return 4x4 matrix of a 3D scaling ## vecnorm3d - compute norm of vector or of set of 3D vectors ## normalize3d - normalize a 3D vector ## drawCurve3d - draw a 3D curve specified by a list of points ## createEulerAnglesRotation - Create a rotation matrix from 3 euler angles endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawCylinder.m0000644000000000000000000000013212676233417020000 xustar0030 mtime=1459173135.517115063 30 atime=1459173135.517115063 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawCylinder.m0000644000175000017500000001375112676233417021166 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawCylinder (@var{cyl}) ## @deftypefnx {Function File} {@var{h} =} drawCylinder (@var{cyl},@var{n}) ## @deftypefnx {Function File} {@var{h} =} drawCylinder (@dots{}, @var{opt}) ## @deftypefnx {Function File} {@var{h} =} drawCylinder (@dots{}, @asis{"Facecolor"},@var{color}) ## @deftypefnx {Function File} {@var{h} =} drawCylinder (@dots{}) ## Draw a cylinder ## ## drawCylinder(@var{cyl}) ## where @var{cyl} is a cylinder defined by [x1 y1 z1 x2 y2 z2 r]: ## [x1 y2 z1] are coordinates of starting point, [x2 y2 z2] are ## coordinates of ending point, and R is the radius of the cylinder, ## draws the corresponding cylinder on the current axis. ## ## drawCylinder(@var{cyl}, @var{N}) ## uses @var{N} points for discretisation of angle. Default value is 32. ## ## drawCylinder(..., @var{opt}) ## with @var{opt} = 'open' (default) or 'closed', specify if bases of the ## cylinder should be drawn. ## ## drawCylinder(..., @asis{"FaceColor"}, @var{color}) ## Specifies the color of the cylinder. Any couple of parameters name and ## value can be given as argument, and will be transfered to the 'surf' ## matlab function ## ## @var{h} = drawCylinder(...) ## returns a handle to the patch representing the cylinder. ## ## Run @code{demo drawCylinder} to see several examples. ## ## WARNING: This function doesn't work in gnuplot (as of version 4.2). ## ## @seealso{drawSphere, drawLine3d, surf} ## @end deftypefn function varargout = drawCylinder(cyl, varargin) ## Input argument processing if iscell(cyl) res = zeros(length(cyl), 1); for i=1:length(cyl) res(i) = drawCylinder(cyl{i}, varargin{:}); end if nargout>0 varargout{1} = res; end return; end # default values N = 32; closed = true; # check number of discretization steps if ~isempty(varargin) var = varargin{1}; if isnumeric(var) N = var; varargin = varargin(2:end); end end # check if cylinder must be closed or open if ~isempty(varargin) var = varargin{1}; if ischar(var) if strncmpi(var, 'open', 4) closed = false; varargin = varargin(2:end); elseif strncmpi(var, 'closed', 5) closed = true; varargin = varargin(2:end); end end end ## Computation of mesh coordinates # extreme points of cylinder p1 = cyl(1:3); p2 = cyl(4:6); # radius of cylinder r = cyl(7); # compute orientation angle of cylinder [theta phi rho] = cart2sph2d(p2 - p1); dphi = linspace(0, 2*pi, N+1); # generate a cylinder oriented upwards x = repmat(cos(dphi) * r, [2 1]); y = repmat(sin(dphi) * r, [2 1]); z = repmat([0 ; rho], [1 length(dphi)]); # transform points trans = localToGlobal3d(p1, theta, phi, 0); pts = transformPoint3d([x(:) y(:) z(:)], trans); # reshape transformed points x2 = reshape(pts(:,1), size(x)); y2 = reshape(pts(:,2), size(x)); z2 = reshape(pts(:,3), size(x)); ## Display cylinder mesh # add default drawing options varargin = [{'FaceColor', 'g', 'edgeColor', 'none'} varargin]; # plot the cylinder as a surface hSurf = surf(x2, y2, z2, varargin{:}); # eventually plot the ends of the cylinder if closed ind = find(strcmpi(varargin, 'facecolor'), 1, 'last'); if isempty(ind) color = 'k'; else color = varargin{ind+1}; end patch(x2(1,:)', y2(1,:)', z2(1,:)', color, 'edgeColor', 'none'); patch(x2(2,:)', y2(2,:)', z2(2,:)', color, 'edgeColor', 'none'); end # format ouptut if nargout == 1 varargout{1} = hSurf; end endfunction %!demo %! figure; %! h = drawCylinder([0 0 0 10 20 30 5],'FaceColor', 'r'); %! set(h, 'facecolor', 'g'); %! axis equal %! view([60 30]) %! %! figure; %! drawCylinder([0 0 0 10 20 30 5], 'open'); %! axis equal %! view([60 30]) %! %! figure; %! drawCylinder([0 0 0 10 20 30 5], 'FaceColor', 'r'); %! axis equal %! view([60 30]) %! %! figure; %! h = drawCylinder([0 0 0 10 20 30 5]); %! set(h, 'facecolor', 'b'); %! axis equal %! view([60 30]) %!demo %! # Draw three mutually intersecting cylinders %! p0 = [30 30 30]; %! p1 = [90 30 30]; %! p2 = [30 90 30]; %! p3 = [30 30 90]; %! %! figure; %! drawCylinder([p0 p1 25], 'FaceColor', 'r'); %! hold on %! drawCylinder([p0 p2 25], 'FaceColor', 'g'); %! drawCylinder([p0 p3 25], 'FaceColor', 'b'); %! axis equal %! view([60 30]) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createRotationOx.m0000644000000000000000000000013212676233417020643 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.505120781 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createRotationOx.m0000644000175000017500000000672612676233417022035 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{trans} =} createRotationOx (@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOx (@var{origin},@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOx (@var{x0},@var{y0},@var{z0},@var{theta}) ## Create the 4x4 matrix of a 3D rotation around x-axis ## ## TRANS = createRotationOx(THETA); ## Returns the transform matrix corresponding to a rotation by the angle ## THETA (in radians) around the Ox axis. A rotation by an angle of PI/2 ## would transform the vector [0 1 0] into the vector [0 0 1]. ## ## The returned matrix has the form: ## [1 0 0 0] ## [0 cos(THETA) -sin(THETA) 0] ## [0 sin(THETA) cos(THETA) 0] ## [0 0 0 1] ## ## TRANS = createRotationOx(ORIGIN, THETA); ## TRANS = createRotationOx(X0, Y0, Z0, THETA); ## Also specifies origin of rotation. The result is similar as performing ## translation(-X0, -Y0, -Z0), rotation, and translation(X0, Y0, Z0). ## ## @seealso{transforms3d, transformPoint3d, createRotationOy, createRotationOz} ## @end deftypefn function trans = createRotationOx(varargin) # default values dx = 0; dy = 0; dz = 0; theta = 0; # get input values if length(varargin)==1 # only angle theta = varargin{1}; elseif length(varargin)==2 # origin point (as array) and angle var = varargin{1}; dx = var(1); dy = var(2); dz = var(3); theta = varargin{2}; elseif length(varargin)==3 # origin (x and y) and angle dx = varargin{1}; dy = varargin{2}; dz = varargin{3}; theta = varargin{3}; end # compute coefs cot = cos(theta); sit = sin(theta); # create transformation trans = [... 1 0 0 0;... 0 cot -sit 0;... 0 sit cot 0;... 0 0 0 1]; # add the translation part t = [1 0 0 dx;0 1 0 dy;0 0 1 dz;0 0 0 1]; trans = t*trans/t; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawPolygon3d.m0000644000000000000000000000013212676233417020105 xustar0030 mtime=1459173135.517115063 30 atime=1459173135.517115063 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawPolygon3d.m0000644000175000017500000000756212676233417021276 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawPolygon3d (@var{poly}) ## @deftypefnx {Function File} {@var{h} =} drawPolygon3d (@var{px},@var{py},@var{pz}) ## @deftypefnx {Function File} {@var{h} =} drawPolygon3d (@dots{},@var{param},@var{value}) ## Draw a 3D polygon specified by a list of vertices ## ## drawPolygon3d(POLY); ## packs coordinates in a single N-by-3 array. ## ## drawPolygon3d(PX, PY, PZ); ## specifies coordinates in separate arrays. ## ## drawPolygon3d(..., PARAM, VALUE); ## Specifies style options to draw the polyline, see plot for details. ## ## H = drawPolygon3d(...); ## also return a handle to the list of line objects. ## ## @seealso{polygons3d, fillPolygon3d, drawPolyline3d} ## @end deftypefn function varargout = drawPolygon3d(varargin) # check case we want to draw several curves, stored in a cell array var = varargin{1}; if iscell(var) holded = false; if !ishold() hold on; holded = true; end h = []; for i = 1:length(var(:)) h = [h; drawPolygon3d(var{i}, varargin{2:end})]; ##ok end if holded hold off end if nargout > 0 varargout{1} = h; end return; end # extract curve coordinate if size(var, 2) == 1 # first argument contains x coord, second argument contains y coord # and third one the z coord px = var; if length(varargin) < 3 error('Wrong number of arguments in drawPolygon3d'); end py = varargin{2}; pz = varargin{3}; varargin = varargin(4:end); else # first argument contains both coordinate px = var(:, 1); py = var(:, 2); pz = var(:, 3); varargin = varargin(2:end); end ## draw the polygon # check that the polygon is closed if px(1) ~= px(end) || py(1) ~= py(end) || pz(1) ~= pz(end) px = [px; px(1)]; py = [py; py(1)]; pz = [pz; pz(1)]; end # draw the closed curve h = plot3(px, py, pz, varargin{:}); if nargout > 0 varargout = {h}; end endfunction %!demo %! l=0.25; %! # Corner Triangle with a wedge %! poly2 = [1 0 0; ... %! ([1 0 0]+l*[-1 1 0]); ... %! mean(eye(3)); ... %! ([1 0 0]+(1-l)*[-1 1 0]); ... %! 0 1 0; ... %! 0 0 1]; %! drawPolygon3d(poly2) %! axis square %! axis equal %! view([74 26]) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/planes3d.m0000644000000000000000000000013212676233417017062 xustar0030 mtime=1459173135.529109344 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/planes3d.m0000644000175000017500000000417412676233417020247 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} planes3d () ##PLANES3D Description of functions operating on 3D planes ## ## Planes are represented by a 3D point (the plane origin) and 2 direction ## vectors, which should not be colinear. ## PLANE = [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2]; ## ## @seealso{createPlane, medianPlane, normalizePlane, ## planeNormal, planePosition, dihedralAngle, ## intersectPlanes, projPointOnPlane, isBelowPlane, ## intersectLinePlane, intersectEdgePlane, distancePointPlane, drawPlane3d} ## @end deftypefn function planes3d(varargin) help planes3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/boxes3d.m0000644000000000000000000000013212676233417016720 xustar0030 mtime=1459173135.501122687 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/boxes3d.m0000644000175000017500000000413312676233417020100 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} boxes3d () ## BOXES3D Description of functions operating on 3D boxes ## ## A box defined by its coordinate extents: ## BOX = [XMIN XMAX YMIN YMAX ZMIN ZMAX]. ## ## Example ## # Draw a polyhedron together with its bounding box ## [n e f]= createIcosahedron; ## drawPolyhedron(n, f); ## hold on; ## drawBox3d(point3dBounds(n)) ## ## ## @seealso{point3dBounds, box3dVolume, drawBox3d ## intersectBoxes3d, mergeBoxes3d, randomPointInBox3d} ## @end deftypefn function boxes3d() help boxes3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/anglePoints3d.m0000644000000000000000000000013212676233417020063 xustar0030 mtime=1459173135.497124593 30 atime=1459173135.497124593 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/anglePoints3d.m0000644000175000017500000000652712676233417021254 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{alpha} =} anglePoints3d (@var{p1}, @var{p2}) ## @deftypefnx {Function File} {@var{alpha} =} anglePoints3d (@var{p1}, @var{p2},@var{p3}) ## @deftypefnx {Function File} {@var{alpha} =} anglePoints3d (@var{pts}) ## Compute angle between three 3D points ## ## @var{alpha} = anglePoints3d(P1, P2) ## Computes angle (P1, O, P2), in radians, between 0 and PI. ## ## @var{alpha} = anglePoints3d(P1, P2, P3) ## Computes angle (P1, P2, P3), in radians, between 0 and PI. ## ## @var{alpha} = anglePoints3d(PTS) ## PTS is a 3x3 or 2x3 array containing coordinate of points. ## ## @seealso{points3d, angles3d} ## @end deftypefn function alpha = anglePoints3d(varargin) p2 = [0 0 0]; if length(varargin)==1 pts = varargin{1}; if size(pts, 1)==2 p1 = pts(1,:); p0 = [0 0 0]; p2 = pts(2,:); else p1 = pts(1,:); p0 = pts(2,:); p2 = pts(3,:); end elseif length(varargin)==2 p1 = varargin{1}; p0 = [0 0 0]; p2 = varargin{2}; elseif length(varargin)==3 p1 = varargin{1}; p0 = varargin{2}; p2 = varargin{3}; end # ensure all data have same size n1 = size(p1, 1); n2 = size(p2, 1); n0 = size(p0, 1); if n1~=n2 if n1==1 p1 = repmat(p1, [n2 1]); elseif n2==1 p2 = repmat(p2, [n1 1]); else error('Arguments P1 and P2 must have the same size'); end end if n1~=n0 if n1==1 p1 = repmat(p1, [n0 1]); elseif n0==1 p0 = repmat(p0, [n1 1]); else error('Arguments P1 and P0 must have the same size'); end end # normalized vectors p1 = normalizeVector(p1-p0); p2 = normalizeVector(p2-p0); # compute angle alpha = acos(dot(p1, p2, 2)); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/lines3d.m0000644000000000000000000000013012676233417016710 xustar0029 mtime=1459173135.52511125 29 atime=1459173135.52511125 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/lines3d.m0000644000175000017500000000375312676233417020101 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} lines3d () ##LINES3D Description of functions operating on 3D lines ## ## A 3D Line is represented by a 3D point (its origin) and a 3D vector ## (its direction): ## LINE = [X0 Y0 Z0 DX DY DZ]; ## ## @seealso{createLine3d, transformLine3d, distancePointLine3d, linePosition3d ## intersectLinePlane, distanceLines3d, clipLine3d, drawLine3d} ## @end deftypefn function lines3d() help lines3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawSphericalTriangle.m0000644000000000000000000000013212676233417021627 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawSphericalTriangle.m0000644000175000017500000000476312676233417023020 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} function_name (@var{sphere}, @var{p1},@var{p2},@var{p3}) ## Draw a triangle on a sphere ## @seealso{drawSphere, fillSphericalTriangle, drawSphericalPolygon} ## @end deftypefn function varargout = drawSphericalTriangle(sphere, p1, p2, p3, varargin) # extract data of the sphere ori = sphere(:, 1:3); # extract direction vectors for each point v1 = normalizeVector (p1 - ori); v2 = normalizeVector (p2 - ori); v3 = normalizeVector (p3 - ori); holded = false; if !ishold() hold on holded = true; endif h1 = drawSphericalEdge (sphere, [v1 v2], varargin{:}); h2 = drawSphericalEdge (sphere, [v2 v3], varargin{:}); h3 = drawSphericalEdge (sphere, [v3 v1], varargin{:}); if holded hold off endif if nargout > 0 varargout = {h1, h2, h3}; end endfunction %!demo %! p = full(eye(3)); %! s = [0 0 0 2]; %! drawSphericalTriangle (s,p(1,:),p(2,:),p(3,:),"r"); %! view(40,35) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createPlane.m0000644000000000000000000000013212676233417017574 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.505120781 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createPlane.m0000644000175000017500000001155412676233417020761 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{PLANE} =} createPlane (@var{pts}) ## @deftypefnx {Function File} {@var{PLANE} =} createPlane (@var{p0}, @var{n}) ## @deftypefnx {Function File} {@var{PLANE} =} createPlane (@var{p1}, @var{p2}, @var{p3}) ## Create a plane in parametrized form ## ## PLANE = createPlane(PTS) ## The 3 points are packed into a single 3x3 array. ## ## PLANE = createPlane(P0, N); ## Creates a plane from a point and from a normal to the plane. The ## parameter N is given either as a 3D vector (1-by-3 row vector), or as ## [THETA PHI], where THETA is the colatitute (angle with the vertical ## axis) and PHI is angle with Ox axis, counted counter-clockwise (both ## given in radians). ## ## PLANE = createPlane(P1, P2, P3) ## creates a plane containing the 3 points ## ## The created plane data has the following format: ## PLANE = [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], with ## - (X0, Y0, Z0) is a point belonging to the plane ## - (DX1, DY1, DZ1) is a first direction vector ## - (DX2, DY2, DZ2) is a second direction vector ## The 2 direction vectors are normalized and orthogonal. ## ## @seealso{planes3d, medianPlane} ## @end deftypefn ## TODO: return closet plane when dim(PTS,1) > 3 function plane = createPlane(varargin) if length (varargin) == 1 var = varargin{1}; if iscell (var) plane = zeros ([length (var) 9]); for i=1:length (var) plane(i,:) = createPlane (var{i}); end elseif size (var, 1) >= 3 # 3 points in a single array p1 = var(1,:); p2 = var(2,:); p3 = var(3,:); # create direction vectors v1 = p2 - p1; v2 = p3 - p1; # create plane plane = normalizePlane ([p1 v1 v2]); return; end elseif length (varargin) == 2 # plane origin p0 = varargin{1}; # second parameter is either a 3D vector or a 3D angle (2 params) var = varargin{2}; if size (var, 2) == 2 # normal is given in spherical coordinates n = sph2cart2 ([var ones(size(var, 1))]); elseif size (var, 2)==3 # normal is given by a 3D vector n = normalizeVector (var); else error ('wrong number of parameters in createPlane'); end # ensure same dimension for parameters if size (p0, 1)==1 p0 = repmat (p0, [size(n, 1) 1]); end if size(n, 1)==1 n = repmat (n, [size(p0, 1) 1]); end # find a vector not colinear to the normal v0 = repmat ([1 0 0], [size(p0, 1) 1]); inds = vectorNorm (cross (n, v0, 2)) < 1e-14; v0(inds, :) = repmat ([0 1 0], [sum(inds) 1]); # if abs(cross(n, v0, 2))<1e-14 # v0 = repmat([0 1 0], [size(p0, 1) 1]); # end # create direction vectors v1 = normalizeVector (cross (n, v0, 2)); v2 = -normalizeVector (cross (v1, n, 2)); # concatenate result in the array representing the plane plane = [p0 v1 v2]; return; elseif length (varargin)==3 p1 = varargin{1}; p2 = varargin{2}; p3 = varargin{3}; # create direction vectors v1 = p2 - p1; v2 = p3 - p1; plane = normalizePlane ([p1 v1 v2]); return; else error ('Wrong number of arguments in "createPlane".'); end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createTranslation3d.m0000644000000000000000000000013212676233417021262 xustar0030 mtime=1459173135.509118875 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createTranslation3d.m0000644000175000017500000000543612676233417022451 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{} =} createTranslation3d (@var{dx}, @var{dy}, @var{dz}) ## @deftypefnx {Function File} {@var{} =} createTranslation3d (@var{vect}) ## Create the 4x4 matrix of a 3D translation ## ## usage: ## TRANS = createTranslation3d(DX, DY, DZ); ## return the translation corresponding to DX and DY. ## The returned matrix has the form : ## [1 0 0 DX] ## [0 1 0 DY] ## [0 0 1 DZ] ## [0 0 0 1] ## ## TRANS = createTranslation3d(VECT); ## return the translation corresponding to the given vector [x y z]. ## ## @seealso{transforms3d, transformPoint3d, transformVector3d, ## createRotationOx, createRotationOy, createRotationOz, createScaling3d} ## @end deftypefn function trans = createTranslation3d(varargin) if isempty(varargin) # assert translation with null vector dx = 0; dy = 0; dz = 0; elseif length(varargin)==1 # translation vector given in a single argument var = varargin{1}; dx = var(1); dy = var(2); dz = var(3); else # translation vector given in 3 arguments dx = varargin{1}; dy = varargin{2}; dz = varargin{3}; end # create the translation matrix trans = [1 0 0 dx ; 0 1 0 dy ; 0 0 1 dz; 0 0 0 1]; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/planeNormal.m0000644000000000000000000000013212676233417017621 xustar0030 mtime=1459173135.529109344 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/planeNormal.m0000644000175000017500000000366512676233417021012 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{n} =} planeNormal (@var{plane}) # Compute the normal to a plane # # N = planeNormal(PLANE) # compute the normal of the given plane # PLANE : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] # N : [dx dy dz] # ## @seealso{planes3d, createPlane} ## @end deftypefn function n = planeNormal(plane) n = cross (plane(:,4:6), plane(:, 7:9), 2); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/sph2cart2d.m0000644000000000000000000000013212676233417017325 xustar0030 mtime=1459173135.537105532 30 atime=1459173135.537105532 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/sph2cart2d.m0000644000175000017500000000651612676233417020514 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} sph2cart2d(@var{theta}, @var{phi}, @var{rho}) ## @deftypefnx {Function File} {@var{c} =} sph2cart2d(@var{theta}, @var{phi}) ## @deftypefnx {Function File} {@var{c} =} sph2cart2d(@var{s}) ## @deftypefnx {Function File} {[@var{x},@var{y},@var{z}] =} sph2cart2d(@var{theta}, @var{phi}, @var{rho}) ## Convert spherical coordinates to cartesian coordinates in degrees ## ## ## @var{c} = SPH2CART2(@var{theta}, @var{phi}) assumes @var{rho} = 1. ## ## @var{s} = [@var{theta}, @var{phi}, @var{rho}] (spherical coordinate). ## @var{c} = [@var{x},@var{y},@var{z}] (cartesian coordinate) ## ## The following convention is used: ## @var{theta} is the colatitude, in degrees, 0 for north pole, +180 degrees for ## south pole, +90 degrees for points with z=0. ## @var{phi} is the azimuth, in degrees, defined as matlab cart2sph: angle from ## Ox axis, counted counter-clockwise. ## @var{rho} is the distance of the point to the origin. ## Discussion on choice for convention can be found at: ## @url{http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf} ## ## @seealso{angles3d, cart2sph2d, sph2cart2} ## @end deftypefn function varargout = sph2cart2d(theta, phi, rho) # Process input arguments if nargin == 1 phi = theta(:, 2); if size(theta, 2) > 2 rho = theta(:, 3); else rho = ones(size(phi)); end theta = theta(:, 1); elseif nargin == 2 rho = ones(size(theta)); end # conversion rz = rho .* sind(theta); x = rz .* cosd(phi); y = rz .* sind(phi); z = rho .* cosd(theta); # Process output arguments if nargout == 1 || nargout == 0 varargout{1} = [x, y, z]; else varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createRotationOz.m0000644000000000000000000000013212676233417020645 xustar0030 mtime=1459173135.509118875 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createRotationOz.m0000644000175000017500000000672612676233417022037 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{trans} =} createRotationOz (@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOz (@var{origin},@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOz (@var{x0},@var{y0},@var{z0},@var{theta}) ## Create the 4x4 matrix of a 3D rotation around x-axis ## ## TRANS = createRotationOz(THETA); ## Returns the transform matrix corresponding to a rotation by the angle ## THETA (in radians) around the Oz axis. A rotation by an angle of PI/2 ## would transform the vector [0 1 0] into the vector [0 0 1]. ## ## The returned matrix has the form: ## [1 0 0 0] ## [0 cos(THETA) -sin(THETA) 0] ## [0 sin(THETA) cos(THETA) 0] ## [0 0 0 1] ## ## TRANS = createRotationOz(ORIGIN, THETA); ## TRANS = createRotationOz(X0, Y0, Z0, THETA); ## Also specifies origin of rotation. The result is similar as performing ## translation(-X0, -Y0, -Z0), rotation, and translation(X0, Y0, Z0). ## ## @seealso{transforms3d, transformPoint3d, createRotationOx, createRotationOy} ## @end deftypefn function trans = createRotationOz(varargin) # default values dx = 0; dy = 0; dz = 0; theta = 0; # get input values if length(varargin)==1 # only angle theta = varargin{1}; elseif length(varargin)==2 # origin point (as array) and angle var = varargin{1}; dx = var(1); dy = var(2); dz = var(3); theta = varargin{2}; elseif length(varargin)==3 # origin (x and y) and angle dx = varargin{1}; dy = varargin{2}; dz = varargin{3}; theta = varargin{3}; end # compute coefs cot = cos(theta); sit = sin(theta); # create transformation trans = [... cot -sit 0 0;... sit cot 0 0;... 0 0 1 0;... 0 0 0 1]; # add the translation part t = [1 0 0 dx;0 1 0 dy;0 0 1 dz;0 0 0 1]; trans = t*trans/t; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawSphericalPolygon.m0000644000000000000000000000013212676233417021511 xustar0030 mtime=1459173135.521113157 30 atime=1459173135.521113157 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawSphericalPolygon.m0000644000175000017500000000436512676233417022700 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{} =} drawSphericalPolygon (@var{sphere}, @var{poly}) ## Draw a spherical polygon ## ## @end deftypefn function varargout = drawSphericalPolygon(sphere, poly, varargin) nv = size(poly, 1); h = zeros(nv, 1); figure(gcf); holded = false; if ~ishold(gca) hold on holded = true; endif for i = 1:nv v1 = poly(i, :); v2 = poly(mod(i, nv) + 1, :); h(i) = drawSphericalEdge(sphere, [v1 v2], varargin{:}); end if holded hold off endif if nargout > 0 varargout = {h}; end endfunction %!demo %! p = full(eye(3)); %! s = [0 0 0 1]; %! drawSphericalPolygon (s,p,"r"); %! drawSphericalPolygon (2*s,p,"g"); %! view(40,35) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/cyl2cart.m0000644000000000000000000000013212676233417017074 xustar0030 mtime=1459173135.509118875 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/cyl2cart.m0000644000175000017500000000602412676233417020255 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{cart} =} cyl2cart (@var{cyl}) ## @deftypefnx {Function File} {@var{cart} =} cyl2cart (@var{theta},@var{r},@var{z}) ## Convert cylindrical to cartesian coordinates ## ## CART = cyl2cart(CYL) ## convert the 3D cylindrical coordinates of points CYL (given by ## [THETA R Z] where THETA, R, and Z have the same size) into cartesian ## coordinates CART, given by [X Y Z]. ## The transforms is the following : ## X = R*cos(THETA); ## Y = R*sin(THETA); ## Z remains inchanged. ## ## CART = cyl2cart(THETA, R, Z) ## provides coordinates as 3 different parameters ## ## Example ## @example ## cyl2cart([-1 0 2]) ## gives : 4.7124 1.0000 2.0000 ## @end example ## ## @seealso{angles3d, cart2pol, cart2sph2, cart2cyl} ## @end deftypefn function varargout = cyl2cart(varargin) # process input parameters if length(varargin)==1 var = varargin{1}; theta = var(:,1); r = var(:,2); z = var(:,3); elseif length(varargin)==3 theta = varargin{1}; r = varargin{2}; z = varargin{3}; end # convert coordinates dim = size(theta); x = reshape(r(:).*cos(theta(:)), dim); y = reshape(r(:).*sin(theta(:)), dim); # process output parameters if nargout==0 ||nargout==1 if length(dim)>2 || dim(2)>1 varargout{1} = {x y z}; else varargout{1} = [x y z]; end elseif nargout==3 varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/polygonArea3d.m0000644000000000000000000000013212676233417020060 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.533107438 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/polygonArea3d.m0000644000175000017500000000606112676233417021242 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{area} =} polygonArea3d(@var{poly}) ## Area of a 3D polygon ## ## @var{poly} is given as a N-by-3 array of vertex coordinates. The resulting ## area is positive. ## ## Example ## @example ## poly = [10 30 20;20 30 20;20 40 20;10 40 20]; ## polygonArea3d(poly) ## ans = ## 100 ## @end example ## ## @seealso{polygons3d, triangleArea3d, polygonArea, polygonCentroid3d} ## @end deftypefn function area = polygonArea3d(poly) # put the first vertex at origin (reducing computation errors for polygons # far from origin) v0 = poly (1, :); poly -= v0; # indices of next vertices N = size (poly, 1); iNext = [2:N 1]; # compute area (vectorized version) # need to compute the sign explicitely, as the norm of the cross product # does not keep orientation within supporting plane. cp = cross (poly, poly(iNext,:), 2); sign_i = sign (cp*cp(2,:)'); area_i = vectorNorm(cp) .* sign_i; # sum up individual triangles area area = sum(area_i) / 2; endfunction %!demo %! poly = [10 30 20;20 30 20;20 40 20;10 40 20]; %! polygonArea3d(poly) %!demo %! l=0.25; %! # Corner Triangle with a wedge %! poly = [1 0 0; ... %! ([1 0 0]+l*[-1 1 0]); ... %! mean(eye(3)); ... %! ([1 0 0]+(1-l)*[-1 1 0]); ... %! 0 1 0; ... %! 0 0 1]; %! %! polygonArea3d(poly) %! %! # Is the same as %! p1 = [1 0 0; 0 1 0; 0 0 1]; # Corner %! p2 = [([1 0 0]+l*[-1 1 0]); ([1 0 0]+(1-l)*[-1 1 0]); mean(eye(3))]; # Wedge %! %! polygonArea3d(p1)-polygonArea3d(p2) geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawCube.m0000644000000000000000000000013212676233417017105 xustar0030 mtime=1459173135.517115063 30 atime=1459173135.517115063 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawCube.m0000644000175000017500000001065312676233417020271 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawCube (@var{cube}) ## @deftypefnx {Function File} {[@var{x},@var{y},@var{z}] =} drawCube (@var{cube}) ## Draw a 3D centered cube, eventually rotated ## ## drawCube(CUBE) ## Displays a 3D cube on current axis. CUBE is given by: ## [XC YC ZC SIDE THETA PHI PSI] ## where (XC, YC, ZC) is the CUBE center, SIDE is the length of the cube ## main sides, and THETA PHI PSI are angles representing the cube ## orientation, in degrees. THETA is the colatitude of the cube, between 0 ## and 90 degrees, PHI is the longitude, and PSI is the rotation angle ## around the axis of the normal. ## ## CUBE can be axis aligned, in this case it should only contain center ## and side information: ## CUBE = [XC YC ZC SIDE] ## ## The function drawCuboid is closely related, but uses a different angle ## convention, and allows for different sizes along directions. ## ## Example ## @example ## # Draw a cube with small rotations ## figure; hold on; ## drawCube([10 20 30 50 10 20 30], 'FaceColor', 'g'); ## axis equal; ## view(3); ## @end example ## ## WARNING: This function doesn't work in gnuplot (as of version 4.2). ## ## @seealso{meshes3d, polyhedra, createCube, drawCuboid} ## @end deftypefn function varargout = drawCube(cube, varargin) # default values theta = 0; phi = 0; psi = 0; ## Parses the input if nargin == 0 # no input: assumes cube with default shape xc = 0; yc = 0; zc = 0; a = 1; else # one argument: parses elements xc = cube(:,1); yc = cube(:,2); zc = cube(:,3); a = cube(:,4); # parses orientation if present k = pi / 180; if size(cube, 2) >= 6 theta = cube(:,5) * k; phi = cube(:,6) * k; end if size(cube, 2) >= 7 psi = cube(:,7) * k; end end ## Compute cube coordinates # create unit centered cube [v f] = createCube; v = bsxfun(@minus, v, mean(v, 1)); # convert unit basis to cube basis sca = createScaling3d (a); rot1 = createRotationOz (psi); rot2 = createRotationOy (theta); rot3 = createRotationOz (phi); tra = createTranslation3d ([xc yc zc]); # concatenate transforms trans = tra * rot3 * rot2 * rot1 * sca; # transform mesh vertices [x y z] = transformPoint3d (v, trans); ## Process output if nargout == 0 # no output: draw the cube drawMesh ([x y z], f, varargin{:}); elseif nargout == 1 # one output: draw the cube and return handle varargout{1} = drawMesh ([x y z], f, varargin{:}); elseif nargout == 3 # 3 outputs: return computed coordinates varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction %!demo %! # Draw a cube with small rotations %! figure; hold on; %! drawCube([10 20 30 50 10 20 30], 'FaceColor', 'g'); %! axis equal; %! view(3); geometry-2.1.1/inst/geom3d/PaxHeaders.5293/planePosition.m0000644000000000000000000000013212676233417020175 xustar0030 mtime=1459173135.529109344 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/planePosition.m0000644000175000017500000000543712676233417021365 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pt2} =} planePosition (@var{point}, @var{plane}) ## Compute position of a point on a plane ## ## PT2 = planePosition(POINT, PLANE) ## POINT has format [X Y Z], and plane has format ## [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], where : ## - (X0, Y0, Z0) is a point belonging to the plane ## - (DX1, DY1, DZ1) is a first direction vector ## - (DX2, DY2, DZ2) is a second direction vector ## ## Result PT2 has the form [XP YP], with [XP YP] coordinate of the point ## in the coordinate system of the plane. ## ## ## CAUTION: ## WORKS ONLY FOR PLANES WITH ORTHOGONAL DIRECTION VECTORS ## ## @seealso{planes3d, points3d, planePoint} ## @end deftypefn function pos = planePosition(point, plane) # unify size of data if size (point, 1) ~= size (plane, 1) if size (point, 1) == 1 point = repmat (point, [size(plane, 1) 1]); elseif size (plane, 1) == 1 plane = repmat (plane, [size(point, 1) 1]); else error ('point and plane do not have the same dimension'); end end p0 = plane(:, 1:3); d1 = plane(:, 4:6); d2 = plane(:, 7:9); s = dot (point-p0, d1, 2) ./ vectorNorm (d1); t = dot (point-p0, d2, 2) ./ vectorNorm (d2); pos = [s t]; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/intersectPlaneSphere.m0000644000000000000000000000013012676233417021476 xustar0029 mtime=1459173135.52511125 29 atime=1459173135.52511125 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/intersectPlaneSphere.m0000644000175000017500000000725112676233417022664 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{circ} =} intersectPlaneSphere(@var{plane}, @var{sphere}) ## Return intersection circle between a plane and a sphere ## ## Returns the circle which is the intersection of the given plane ## and sphere. ## @var{plane} : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] ## @var{sphere} : [XS YS ZS RS] ## @var{circ} : [XC YC ZC RC THETA PHI PSI] ## [x0 y0 z0] is the origin of the plane, [dx1 dy1 dz1] and [dx2 dy2 dz2] ## are two direction vectors, ## [XS YS ZS] are coordinates of the sphere center, RS is the sphere ## radius, ## [XC YC ZC] are coordinates of the circle center, RC is the radius of ## the circle, [THETA PHI] is the normal of the plane containing the ## circle (THETA being the colatitude, and PHI the azimut), and PSI is a ## rotation angle around the normal (equal to zero in this function, but ## kept for compatibility with other functions). All angles are given in ## degrees. ## ## @seealso{planes3d, spheres, circles3d, intersectLinePlane, intersectLineSphere} ## @end deftypefn function circle = intersectPlaneSphere(plane, sphere) # number of inputs of each type Ns = size(sphere, 1); Np = size(plane, 1); # unify data dimension if Ns ~= Np if Ns == 1 sphere = sphere(ones(Np, 1), :); elseif Np == 1 plane = plane(ones(Ns, 1), :); else error('data should have same length, or one data should have length 1'); end end # center of the spheres center = sphere(:,1:3); # radius of spheres if size(sphere, 2) == 4 Rs = sphere(:,4); else # assume default radius equal to 1 Rs = ones(size(sphere, 1), 1); end # projection of sphere center on plane -> gives circle center circle0 = projPointOnPlane(center, plane); # radius of circles d = distancePoints (center, circle0); Rc = sqrt(Rs.*Rs - d.*d); # normal of planes = normal of circles nor = planeNormal(plane); # convert to angles [theta phi] = cart2sph2(nor(:,1), nor(:,2), nor(:,3)); psi = zeros(Np, 1); # create structure for circle k = 180 / pi; circle = [circle0 Rc [theta phi psi]*k]; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawCircle3d.m0000644000000000000000000000013212676233417017657 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.513116969 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawCircle3d.m0000644000175000017500000002067712676233417021052 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawCircle3d (@var{circle2d}, @var{normal}) ## @deftypefnx {Function File} {@var{h} =} drawCircle3d (@var{xc}, @var{yc}, @var{zc}, @var{r}, @var{theta}, @var{phi}, @var{psi}) ## Draw a 3D circle ## ## Possible calls for the function: ## drawCircle3d([XC YC ZC R THETA PHI]) ## drawCircle3d([XC YC ZC R], [THETA PHI]) ## ## where XC, YC, ZY are coordinates of circle center, R is the circle ## radius, PHI and THETA are 3D angles in degrees of the normal to the ## plane containing the circle: ## * THETA between 0 and 180 degrees, corresponding to the colatitude ## (angle with Oz axis). ## * PHI between 0 and 360 degrees corresponding to the longitude (angle ## with Ox axis) ## ## drawCircle3d([XC YC ZC R THETA PHI PSI]) ## drawCircle3d([XC YC ZC R], [THETA PHI PSI]) ## drawCircle3d([XC YC ZC R], THETA, PHI) ## drawCircle3d([XC YC ZC], R, THETA, PHI) ## drawCircle3d([XC YC ZC R], THETA, PHI, PSI) ## drawCircle3d([XC YC ZC], R, THETA, PHI, PSI) ## drawCircle3d(XC, YC, ZC, R, THETA, PHI) ## drawCircle3d(XC, YC, ZC, R, THETA, PHI, PSI) ## Are other possible syntaxes for this function. ## ## H = drawCircle3d(...) ## return handle on the created LINE object ## ## Example ## @example ## # display 3 mutually orthogonal 3D circles ## figure; hold on; ## drawCircle3d([10 20 30 50 0 0], 'LineWidth', 2, 'Color', 'b'); ## drawCircle3d([10 20 30 50 90 0], 'LineWidth', 2, 'Color', 'r'); ## drawCircle3d([10 20 30 50 90 90], 'LineWidth', 2, 'Color', 'g'); ## axis equal; ## axis([-50 100 -50 100 -50 100]); ## view([-10 20]) ## ## # Draw several circles at once ## center = [10 20 30]; ## circ1 = [center 50 0 0]; ## circ2 = [center 50 90 0]; ## circ3 = [center 50 90 90]; ## figure; hold on; ## drawCircle3d([circ1 ; circ2 ; circ3]); ## axis equal; ## @end example # ## @seealso{circles3d, drawCircleArc3d, drawEllipse3d, drawSphere} ## @end deftypefn function varargout = drawCircle3d(varargin) # Possible calls for the function, with number of arguments : # drawCircle3d([XC YC ZC R THETA PHI]) 1 # drawCircle3d([XC YC ZC R THETA PHI PSI]) 1 # drawCircle3d([XC YC ZC R], [THETA PHI]) 2 # drawCircle3d([XC YC ZC R], [THETA PHI PSI]) 2 # drawCircle3d([XC YC ZC R], THETA, PHI) 3 # drawCircle3d([XC YC ZC], R, THETA, PHI) 4 # drawCircle3d([XC YC ZC R], THETA, PHI, PSI) 4 # drawCircle3d([XC YC ZC], R, THETA, PHI, PSI) 5 # drawCircle3d(XC, YC, ZC, R, THETA, PHI) 6 # drawCircle3d(XC, YC, ZC, R, THETA, PHI, PSI) 7 # extract drawing options ind = find(cellfun(@ischar, varargin), 1, 'first'); options = {}; if ~isempty(ind) options = varargin(ind:end); varargin(ind:end) = []; end # Extract circle data if length(varargin) == 1 # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); r = circle(:,4); # get colatitude of normal if size(circle, 2) >= 5 theta = circle(:,5); else theta = zeros(size(circle, 1), 1); end # get azimut of normal if size(circle, 2)>=6 phi = circle(:,6); else phi = zeros(size(circle, 1), 1); end # get roll if size(circle, 2)==7 psi = circle(:,7); else psi = zeros(size(circle, 1), 1); end elseif length(varargin) == 2 # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); r = circle(:,4); # get angle of normal angle = varargin{2}; theta = angle(:,1); phi = angle(:,2); # get roll if size(angle, 2)==3 psi = angle(:,3); else psi = zeros(size(angle, 1), 1); end elseif length(varargin) == 3 # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); r = circle(:,4); # get angle of normal and roll theta = varargin{2}; phi = varargin{3}; psi = zeros(size(phi, 1), 1); elseif length(varargin) == 4 # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); if size(circle, 2)==4 r = circle(:,4); theta = varargin{2}; phi = varargin{3}; psi = varargin{4}; else r = varargin{2}; theta = varargin{3}; phi = varargin{4}; psi = zeros(size(phi, 1), 1); end elseif length(varargin) == 5 # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); r = varargin{2}; theta = varargin{3}; phi = varargin{4}; psi = varargin{5}; elseif length(varargin) == 6 xc = varargin{1}; yc = varargin{2}; zc = varargin{3}; r = varargin{4}; theta = varargin{5}; phi = varargin{6}; psi = zeros(size(phi, 1), 1); elseif length(varargin) == 7 xc = varargin{1}; yc = varargin{2}; zc = varargin{3}; r = varargin{4}; theta = varargin{5}; phi = varargin{6}; psi = varargin{7}; else error('drawCircle3d: please specify center and radius'); end # circle parametrisation (by using N=60, some vertices are located at # special angles like 45°, 30°...) Nt = 60; t = linspace(0, 2*pi, Nt+1); nCircles = length(xc); h = zeros(nCircles, 1); for i = 1:nCircles # compute position of circle points x = r(i) * cos(t)'; y = r(i) * sin(t)'; z = zeros(length(t), 1); circle0 = [x y z]; # compute transformation from local basis to world basis trans = localToGlobal3d(xc(i), yc(i), zc(i), theta(i), phi(i), psi(i)); # compute points of transformed circle circle = transformPoint3d(circle0, trans); # draw the curve of circle points h(i) = drawPolyline3d(circle, options{:}); end if nargout > 0 varargout = {h}; end endfunction %!demo %! # display 3 mutually orthogonal 3D circles %! figure; hold on; %! drawCircle3d([10 20 30 50 0 0], 'LineWidth', 2, 'Color', 'b'); %! drawCircle3d([10 20 30 50 90 0], 'LineWidth', 2, 'Color', 'r'); %! drawCircle3d([10 20 30 50 90 90], 'LineWidth', 2, 'Color', 'g'); %! axis square equal; %! axis([-50 100 -50 100 -50 100]); %! view([-10 20]) %! %! # Draw several circles at once %! center = [10 20 30]; %! circ1 = [center 50 0 0]; %! circ2 = [center 50 90 0]; %! circ3 = [center 50 90 90]; %! figure; hold on; %! drawCircle3d([circ1 ; circ2 ; circ3]); %! axis square equal; geometry-2.1.1/inst/geom3d/PaxHeaders.5293/vectorAngle3d.m0000644000000000000000000000013212676233417020051 xustar0030 mtime=1459173135.537105532 30 atime=1459173135.537105532 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/vectorAngle3d.m0000644000175000017500000000501012676233417021224 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{theta} =} vectorAngle3d (@var{v1}, @var{v2}) ## Angle between two 3D vectors ## ## THETA = vectorAngle3d(V1, V2) ## Computes the angle between the 2 3D vectors V1 and V2. The result THETA ## is given in radians, between 0 and PI. ## ## ## Example ## # angle between 2 orthogonal vectors ## vectorAngle3d([1 0 0], [0 1 0]) ## ans = ## 1.5708 ## ## # angle between 2 parallel vectors ## v0 = [3 4 5]; ## vectorAngle3d(3*v0, 5*v0) ## ans = ## 0 ## ## @seealso{vectors3d, vectorNorm} ## @end deftypefn function theta = vectorAngle3d(v1, v2) # compute angle using arc-tangent to get better precision for angles near # zero, see the discussion in: # http://www.mathworks.com/matlabcentral/newsreader/view_thread/151925#381952 # equivalent to: # v1 = normalizeVector(v1); # v2 = normalizeVector(v2); # theta = acos(dot(v1, v2, 2)); theta = atan2(vectorNorm(cross (v1, v2)), sum(v1.*v2,2)); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/circles3d.m0000644000000000000000000000013212676233417017224 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.505120781 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/circles3d.m0000644000175000017500000000451112676233417020404 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} circles3d () ##CIRCLES3D Description of functions operating on 3D circles ## ## Circles are represented by a center, a radius and a 3D angle ## representing the normal of the plane containing the circle. ## C = [xc yc zc R theta phi psi]. ## THETA is the colatitude of the normal, in degrees, between 0 and 180 ## PHI is the azimut of the normal, in degrees, between 0 and 360 ## PSI is the proper rotation of the circle around the normal, between 0 ## and 360 degrees ## The parameter PSI is used to locate a point on the 3D circle. ## ## @seealso{circle3dOrigin, circle3dPosition, circle3dPoint, intersectPlaneSphere ## drawCircle3d, drawCircleArc3d, drawEllipse3d} ## @end deftypefn function circles3d () help circles3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawCircleArc3d.m0000644000000000000000000000013212676233417020305 xustar0030 mtime=1459173135.513116969 30 atime=1459173135.513116969 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawCircleArc3d.m0000644000175000017500000000707512676233417021475 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawCircleArc3d([@var{xc} @var{yc} @var{zc} @var{r} @var{theta} @var{phi} @var{psi} @var{start} @var{extent}]) ## Draw a 3D circle arc ## ## [@var{xc} @var{yc} @var{zc}] : coordinate of arc center ## @var{r} : arc radius ## [@var{theta} @var{phi}] : orientation of arc normal, in degrees (theta: 0->180). ## @var{psi} : roll of arc (rotation of circle origin) ## @var{start} : starting angle of arc, from arc origin, in degrees ## @var{extent} : extent of circle arc, in degrees (can be negative) ## ## Drawing options can be specified, as for the plot command. ## ## @seealso{angles3, circles3d, drawCircle3d, drawCircleArc} ## @end deftypefn function varargout = drawCircleArc3d(arc, varargin) if iscell(arc) h = []; for i = 1:length(arc) h = [h drawCircleArc3d(arc{i}, varargin{:})]; ##ok end if nargout > 0 varargout = {h}; end return; end if size(arc, 1) > 1 h = []; for i = 1:size(arc, 1) h = [h drawCircleArc3d(arc(i,:), varargin{:})]; ##ok end if nargout > 0 varargout = {h}; end return; end # get center and radius xc = arc(:,1); yc = arc(:,2); zc = arc(:,3); r = arc(:,4); # get angle of normal theta = arc(:,5); phi = arc(:,6); psi = arc(:,7); # get starting angle and angle extent of arc start = arc(:,8); extent = arc(:,9); # positions on circle arc N = 60; t = linspace(start, start+extent, N+1) * pi / 180; # compute coordinate of points x = r*cos(t)'; y = r*sin(t)'; z = zeros(length(t), 1); curve = [x y z]; # compute transformation from local basis to world basis trans = localToGlobal3d(xc, yc, zc, theta, phi, psi); # transform circle arc curve = transformPoint3d(curve, trans); # draw the curve with specified options h = drawPolyline3d(curve, varargin{:}); if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/vectors3d.m0000644000000000000000000000013212676233417017265 xustar0030 mtime=1459173135.541103626 30 atime=1459173135.541103626 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/vectors3d.m0000644000175000017500000000404312676233417020445 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} vectors3d () ##VECTORS3D Description of functions operating on 3D vectors ## ## Vectors are represented by their 3 Cartesian coordinates: ## V = [VX VY VZ]; ## ## List of vectors are represented by N*3 arrays, with the coordinates of ## each vector on a row. ## ## ## @seealso{vectorNorm3d, normalizeVector3d, vectorAngle3d isParallel3d, ## isPerpendicular3d, createTranslation3d} ## @end deftypefn function vectors3d(varargin) help vectors3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/spheres.m0000644000000000000000000000013212676233417017022 xustar0030 mtime=1459173135.537105532 30 atime=1459173135.537105532 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/spheres.m0000644000175000017500000000446212676233417020207 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} spheres () ## Description of functions operating on 3D spheres ## ## Spheres are represented by their center and their radius: ## S = [xc yc zc r]; ## ## An ellipsoid is defined by: ## ELL = [XC YC ZC A B C PHI THETA PSI] ## where [XC YC ZY] is the center, [A B C] are length of semi-axes (in ## decreasing order), and [PHI THETA PSI] are euler angles representing ## the ellipsoid orientation. ## @seealso{createSphere, inertiaEllipsoid, intersectLineSphere, ## intersectPlaneSphere, sphericalVoronoiDomain, drawSphere, drawEllipsoid, ## drawSphericalEdge, drawSphericalTriangle, drawSphericalPolygon, ## fillSphericalTriangle, fillSphericalPolygon} ## @end deftypefn function spheres(varargin) help spheres endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/createRotationOy.m0000644000000000000000000000013212676233417020644 xustar0030 mtime=1459173135.509118875 30 atime=1459173135.509118875 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/createRotationOy.m0000644000175000017500000000720212676233417022024 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{trans} =} createRotationOy (@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOy (@var{origin},@var{theta}) ## @deftypefnx {Function File} {@var{trans} =} createRotationOy (@var{x0},@var{y0},@var{z0},@var{theta}) ## Create the 4x4 matrix of a 3D rotation around x-axis ## ## TRANS = createRotationOy(THETA); ## Returns the transform matrix corresponding to a rotation by the angle ## THETA (in radians) around the Oy axis. A rotation by an angle of PI/2 ## would transform the vector [0 1 0] into the vector [0 0 1]. ## ## The returned matrix has the form: ## [1 0 0 0] ## [0 cos(THETA) -sin(THETA) 0] ## [0 sin(THETA) cos(THETA) 0] ## [0 0 0 1] ## ## TRANS = createRotationOy(ORIGIN, THETA); ## TRANS = createRotationOy(X0, Y0, Z0, THETA); ## Also specifies origin of rotation. The result is similar as performing ## translation(-X0, -Y0, -Z0), rotation, and translation(X0, Y0, Z0). ## ## @seealso{transforms3d, transformPoint3d, createRotationOx, createRotationOz} ## @end deftypefn function trans = createRotationOy(varargin) # default values dx = 0; dy = 0; dz = 0; theta = 0; # get input values if length(varargin)==1 # only angle theta = varargin{1}; elseif length(varargin)==2 # origin point (as array) and angle var = varargin{1}; dx = var(1); dy = var(2); dz = var(3); theta = varargin{2}; elseif length(varargin)==3 # origin (x and y) and angle dx = varargin{1}; dy = 0; dz = varargin{2}; theta = varargin{3}; elseif length(varargin)==4 # origin (x and y) and angle dx = varargin{1}; dy = varargin{2}; dz = varargin{3}; theta = varargin{4}; end # compute coefs cot = cos(theta); sit = sin(theta); # create transformation trans = [... cot 0 sit 0;... 0 1 0 0;... -sit 0 cot 0;... 0 0 0 1]; # add the translation part t = [1 0 0 dx;0 1 0 dy;0 0 1 dz;0 0 0 1]; trans = t*trans/t; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/polygons3d.m0000644000000000000000000000013212676233417017452 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.533107438 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/polygons3d.m0000644000175000017500000000427412676233417020640 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} polygons3d () ## POLYGONS3D Description of functions operating on 3D polygons ## ## A 3D polygon is simply a set of 3D points (called vertices) which are ## assumed to be located in the same plane. ## Several functions are provided for computing basic geometrical ## parameters (centroid, angles), or intersections with lines or planes. ## ## @seealso{polygon3dNormalAngle, polygonCentroid3d, clipConvexPolygon3dHP ## intersectLinePolygon3d, intersectLineTriangle3d, intersectRayPolygon3d ## drawPolygon3d, drawPolyline3d, fillPolygon3d} ## @end deftypefn function polygons3d() help polygons3d endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/normalizePlane.m0000644000000000000000000000013212676233417020331 xustar0030 mtime=1459173135.529109344 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/normalizePlane.m0000644000175000017500000000532712676233417021517 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{plane2} =} normalizePlane (@var{plane1}) ## Normalize parametric representation of a plane ## ## PLANE2 = normalizePlane(PLANE1); ## Transforms the plane PLANE1 in the following format: ## [X0 Y0 Z0 DX1 DY1 DZ1 DX2 DY2 DZ2], where: ## - (X0, Y0, Z0) is a point belonging to the plane ## - (DX1, DY1, DZ1) is a first direction vector ## - (DX2, DY2, DZ2) is a second direction vector ## into another plane, with the same format, but with: ## - (x0 y0 z0) is the closest point of plane to the origin ## - (DX1 DY1 DZ1) has norm equal to 1 ## - (DX2 DY2 DZ2) has norm equal to 1 and is orthogonal to (DX1 DY1 DZ1) ## ## @seealso{planes3d, createPlane} ## @end deftypefn function plane2 = normalizePlane (plane1) # compute first direction vector d1 = normalizeVector (plane1(:,4:6)); # compute second direction vector n = normalizeVector (planeNormal (plane1)); d2 = -normalizeVector (cross (d1, n)); # compute origin point of the plane origins = repmat ([0 0 0], [size(plane1, 1) 1]); p0 = projPointOnPlane (origins, [plane1(:,1:3) d1 d2]); # create the resulting plane plane2 = [p0 d1 d2]; endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/drawVector3d.m0000644000000000000000000000013012676233417017716 xustar0029 mtime=1459173135.52511125 29 atime=1459173135.52511125 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/drawVector3d.m0000644000175000017500000000445412676233417021106 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} function_name (@var{pos}, @var{vect}) ## Draw vector at a given position ## ## Example ## @example ## figure; hold on; ## drawVector3d([2 3 4], [1 0 0]); ## drawVector3d([2 3 4], [0 1 0]); ## drawVector3d([2 3 4], [0 0 1]); ## view(3); ## @end example ## ## @seealso{quiver3} ## @end deftypefn function varargout = drawVector3d(pos, vect, varargin) h = quiver3 (pos(:, 1), pos(:, 2), pos(:, 3), ... vect(:, 1), vect(:, 2), vect(:, 3), varargin{:}); # format output if nargout > 0 varargout{1} = h; end endfunction %!demo %! figure; hold on; %! drawVector3d([2 3 4], [1 0 0]); %! drawVector3d([2 3 4], [0 1 0]); %! drawVector3d([2 3 4], [0 0 1]); %! view(3); geometry-2.1.1/inst/geom3d/PaxHeaders.5293/circle3dOrigin.m0000644000000000000000000000013212676233417020211 xustar0030 mtime=1459173135.505120781 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/circle3dOrigin.m0000644000175000017500000000511412676233417021371 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} circle3dOrigin([@var{xc} @var{yc} @var{zc} @var{r} @var{theta} @var{phi}]) ## @deftypefnx {Function File} {@var{p} =} circle3dOrigin([@var{xc} @var{yc} @var{zc} @var{r} @var{theta} @var{phi} @var{psi}]) ## Return the first point of a 3D circle ## ## Returns the origin point of the circle, i.e. the first point used for ## drawing circle. ## ## @seealso{circles3d, points3d, circle3dPosition} ## @end deftypefn function ori = circle3dOrigin(varargin) # get center and radius circle = varargin{1}; xc = circle(:,1); yc = circle(:,2); zc = circle(:,3); r = circle(:,4); # get angle of normal theta = circle(:,5); phi = circle(:,6); # get roll if size(circle, 2)==7 psi = circle(:,7); else psi = zeros(size(circle, 1), 1); end # create origin point pt0 = [r 0 0]; # compute transformation from local basis to world basis trans = localToGlobal3d(xc, yc, zc, theta, phi, psi); # transform the point ori = transformPoint3d(pt0, trans); endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/cart2cyl.m0000644000000000000000000000013212676233417017074 xustar0030 mtime=1459173135.501122687 30 atime=1459173135.501122687 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/cart2cyl.m0000644000175000017500000000620112676233417020252 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{cyl} =} cart2cyl (@var{point}) ## @deftypefnx {Function File} {@var{cyl} =} cart2cyl (@var{x}, @var{y}, @var{z}) ## Convert cartesian to cylindrical coordinates ## ## CYL = cart2cyl(POINT) ## convert the 3D cartesian coordinates of points POINT (given by [X Y Z] ## where X, Y, Z have the same size) into cylindrical coordinates CYL, ## given by [THETA R Z]. ## THETA is the arctangent of the ratio Y/X (between 0 and 2*PI) ## R can be computed using sqrt(X^2+Y^2) ## Z keeps the same value. ## The size of THETA, and R is the same as the size of X, Y and Z. ## ## CYL = cart2cyl(X, Y, Z) ## provides coordinates as 3 different parameters ## ## Example ## @example ## cart2cyl([-1 0 2]) ## gives : 4.7124 1.0000 2.0000 ## @end example ## ## @seealso{agles3d, cart2pol, cart2sph2} ## @end deftypefn function varargout = cart2cyl(varargin) # process input parameters if length(varargin)==1 var = varargin{1}; x = var(:,1); y = var(:,2); z = var(:,3); elseif length(varargin)==3 x = varargin{1}; y = varargin{2}; z = varargin{3}; end # convert coordinates dim = size(x); theta = reshape(mod(atan2(y(:), x(:))+2*pi, 2*pi), dim); r = reshape(sqrt(x(:).*x(:) + y(:).*y(:)), dim); # process output parameters if nargout==0 ||nargout==1 if length(dim)>2 || dim(2)>1 varargout{1} = {theta r z}; else varargout{1} = [theta r z]; end elseif nargout==3 varargout{1} = theta; varargout{2} = r; varargout{3} = z; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/sph2cart2.m0000644000000000000000000000013212676233417017161 xustar0030 mtime=1459173135.537105532 30 atime=1459173135.537105532 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/sph2cart2.m0000644000175000017500000000633212676233417020344 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} sph2cart2 (@var{s}) ## @deftypefnx {Function File} {@var{c} =} sph2cart2 (@var{theta}, @var{phi}) ## @deftypefnx {Function File} {@var{c} =} sph2cart2 (@var{theta}, @var{phi}, @var{rho}) ## @deftypefnx {Function File} {[@var{x} @var{y} @var{z}]=} sph2cart2 (@dots{}) ## Convert spherical coordinates to cartesian coordinates ## ## C = SPH2CART2(S) ## C = SPH2CART2(THETA, PHI) (assume rho = 1) ## C = SPH2CART2(THETA, PHI, RHO) ## [X, Y, Z] = SPH2CART2(THETA, PHI, RHO); ## ## S = [phi theta rho] (spherical coordinate). ## C = [X Y Z] (cartesian coordinate) ## ## The following convention is used: ## THETA is the colatitude, in radians, 0 for north pole, +pi for south ## pole, pi/2 for points with z=0. ## PHI is the azimuth, in radians, defined as matlab cart2sph: angle from ## Ox axis, counted counter-clockwise. ## RHO is the distance of the point to the origin. ## Discussion on choice for convention can be found at: ## http://www.physics.oregonstate.edu/bridge/papers/spherical.pdf ## ## @seealso{angles3d, cart2sph2, sph2cart, sph2cart2d} ## @end deftypefn function varargout = sph2cart2(theta, phi, rho) # Process input arguments if nargin == 1 phi = theta(:, 2); if size (theta, 2) > 2 rho = theta(:, 3); else rho = ones (size (phi)); end theta = theta(:, 1); elseif nargin == 2 rho = ones (size (theta)); end # conversion rz = rho .* sin(theta); x = rz .* cos(phi); y = rz .* sin(phi); z = rho .* cos(theta); if nargout <= 1 varargout{1} = [x, y, z]; else varargout{1} = x; varargout{2} = y; varargout{3} = z; end endfunction geometry-2.1.1/inst/geom3d/PaxHeaders.5293/revolutionSurface.m0000644000000000000000000000013212676233417021070 xustar0030 mtime=1459173135.533107438 30 atime=1459173135.533107438 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/revolutionSurface.m0000644000175000017500000001331212676233417022247 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{x}, @var{y}, @var{z}] =} revolutionSurface (@var{c1}, @var{c2}, @var{n}) ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} revolutionSurface (@var{curve}, @var{n}) ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} revolutionSurface (@dots{}, @var{theta}) ## @deftypefnx {Function File} {[@var{x}, @var{y}, @var{z}] =} revolutionSurface (@dots{}, @var{line}) ## Create a surface of revolution from a planar curve ## ## usage ## [X Y Z] = revolutionSurface(C1, C2, N); ## create the surface of revolution of parametrized function (xt, yt), ## with N+1 equally spaced slices, around the Oz axis. ## It assumed that C1 corresponds to the x coordinate, and that C2 ## corresponds to the Oz coordinate. ## ## [X Y Z] = revolutionSurface(CURVE, N); ## is the same, but generating curve is given in a single parameter CURVE, ## which is a [Nx2] array of 2D points. ## ## [X Y Z] = revolutionSurface(..., THETA) ## where THETA is a vector, uses values of THETA for computing revolution ## angles. ## ## [X Y Z] = revolutionSurface(..., LINE); ## where LINE is a 1x4 array, specifes the revolution axis in the ## coordinate system of the curve. LINE is a row vector of 4 parameters, ## containing [x0 y0 dx dy], where (x0,y0) is the origin of the line and ## (dx,dy) is a direction vector of the line. ## The resulting revolution surface still has Oz axis as symmetry axis. It ## can be transformed using transformPoint3d function. ## Surface can be displayed using : ## @code{H = surf(X, Y, Z);} ## H is a handle to the created patch. ## ## revolutionSurface(...); ## by itself, directly shows the created patch. ## ## Example ## @example ## # draws a piece of torus ## circle = circleAsPolygon([10 0 3], 50); ## [x y z] = revolutionSurface(circle, linspace(0, 4*pi/3, 50)); ## surf(x, y, z); ## axis square equal; ## @end example ## ## @seealso{surf, transformPoint3d, drawSphere, drawTorus, drawEllipsoid} ## @end deftypefn function varargout = revolutionSurface(varargin) ## Initialisations # default values # use revolution using the full unit circle, decomposed into 24 angular # segments (thus, some vertices correspond to particular angles 30°, # 45°...) theta = linspace(0, 2*pi, 25); # use planar vertical axis as default revolution axis revol = [0 0 0 1]; # extract the generating curve var = varargin{1}; if size(var, 2)==1 xt = var; yt = varargin{2}; varargin(1:2) = []; else xt = var(:,1); yt = var(:,2); varargin(1) = []; end # extract optional parameters: angles, axis of revolution # parameters are identified from their length while ~isempty(varargin) var = varargin{1}; if length(var) == 4 # axis of rotation in the base plane revol = var; elseif length(var) == 1 # number of points -> create row vector of angles theta = linspace(0, 2*pi, var); else # use all specified angle values theta = var(:)'; end varargin(1) = []; end ## Create revolution surface # ensure length is enough m = length(xt); if m==1 xt = [xt xt]; end # ensure x and y are vertical vectors xt = xt(:); yt = yt(:); # transform xt and yt to replace in the reference of the revolution axis tra = createTranslation(-revol(1:2)); rot = createRotation(pi/2 - lineAngle(revol)); [xt yt] = transformPoint(xt, yt, tra*rot); # compute surface vertices x = xt * cos(theta); y = xt * sin(theta); z = yt * ones(size(theta)); ## Process output arguments # format output depending on how many output parameters are required if nargout == 0 # draw the revolution surface surf(x, y, z); elseif nargout == 1 # draw the surface and return a handle to the shown structure h = surf(x, y, z); varargout{1} = h; elseif nargout == 3 # return computed mesh varargout = {x, y, z}; end endfunction %!demo %! # draws a piece of torus %! circle = circleAsPolygon ([10 0 3], 50); %! [x y z] = revolutionSurface (circle, linspace(0, 4*pi/3, 50)); %! surf (x, y, z); %! axis square equal; geometry-2.1.1/inst/geom3d/PaxHeaders.5293/planePoint.m0000644000000000000000000000013212676233417017462 xustar0030 mtime=1459173135.529109344 30 atime=1459173135.529109344 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom3d/planePoint.m0000644000175000017500000000463212676233417020646 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} =} planePoint (@var{plane}, @var{pos}) ## PLANEPOINT Compute 3D position of a point in a plane ## ## POINT = planePoint(PLANE, POS) ## PLANE is a 9 element row vector [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] ## POS is the coordinate of a point in the plane basis, ## POINT is the 3D coordinate in global basis. ## ## @seealso{planes3d, planePosition} ## @end deftypefn function coord = planePoint (plane, point) # check size of input arguments npl = size (plane, 1); npt = size (point, 1); if npl ~= npt && (npl ~= 1 && npt ~= 1) error ("geometry:InvalidArgument", ... "plane and point should have same size or one of them must have a single row.\n"); end # compute 3D coordinate coord = plane(:,1:3) + ... plane(:,4:6) .* point(:,1) + ... plane(:,7:9) .* point(:,2) endfunction geometry-2.1.1/inst/PaxHeaders.5293/shape2d0000644000000000000000000000013212676233417015266 xustar0030 mtime=1459173135.633059786 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/0000755000175000017500000000000012676233417016522 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/shape2d/PaxHeaders.5293/shapecentroid.m0000644000000000000000000000013212676233417020351 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/shapecentroid.m0000644000175000017500000001244512676233417021536 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} { @var{cm} =} shapecentroid (@var{pp}) ## Centroid of a simple plane shape defined with piecewise smooth polynomials. ## ## The shape is defined with piecewise smooth polynomials. @var{pp} is a ## cell where each elements is a 2-by-(poly_degree+1) matrix containing a pair ## of polynomials. ## @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}. ## ## The edges of the shape should not self-intersect. This function does not check for the ## sanity of the shape. ## ## @seealso{shapearea, shape2polygon} ## @end deftypefn function cm = shapecentroid (shape) cm = sum( cell2mat ( cellfun (@CMint, shape, 'UniformOutput', false)), 1); [A ccw] = shapearea (shape); cm = cm / A; if (ccw < 0) warning ('geom2d:cw-shape', ... 'Clockwise parametrized shape, inverting centroid.'); cm = -cm; end endfunction function dcm = CMint (x) px = x(1,:); py = x(2,:); Px = polyint (conv(conv (-px , py) , polyder (px))); Py = polyint (conv(conv (px , py) , polyder (py))); dcm = zeros (1,2); dcm(1) = diff(polyval(Px,[0 1])); dcm(2) = diff(polyval(Py,[0 1])); endfunction %!demo # non-convex bezier shape %! boomerang = {[ 0 -2 1; ... %! -4 4 0]; ... %! [0.25 -1; ... %! 0 0]; ... %! [ 0 1.5 -0.75; ... %! -3 3 0]; %! [0.25 0.75; ... %! 0 0]}; %! CoM = shapecentroid (boomerang) %! Gcentroid = centroid(shape2polygon(boomerang)) %! figure(1); clf; %! shapeplot(boomerang,'-o'); %! hold on %! drawPoint(CoM,'xk;shape centroid;'); %! drawPoint(Gcentroid,'xr;point centroid;'); %! hold off %! axis equal %!demo %! Lshape = {[0.00000 0.76635; -0.67579 -0.24067]; ... %! [0.77976 0.76635; 0.00000 -0.91646]; ... %! [0.00000 1.54611; 0.38614 -0.91646]; ... %! [-0.43813 1.54611; 0.00000 -0.53032]; ... %! [0.00000 1.10798; 0.28965 -0.53032]; ... %! [-0.34163 1.10798; 0.00000 -0.24067]};... %! CoM = shapecentroid (Lshape) %! Gcentroid = centroid (shape2polygon (Lshape)) %! %! shapeplot(Lshape,'-o'); %! hold on %! drawPoint(CoM,'xk;shape centroid;'); %! drawPoint(Gcentroid,'xr;point centroid;'); %! hold off %! axis equal %!test %! warning('off', 'geom2d:cw-shape', 'local'); %! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]}; %! CoM = shapecentroid (square); %! assert (CoM, [0 0], sqrt(eps)); %!test %! warning('off', 'geom2d:cw-shape', 'local'); %! square = {[1 -0.5; 0 -0.5]; [0 0.5; 1 -0.5]; [-1 0.5; 0 0.5]; [0 -0.5; -1 0.5]}; %! square_t = shapetransform (square,[1;1]); %! CoM = shapecentroid (square_t); %! assert (CoM, [1 1], sqrt(eps)); %!test %! warning('off', 'geom2d:cw-shape', 'local'); %! circle = {[1.715729 -6.715729 0 5; ... %! -1.715729 -1.568542 8.284271 0]; ... %! [1.715729 1.568542 -8.284271 0; ... %! 1.715729 -6.715729 0 5]; ... %! [-1.715729 6.715729 0 -5; ... %! 1.715729 1.568542 -8.284271 0]; ... %! [-1.715729 -1.568542 8.284271 0; ... %! -1.715729 6.715729 0 -5]}; %! CoM = shapecentroid (circle); %! assert (CoM , [0 0], 5e-3); %!shared shape %! shape = {[-93.172 606.368 -476.054 291.429; ... %! -431.196 637.253 11.085 163.791]; ... %! [-75.3626 -253.2337 457.1678 328.5714; ... %! 438.7659 -653.6278 -7.9953 380.9336]; ... %! [-89.5841 344.9716 -275.3876 457.1429; ... %! -170.3613 237.8858 1.0469 158.0765];... %! [32.900 -298.704 145.804 437.143; ... %! -243.903 369.597 -34.265 226.648]; ... %! [-99.081 409.127 -352.903 317.143; ... %! 55.289 -114.223 -26.781 318.076]; ... %! [-342.231 191.266 168.108 274.286; ... %! 58.870 -38.083 -89.358 232.362]}; %!test # x-Reflection %! warning('off', 'geom2d:cw-shape', 'local'); %! v = shapecentroid (shape)(:); %! T = createLineReflection([0 0 1 0]); %! nshape = shapetransform (shape, T); %! vn = shapecentroid (nshape)(:); %! assert(vn,T(1:2,1:2)*v); %!test # Rotation %! warning('off', 'geom2d:cw-shape', 'local'); %! v = shapecentroid (shape)(:); %! T = createRotation(v.',pi/2); %! nshape = shapetransform (shape, T); %! vn = shapecentroid (nshape)(:); %! assert(vn,v,1e-2); %!test # Translation %! warning('off', 'geom2d:cw-shape', 'local'); %! v = shapecentroid (shape)(:); %! nshape = shapetransform (shape, -v); %! vn = shapecentroid (nshape)(:); %! assert(vn,[0; 0],1e-2); geometry-2.1.1/inst/shape2d/PaxHeaders.5293/curveval.m0000644000000000000000000000013212676233417017350 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/curveval.m0000644000175000017500000000202012676233417020521 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} = } curveval (@var{curve}, @var{t}) ## Evaluates parametric @var{curve} at @var{t}. ## ## @end deftypefn function p = curveval (curve, t) dim = size (curve,1); p = zeros (length(t), dim); for i = 1:dim p(:,i) = polyval (curve(i,:), t); end endfunction geometry-2.1.1/inst/shape2d/PaxHeaders.5293/shapetransform.m0000644000000000000000000000013212676233417020555 xustar0030 mtime=1459173135.633059786 30 atime=1459173135.633059786 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/shapetransform.m0000644000175000017500000000620012676233417021732 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nshape} = } shapetransform (@var{shape}, @var{T}) ## Applies transformation to a shape defined by piecewise smooth polynomials. ## ## @var{shape} is a cell where each elements is a 2-by-(poly_degree+1) matrix ## containing a pair of polynomials. ## ## Format of @var{T} can be one of : ## @example ## @group ## [c] , [a b] , [a b c] or [a b c] ## [f] [d e] [d e f] [d e f] ## [0 0 1] ## @end group ## @end example ## ## @seealso{shape2polygon, shapeplot} ## @end deftypefn function nshape = shapetransform (shape, Trans) if size(Trans,1) < 2 error("geometry:invalid-input-arg", ... "Transformation can be 2x1, 2x2, 2x3 or 3x3. See help."); end if ~iscell(shape) error("geometry:invalid-input-arg", "Shape must be a cell of 2D polynomials."); end A =[]; v = []; switch size(Trans,2) case 1 # Just translation v = Trans; case 2 # Just linear transformation A = Trans; case 3 # Affine transform A = Trans(1:2,1:2); v = Trans(1:2,3); end nshape = cellfun (@(x)polytransform (x,A,v), shape, 'UniformOutput',false); endfunction function np = polytransform(p,A,v) np = p; if ~isempty (A) np = A*np; end if ~isempty (v) np(:,end) = np(:,end) + v; end endfunction %!demo %! shape = {[-93.172 606.368 -476.054 291.429; ... %! -431.196 637.253 11.085 163.791]; ... %! [-75.3626 -253.2337 457.1678 328.5714; ... %! 438.7659 -653.6278 -7.9953 380.9336]; ... %! [-89.5841 344.9716 -275.3876 457.1429; ... %! -170.3613 237.8858 1.0469 158.0765];... %! [32.900 -298.704 145.804 437.143; ... %! -243.903 369.597 -34.265 226.648]; ... %! [-99.081 409.127 -352.903 317.143; ... %! 55.289 -114.223 -26.781 318.076]; ... %! [-342.231 191.266 168.108 274.286; ... %! 58.870 -38.083 -89.358 232.362]}; %! %! A = shapearea (shape); %! T = eye(2)/sqrt(A); %! shape = shapetransform (shape,T); %! T = shapecentroid (shape)(:); %! shape = shapetransform (shape,-T + [2; 0]); %! %! close %! shapeplot (shape,'-r','linewidth',2); %! hold on %! for i = 1:9 %! T = createRotation (i*pi/5)(1:2,1:2)/exp(0.3*i); %! shapeplot (shapetransform(shape, T), 'color',rand(1,3),'linewidth',2); %! end %! hold off %! axis tight %! axis square geometry-2.1.1/inst/shape2d/PaxHeaders.5293/shapeplot.m0000644000000000000000000000013212676233417017520 xustar0030 mtime=1459173135.633059786 30 atime=1459173135.633059786 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/shapeplot.m0000644000175000017500000000314412676233417020701 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } shapeplot (@var{shape}) ## @deftypefnx {Function File} {@var{h} = } shapeplot (@var{shape}, @var{N}) ## @deftypefnx {Function File} {@var{h} = } shapeplot (@dots{}, @var{param}, @var{value}) ## Pots a 2D shape defined by piecewise smooth polynomials in the current axis. ## ## @var{pp} is a cell where each elements is a 2-by-(poly_degree+1) matrix ## containing a pair of polynomials. ## @var{N} is the number of points to be used in non-straight edges. ## Additional parameter value pairs are passed to @code{drawPolygon}. ## ## @seealso{drawPolygon, shape2polygon} ## @end deftypefn function h = shapeplot(shape, varargin) n = cell2mat(cellfun(@(x)curveval(x,rand(1,5)), shape, 'uniformoutput',false)); dr = (max(n(:,1))-min(n(:,1)))*(max(n(:,2))-min(n(:,2)))/100; p = shape2polygon(shape,'tol', dr); h = drawPolygon(p,varargin{:}); endfunction geometry-2.1.1/inst/shape2d/PaxHeaders.5293/shape2polygon.m0000644000000000000000000000013212676233417020313 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/shape2polygon.m0000644000175000017500000000516512676233417021501 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{polygon} = } shape2polygon (@var{shape}) ## @deftypefnx {Function File} {@var{polygon} = } shape2polygon (@dots{},@var{property},@var{value},@dots{}) ## Transforms a 2D shape described by piecewise smooth polynomials into a polygon. ## ## @var{shape} is a n-by-1 cell where each element is a pair of polynomials ## compatible with polyval. ## @var{polygon} is a k-by-2 matrix, where each row represents a vertex. ## The property-value pairs are passed to @code{curve2polyline}. ## ## @seealso{polygon2shape, curve2poyline} ## @end deftypefn function polygon = shape2polygon (shape, varargin) polygon = cell2mat ( ... cellfun (@(x) curve2polyline(x,varargin{:}), shape,'UniformOutput',false) ); polygon = simplifypolygon(polygon); if size (polygon, 1) == 1 polygon(2,1) = polyval (shape{1}(1,:), 1); polygon(2,2) = polyval (shape{1}(2,:), 1); end endfunction %!demo %! shape = {[-93.172 606.368 -476.054 291.429; ... %! -431.196 637.253 11.085 163.791]; ... %! [-75.3626 -253.2337 457.1678 328.5714; ... %! 438.7659 -653.6278 -7.9953 380.9336]; ... %! [-89.5841 344.9716 -275.3876 457.1429; ... %! -170.3613 237.8858 1.0469 158.0765];... %! [32.900 -298.704 145.804 437.143; ... %! -243.903 369.597 -34.265 226.648]; ... %! [-99.081 409.127 -352.903 317.143; ... %! 55.289 -114.223 -26.781 318.076]; ... %! [-342.231 191.266 168.108 274.286; ... %! 58.870 -38.083 -89.358 232.362]}; %! %! # Estimate a good tolerance %! n = cell2mat(cellfun(@(x)curveval(x,rand(1,10)), shape, 'uniformoutput',false)); %! dr = (max(n(:,1))-min(n(:,1)))*(max(n(:,2))-min(n(:,2)))*40; %! p = shape2polygon (shape,'tol',dr); %! %! figure(1) %! shapeplot(shape,'-b'); %! hold on; %! drawPolygon (p,'-or'); %! hold off geometry-2.1.1/inst/shape2d/PaxHeaders.5293/curve2polyline.m0000644000000000000000000000013212676233417020503 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/curve2polyline.m0000644000175000017500000001001112676233417021653 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{polyline} = } curve2polyline (@var{curve}) ## @deftypefnx {Function File} {@var{polyline} = } curve2polyline (@dots{},@var{property},@var{value},@dots{}) ## Adaptive sampling of a parametric curve. ## ## The @var{curve} is described as a 2-by-N matrix. Rows correspond to the ## polynomial (compatible with @code{polyval}) describing the respective component ## of the curve. The curve must be parametrized in the interval [0,1]. ## The vertices of the polyline are accumulated in regions of the curve where ## the curvature is higher. ## ## @strong{Parameters} ## @table @samp ## @item 'Nmax' ## Maximum number of vertices. Not used. ## @item 'Tol' ## Tolerance for the error criteria. Default value @code{1e-4}. ## @item 'MaxIter' ## Maximum number of iterations. Default value @code{10}. ## @item 'Method' ## Not implemented. ## @end table ## ## @seealso{shape2polygon, curveval} ## @end deftypefn ## This function is based on the algorithm described in ## L. H. de Figueiredo (1993). "Adaptive Sampling of Parametric Curves". Graphic Gems III. ## I had to remove the recursion so this version could be improved. ## Thursday, April 12 2012 -- JuanPi function [polyline t bump]= curve2polyline (curve, varargin) ## TODO make tolerance relative to the "diameter" of the curve. # --- Parse arguments --- # parser = inputParser (); parser.FunctionName = "curve2polyline"; parser.addParamValue ('Nmax', 32, @(x)x>0); parser.addParamValue ('Tol', 1e-4, @(x)x>0); parser.addParamValue ('MaxIter', 10, @(x)x>0); parser.parse(varargin{:}); Nmax = parser.Results.Nmax; tol = parser.Results.Tol; MaxIter = parser.Results.MaxIter; clear parser toldef # ------ # t = [0; 1]; tf = 1; points = 1; for iter = 1:MaxIter # Add parameter values where error is still bigger than tol. t = interleave(t, tf); nt = length(t); # Update error polyline = curveval (curve,t); bump = bumpyness(polyline); # Check which intervals must be subdivided idx = find(bump > tol); # The position of the bumps mpas into intervals # 1 -> 1 2 # 2 -> 3 4 # 3 -> 5 6 # and so on idx = [2*(idx-1)+1; 2*idx](:); tf = false (nt-1,1); tf(idx) = true; if all (!tf) break; end end endfunction function f = bumpyness (p) ## Check for co-linearity ## TODO implement various method for this ## -- Area of the triangle close to zero (used currently). ## -- Angle close to pi. ## -- abs(p0-pt) + abs(pt-p1) - abs(p0-p1) almost zero. ## -- Curve's tange at 0,t,1 are almost parallel. ## -- pt is in chord p0 -> p1. ## Do this in isParallel.m and remove this function PL = p(1:2:end-2,:); PC = p(2:2:end-1,:); PR = p(3:2:end,:); a = PL - PC; b = PR - PC; f = (a(:,1).*b(:,2) - a(:,2).*b(:,1)).^2; endfunction function tt = interleave (t,varargin) nt = length(t); ntt = 2 * nt -1; tt = zeros(ntt,1); tt(1:2:ntt) = t; beta = 0.4 + 0.2*rand(nt-1, 1); tt(2:2:ntt) = t(1:end-1) + beta.*(t(2:end)-t(1:end-1)); if nargin > 1 tf = true (ntt,1); tf(2:2:ntt) = varargin{1}; tt(!tf) = []; end endfunction %!demo %! curve = [0 0 1 0;1 -0.3-1 0.3 0]; %! polyline = curve2polyline(curve,'tol',1e-8); %! %! t = linspace(0,1,100)'; %! pc = curveval(curve,t); %! %! plot(polyline(:,1),polyline(:,2),'-o',pc(:,1),pc(:,2),'-r') geometry-2.1.1/inst/shape2d/PaxHeaders.5293/shapearea.m0000644000000000000000000000013212676233417017452 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/shape2d/shapearea.m0000644000175000017500000000547312676233417020642 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} { [@var{a}, @var{ccw}]=} shapearea (@var{pp}) ## Calculate the area of a 2D shape defined with piecewise smooth polynomials. ## ## Shape is defined with piecewise smooth polynomials. @var{pp} is a ## cell where each elements is a 2-by-(poly_degree+1) array containing a pair of ## polynomials. ## ## @code{px(i,:) = pp@{i@}(1,:)} and @code{py(i,:) = pp@{i@}(2,:)}. ## ## The returned area is always positive even if the shape is parametrized ## in a clockwise direction. If the case of a clockwise parametrized shape ## @code{@var{ccw} == -1} otherwise @code{@var{ccw} == 1}. ## ## @seealso{shapecentroid, shape2polygon, shapeplot} ## @end deftypefn function [A ccw] = shapearea (shape) A = sum (cellfun (@Aint, shape)); ccw = sign (A); if (A < 0) warning ('geom2d:cw-shape', ... ['Shape has negative area. ' ... 'Assuming this is due to a clockwise parametrization of the boundary']); A = ccw * A; end endfunction function dA = Aint (x) px = x(1,:); py = x(2,:); P = polyint (conv (px, polyder(py))); dA = diff(polyval(P,[0 1])); end %!demo # non-convex piece-wise polynomial shape %! boomerang = {[ 0 -2 1; ... %! -4 4 0]; ... %! [0.25 -1; ... %! 0 0]; ... %! [ 0 1.5 -0.75; ... %! -3 3 0]; %! [0.25 0.75; ... %! 0 0]}; %! A = shapearea (boomerang) %!test %! warning('off', 'geom2d:cw-shape', 'local'); %! triangle = {[1 0; 0 0]; [-0.5 1; 1 0]; [-0.5 0.5; -1 1]}; %! A = shapearea (triangle); %! assert (0.5, A); %!test %! warning('off', 'geom2d:cw-shape', 'local'); %! circle = {[1.715729 -6.715729 0 5; ... %! -1.715729 -1.568542 8.284271 0]; ... %! [1.715729 1.568542 -8.284271 0; ... %! 1.715729 -6.715729 0 5]; ... %! [-1.715729 6.715729 0 -5; ... %! 1.715729 1.568542 -8.284271 0]; ... %! [-1.715729 -1.568542 8.284271 0; ... %! -1.715729 6.715729 0 -5]}; %! A = shapearea (circle); %! assert (pi*5^2, A, 5e-2); geometry-2.1.1/inst/PaxHeaders.5293/polynomialCurves2d0000644000000000000000000000013212676233417017541 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/0000755000175000017500000000000012676233417020775 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/polynomialCurveCentroid.m0000644000000000000000000000013212676233417024654 xustar0030 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/polynomialCurveCentroid.m0000644000175000017500000000775112676233417026045 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} =} polynomialCurveCentroid (@var{t}, @var{xcoef}, @var{ycoef}) ## @deftypefnx {Function File} {@var{c} =} polynomialCurveCentroid (@var{t}, @var{coefs}) ## @deftypefnx {Function File} {@var{c} =} polynomialCurveCentroid (@dots{}, @var{tol}) ## Compute the centroid of a polynomial curve ## ## @var{xcoef} and @var{ycoef} are row vectors of coefficients, in the form: ## [a0 a1 a2 ... an] ## @var{t} is a 1x2 row vector, containing the bounds of the parametrization ## variable: @var{t} = [T0 T1], with @var{t} taking all values between T0 and T1. ## @var{c} contains coordinate of the polynomial curve centroid. ## ## @var{coefs} is either a 2xN matrix (one row for the coefficients of each ## coordinate), or a cell array. ## ## @var{tol} is the tolerance fo computation (absolute). ## ## @seealso{polynomialCurves2d, polynomialCurveLength} ## @end deftypefn function centroid = polynomialCurveCentroid(tBounds, varargin) ## Extract input parameters # parametrization bounds t0 = tBounds(1); t1 = tBounds(end); # polynomial coefficients for each coordinate var = varargin{1}; if iscell(var) cx = var{1}; cy = var{2}; varargin(1) = []; elseif size(var, 1)==1 cx = varargin{1}; cy = varargin{2}; varargin(1:2)=[]; else cx = var(1,:); cy = var(2,:); varargin(1)=[]; end # convert to Octave polyval format cx = cx(end:-1:1); cy = cy(end:-1:1); # tolerance tol = 1e-6; if ~isempty(varargin) tol = varargin{1}; end ## compute length by numerical integration # compute derivative of the polynomial dx = polyder (cx); dy = polyder (cy); # compute curve length by integrating the Jacobian L = quad(@(t)sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol); # compute first coordinate of centroid xc = quad(@(t)polyval(cx, t).*sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol); # compute first coordinate of centroid yc = quad(@(t)polyval(cy, t).*sqrt(polyval(dx, t).^2+polyval(dy, t).^2), t0, t1, tol); # divide result of integration by total length of the curve centroid = [xc yc]/L; endfunction %!demo %! bounds = [-1 1]; %! coefs = [0 1 1; 0 -1 2]; %! c = polynomialCurveCentroid (bounds, coefs); %! %! drawPolynomialCurve (bounds, coefs(1,:), coefs(2,:)); %! hold on %! plot (c(1),c(2),'sr') %! hold off %! # ------------------------------------------------- %! # Centriod of a polynomial curve geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/polynomialCurveSetFit.m0000644000000000000000000000013212676233417024303 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/polynomialCurveSetFit.m0000644000175000017500000001746312676233417025475 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{coefs}=} polynomialCurveSetFit (@var{img}) ## @deftypefnx {Function File} {@dots{} =} polynomalCurveSetFit (@var{img}, @var{deg}) ## @deftypefnx {Function File} {[@dots{} @var{lbl}] =} polynomalCurveSetFit (@dots{}) ## Fit a set of polynomial curves to a segmented image ## ## Result is a cell array of matrices. Each matrix is @var{deg}+1-by-2, and ## contains coefficients of polynomial curve for each coordinate. ## @var{bnds} contains the boundary of the parametrizations. ## @var{img} is first binarised, then skeletonized. ## ## Also returns an image of labels @var{lbl} for the segmented curves. The max label ## is the number of curves, and the length of @var{coefs}. ## ## Requires the toolboxes: ## - Optimization ## - Image Processing ## ## @seealso{polynomialCurves2d, polynomialCurveFit} ## @end deftypefn function [coefs lblBranches] = polynomialCurveSetFit(seg, varargin) # default degree for curves deg = 2; if ~isempty(varargin) deg = varargin{1}; end # ajoute un contour seg([1 end], :) = 1; seg(:, [1 end]) = 1; # skeletise le segmentat seg = bwmorph(seg, 'shrink', Inf); # compute image of multiple points (intersections between curves) imgNodes = imfilter(double(seg), ones([3 3])) .* seg > 3; # compute coordinate of nodes, as c entroids of the multiple points lblNodes = bwlabel(imgNodes, 8); struct = regionprops(lblNodes, 'Centroid'); nodes = zeros(length(struct), 2); for i=1:length(struct) nodes(i, [2 1]) = struct(i).Centroid; end # debug # figure(1) # subplot(1,2,1) # imshow(seg); # hold on # plot(nodes(:,1),nodes(:,2),'og') # subplot(1,2,2) # imshow(imgNodes); # hold on # plot(nodes(:,1),nodes(:,2),'og') # keyboard # enleve les bords de l'image seg([1 end], :) = 0; seg(:, [1 end]) = 0; # Isolate the branches imgBranches = seg & ~imgNodes; lblBranches = bwlabel(imgBranches, 8); # # donne une couleur a chaque branche, et affiche # map = colorcube(max(lblBranches(:))+1); # rgbBranches = label2rgb(lblBranches, map, 'w', 'shuffle'); # imshow(rgbBranches); # number of curves nBranches = max(lblBranches(:)); # allocate memory coefs = cell(nBranches, 1); bnds = cell(nBranches, 1); # For each curve, find interpolated polynomial curve for i = 1:nBranches # extract points corresponding to current curve imgBranch = lblBranches == i; points = chainPixels (imgBranch); # check number of points is sufficient if size(points, 1) < max(deg+1-2, 2) # find labels of nodes inds = unique(lblNodes(imdilate(imgBranch, true (3,3)))); inds = inds(inds ~= 0); if length(inds) < 2 warning ("geometry:poylnomialCurveSetFit", ... ['Could not find extremities of branch number ' num2str(i)]); continue; end # consider extremity nodes node0 = nodes(inds(1), :); node1 = nodes(inds(2), :); # use only a linear approximation xc = zeros(1, deg+1); yc = zeros(1, deg+1); xc(1) = node0(1); yc(1) = node0(2); xc(2) = node1(1)-node0(1); yc(2) = node1(2)-node0(2); # assigne au tableau de courbes coefs{i} = [xc;yc]; # next branch continue; end # find nodes closest to first and last points of the current curve [dist, ind0] = minDistancePoints(points(1, :), nodes); ##ok<*ASGLU> [dist, ind1] = minDistancePoints(points(end, :), nodes); # add nodes to the curve. points = [nodes(ind0,:); points; nodes(ind1,:)]; ##ok # parametrization of the polyline t = parametrize(points); t = t / max(t); # fit a polynomial curve to the set of points [xc yc] = polynomialCurveFit(... t, points, deg, ... 0, {points(1,1), points(1,2)},... 1, {points(end,1), points(end,2)}); #debug # plot(points(:,1),points(:,2),'or') # hold on # drawPolynomialCurve ([0 1], xc,yc); # axis tight # v = axis(); # hold off # imshow (~imgBranch) # hold on # plot(points(:,1),points(:,2),'or') # drawPolynomialCurve ([0 1], xc,yc); # axis xy # axis (v); # pause # stores result coefs{i} = [xc;yc]; end endfunction function points = chainPixels(img, varargin) #CHAINPIXELS return the list of points which constitute a curve on image # output = chainPixels(input) conn = 8; if ~isempty(varargin) conn = varargin{1}; end # matrice de voisinage if conn == 4 f = [0 1 0;1 1 1;0 1 0]; elseif conn == 8 f = ones([3 3]); end # find extremity points nb = imfilter(double(img), f) .* img; imgEnding = nb == 2 | nb == 1; [yi xi] = find(imgEnding); # extract coordinates of points [y x] = find(img); # index of first point if isempty(xi) # take arbitrary point ind = 1; else ind = find(x==xi(1) & y==yi(1)); end # allocate memory points = zeros(length(x), 2); if conn == 8 for i = 1:size(points, 1) # avoid multiple neighbors (can happen in loops) ind = ind(1); # add current point to chained curve points(i,:) = [x(ind) y(ind)]; # remove processed coordinate x(ind) = []; y(ind) = []; # find next candidate ind = find(abs(x-points(i,1))<=1 & abs(y-points(i,2))<=1); end else for i = 1:size(points, 1) # avoid multiple neighbors (can happen in loops) ind = ind(1); # add current point to chained curve points(i,:) = [x(ind) y(ind)]; # remove processed coordinate x(ind) = []; y(ind) = []; # find next candidate ind = find(abs(x-points(i,1)) + abs(y-points(i,2)) <=1 ); end end endfunction %!demo %! try %! pkg load image %! catch %! error ('You need the image package'); %! end %! %! [m, cmap] = imread ("default.img"); %! m = ind2gray (m, cmap); %! mbw = im2bw(m, graythresh(m)*1.3); %! %! [c t] = polynomialCurveSetFit (mbw); %! %! figure(1) %! clf; %! imshow (m) %! hold on %! for i=1:numel(c) %! if !isempty (c{i}) %! drawPolynomialCurve ([0 1], c{i}); %! endif %! endfor %! %! hold off geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/polynomialCurvePoint.m0000644000000000000000000000013212676233417024176 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/polynomialCurvePoint.m0000644000175000017500000000574212676233417025365 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} =} polynomialCurvePoint (@var{t}, @var{xcoef},@var{ycoef}) ## @deftypefnx {Function File} {@var{point} =} polynomialCurvePoint (@var{t}, @var{coefs}) ## Compute point corresponding to a position ## ## @var{xcoef} and @var{ycoef} are row vectors of coefficients, in the form: ## [a0 a1 a2 ... an] ## @var{t} is a either a scalar, or a column vector, containing values of the ## parametrization variable. ## @var{point} is a 1x2 array containing coordinate of point corresponding to ## position given by @var{t}. If @var{t} is a vector, @var{point} has as many rows as @var{t}. ## ## @var{coefs} is either a 2xN matrix (one row for the coefficients of each ## coordinate), or a cell array. ## ## @seealso{polynomialCurves2d, polynomialCurveLength} ## @end deftypefn function point = polynomialCurvePoint (t, varargin) ## Extract input parameters # polynomial coefficients for each coordinate var = varargin{1}; if iscell (var) xCoef = var{1}; yCoef = var{2}; elseif size (var, 1)==1 xCoef = varargin{1}; yCoef = varargin{2}; else xCoef = var(1,:); yCoef = var(2,:); end ## compute length by numerical integration # convert polynomial coefficients to polyval convention cx = xCoef(end:-1:1); cy = yCoef(end:-1:1); # numerical integration of the Jacobian of parametrized curve point = [polyval(cx, t) polyval(cy, t)]; endfunction geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/polynomialCurveDerivative.m0000644000000000000000000000013212676233417025207 xustar0030 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/polynomialCurveDerivative.m0000644000175000017500000000575512676233417026402 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{v} =} polynomialCurveDerivative (@var{t}, @var{xcoef},@var{ycoef}) ## @deftypefnx {Function File} {@var{v} =} polynomialCurveDerivative (@var{t}, @var{coefs}) ## Compute derivative vector of a polynomial curve ## ## @var{xcoef} and @var{ycoef} are row vectors of coefficients, in the form: ## [a0 a1 a2 ... an] ## @var{v} is a 1x2 array containing direction of derivative of polynomial ## curve, computed for position @var{t}. If @var{t} is a vector, @var{v} has as many rows ## as the length of @var{t}. ## ## @var{coefs} is either a 2xN matrix (one row for the coefficients of each ## coordinate), or a cell array. ## ## @seealso{polynomialCurves2d, polynomialCurveNormal, polynomialCurvePoint, ## polynomialCurveCurvature} ## @end deftypefn function v = polynomialCurveDerivative(t, varargin) ## Extract input parameters # polynomial coefficients for each coordinate var = varargin{1}; if iscell(var) xCoef = var{1}; yCoef = var{2}; elseif size(var, 1)==1 xCoef = varargin{1}; yCoef = varargin{2}; else xCoef = var(1,:); yCoef = var(2,:); end # convert to Octave polynomial convention xCoef = xCoef(end:-1:1); yCoef = yCoef(end:-1:1); # compute derivative of the polynomial dx = polyder (xCoef); dy = polyder (yCoef); # numerical integration of the Jacobian of parametrized curve v = [polyval(dx, t) polyval(dy, t)]; endfunction geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/drawPolynomialCurve.m0000644000000000000000000000013212676233417024002 xustar0030 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/drawPolynomialCurve.m0000644000175000017500000000535612676233417025172 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawPolynomialCurve (@var{bnd}, @var{xcoef}, @var{ycoef}) ## @deftypefnx {Function File} {@var{h} =} drawPolynomialCurve (@var{bnd}, @var{coefs}) ## @deftypefnx {Function File} {@var{h} =} drawPolynomialCurve (@dots{}, @var{npts}) ## Draw a polynomial curve approximation ## @end deftypefn function varargout = drawPolynomialCurve(tBounds, varargin) ## Extract input parameters % polynomial coefficients for each coordinate var = varargin{1}; if iscell(var) xCoef = var{1}; yCoef = var{2}; varargin(1) = []; elseif size(var, 1)==1 xCoef = varargin{1}; yCoef = varargin{2}; varargin(1:2) = []; else xCoef = var(1,:); yCoef = var(2,:); varargin(1) = []; end nPts = 120; if ~isempty(varargin) nPts = varargin{1}; end # parametrization bounds t0 = tBounds(1); t1 = tBounds(end); ## Drawing the polyline approximation # generate vector of absissa t = linspace (t0, t1, nPts+1)'; # compute corresponding positions pts = polynomialCurvePoint (t, xCoef, yCoef); # draw the resulting curve h = drawPolyline (pts); if nargout > 0 varargout{1} = h; end endfunction geometry-2.1.1/inst/polynomialCurves2d/PaxHeaders.5293/polynomialCurveFit.m0000644000000000000000000000013212676233417023627 xustar0030 mtime=1459173135.629061692 30 atime=1459173135.629061692 30 ctime=1459173135.645054067 geometry-2.1.1/inst/polynomialCurves2d/polynomialCurveFit.m0000644000175000017500000002245312676233417025014 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{xc}, @var{yc}] =} polynomialCurveFit (@var{t}, @var{xt}, @var{yt}, @var{order}) ## @deftypefnx {Function File} {[@var{xc}, @var{yc}] =} polynomialCurveFit (@var{t}, @var{points}, @var{order}) ## @deftypefnx {Function File} {[@var{xc}, @var{yc}] =} polynomialCurveFit (@dots{}, @var{ti}, @var{condi}) ## Fit a polynomial curve to a series of points ## ## @var{t} is a Nx1 vector. ## ## @var{xt} and @var{yt} are coordinate for each parameter value (column vectors). ## @var{order} is the degree of the polynomial used for interpolation. ## @var{xc} and @var{yc} are polynomial coefficients, given in @var{order}+1 row vectors, ## starting from degree 0 and up to degree @var{order}. ## @var{points} specifies coordinate of points in a Nx2 array. ## ## Impose some specific conditions using @var{ti} and @var{condi}. ## ## @var{ti} is a value of the parametrization variable. @var{condi} is a cell ## array, with 2 columns, and as many rows as ## the derivatives specified for the given @var{ti}. Format for @var{condi} is: ## ## @var{condi} = @{X_I, Y_I; X_I', Y_I'; X_I", Y_I"; ...@}; ## ## with X_I and Y_I being the imposed coordinate at position @var{ti}, X_I' and ## Y_I' being the imposed first derivatives, X_I" and Y_I" the imposed ## second derivatives, and so on... ## To specify a derivative without specifying derivative with lower ## degree, value of lower derivative can be let empty, using '[]'. ## ## ## Requires the optimization Toolbox. ## ## Run @command{demo polynomialCurveFit} to see exaples of use. ## ## @seealso{polynomialCurves2d} ## @end deftypefn function varargout = polynomialCurveFit(t, varargin) ## extract input arguments # extract curve coordinate var = varargin{1}; if min(size(var))==1 # curve given as separate arguments xt = varargin{1}; yt = varargin{2}; varargin(1:2)=[]; else # curve coordinate bundled in a matrix if size(var, 1)1 Dx = var(1); Dy = var(2); else Dx = var; Dy = var; end varargin(1)=[]; ## Initialize local conditions # For a solution vector 'x', the following relation must hold: # Aeq * x == beq, # with: # Aeq Matrix M*N # beq column vector with length M # The coefficients of the Aeq matrix are initialized as follow: # First point and last point are considered successively. For each point, # k-th condition is the value of the (k-1)th derivative. This value is # computed using relation of the form: # value = sum_i ( fact(i) * t_j^pow(i) ) # with: # i indice of the (i-1) derivative. # fact row vector containing coefficient of each power of t, initialized # with a row vector equals to [1 1 ... 1], and updated for each # derivative by multiplying by corresponding power minus 1. # pow row vector of the powers of each monome. It is represented by a # row vector containing an increasing series of power, eventually # completed with zeros for lower degrees (for the k-th derivative, # the coefficients with power lower than k are not relevant). # Example for degree 5 polynom: # iter deriv pow fact # 1 0 [0 1 2 3 4 5] [1 1 1 1 1 1] # 2 1 [0 0 1 2 3 4] [0 1 2 3 4 5] # 3 2 [0 0 0 1 2 3] [0 0 1 2 3 4] # 4 3 [0 0 0 0 1 2] [0 0 0 1 2 3] # ... # The process is repeated for coordinate x and for coordinate y. # Initialize empty matrices Aeqx = zeros(0, Dx+1); beqx = zeros(0, 1); Aeqy = zeros(0, Dy+1); beqy = zeros(0, 1); # Process local conditions while ~isempty(varargin) if length(varargin)==1 warning('MatGeom:PolynomialCurveFit:ArgumentNumber', ... 'Wrong number of arguments in polynomialCurvefit'); end # extract parameter t, and cell array of local conditions ti = varargin{1}; cond = varargin{2}; # factors for coefficients of each polynomial. At the beginning, they # all equal 1. With successive derivatives, their value increase by the # corresponding powers. factX = ones(1, Dx+1); factY = ones(1, Dy+1); # start condition initialisations for i = 1:size(cond, 1) # degrees of each polynomial powX = [zeros(1, i) 1:Dx+1-i]; powY = [zeros(1, i) 1:Dy+1-i]; # update conditions for x coordinate if ~isempty(cond{i,1}) Aeqx = [Aeqx ; factY.*power(ti, powX)]; ##ok beqx = [beqx; cond{i,1}]; ##ok end # update conditions for y coordinate if ~isempty(cond{i,2}) Aeqy = [Aeqy ; factY.*power(ti, powY)]; ##ok beqy = [beqy; cond{i,2}]; ##ok end # update polynomial degrees for next derivative factX = factX.*powX; factY = factY.*powY; end varargin(1:2)=[]; end ## Initialisations # ensure column vectors t = t(:); xt = xt(:); yt = yt(:); # number of points to fit L = length(t); ## Compute coefficients of each polynomial # main matrix for x coordinate, size L*(degX+1) T = ones(L, Dx+1); for i = 1:Dx T(:, i+1) = power(t, i); end # compute interpolation # Octave compatibility - JPi 2013 xc = lsqlin (T, xt, zeros(1, Dx+1), 1, Aeqx, beqx)'; # main matrix for y coordinate, size L*(degY+1) T = ones(L, Dy+1); for i = 1:Dy T(:, i+1) = power(t, i); end # compute interpolation # Octave compatibility - JPi 2013 yc = lsqlin (T, yt, zeros(1, Dy+1), 1, Aeqy, beqy)'; ## Format output arguments if nargout <= 1 varargout{1} = {xc, yc}; else varargout{1} = xc; varargout{2} = yc; end endfunction function x = lsqlin (C, d, A, b, Aeq, beq) H = C'*C; q = -C'*d; x0 = zeros (size(C,2),size(d,2)); x = qp (x0, H, q, Aeq, beq, [], [],[], A, b); endfunction %!demo %! # defines a curve (circle arc) with small perturbations %! N = 50; %! t = linspace(0, 3*pi/4, N)'; %! xp = cos(t) + 5e-2*randn(size(t)); %! yp = sin(t) + 5e-2*randn(size(t)); %! %! [xc yc] = polynomialCurveFit(t, xp, yp, 3); %! %! figure(1); %! clf; %! drawPolynomialCurve(t([1 end]), xc, yc); %! hold on %! plot(xp,yp,'.g'); %! hold off %! axis tight %! axis equal %!demo %! # defines a curve (circle arc) with small perturbations %! N = 100; %! t = linspace(0, 3*pi/4, N)'; %! xp = cos(t) + 7e-2*randn(size(t)); %! yp = sin(t) + 7e-2*randn(size(t)); %! %! # plot the points %! figure (1); clf; hold on; %! axis ([-1.2 1.2 -.2 1.2]); axis equal; %! drawPoint (xp, yp, ".g"); %! %! # fit without knowledge on bounds %! [xc0 yc0] = polynomialCurveFit (t, xp, yp, 5); %! h = drawPolynomialCurve (t([1 end]), xc0, yc0); %! set(h, "color", "b") %! %! # fit by imposing coordinate on first point %! [xc1 yc1] = polynomialCurveFit (t, xp, yp, 5, 0, {1, 0}); %! h = drawPolynomialCurve (t([1 end]), xc1, yc1); %! set(h, "color", "r") %! %! # fit by imposing coordinate (1,0) and derivative (0,1) on first point %! [xc2 yc2] = polynomialCurveFit (t, xp, yp, 5, 0, {1, 0;0 1}); %! h = drawPolynomialCurve (t([1 end]), xc2, yc2); %! set(h, "color", "m") %! %! # fit by imposing several conditions on various points %! [xc3 yc3] = polynomialCurveFit (t, xp, yp, 5, ... %! 0, {1, 0;0 1}, ... # coord and first derivative of first point %! 3*pi/4, {-sqrt(2)/2, sqrt(2)/2}, ... # coord of last point %! pi/2, {[], [];-1, 0}); # derivative of point on the top of arc %! h = drawPolynomialCurve (t([1 end]), xc3, yc3); %! set(h, "color", "k") %! axis tight %! axis equal geometry-2.1.1/inst/PaxHeaders.5293/geom2d0000644000000000000000000000013212676233417015115 xustar0030 mtime=1459173135.485130312 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/0000755000175000017500000000000012676233417016351 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/geom2d/PaxHeaders.5293/polarPoint.m0000644000000000000000000000013212676233417017477 xustar0030 mtime=1459173135.465139842 30 atime=1459173135.465139842 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/polarPoint.m0000644000175000017500000000606012676233417020660 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} = } polarPoint (@var{rho}, @var{theta}) ## @deftypefnx {Function File} {@var{point} = } polarPoint (@var{theta}) ## @deftypefnx {Function File} {@var{point} = } polarPoint (@var{point}, @var{rho}, @var{theta}) ## @deftypefnx {Function File} {@var{point} = } polarPoint (@var{x0}, @var{y0}, @var{rho}, @var{theta}) ##Create a point from polar coordinates (rho + theta) ## ## Creates a point using polar coordinate. @var{theta} is angle with horizontal ## (counted counter-clockwise, and in radians), and @var{rho} is the distance to ## origin. If only angle is given radius @var{rho} is assumed to be 1. ## ## If a point is given, adds the coordinate of the point to the coordinate of the specified ## point. For example, creating a point with : ## P = polarPoint([10 20], 30, pi/2); ## will give a result of [40 20]. ## ## @seealso{points2d} ## @end deftypefn function point = polarPoint(varargin) # default values x0 = 0; y0=0; rho = 1; theta =0; # process input parameters if length(varargin)==1 theta = varargin{1}; elseif length(varargin)==2 rho = varargin{1}; theta = varargin{2}; elseif length(varargin)==3 var = varargin{1}; x0 = var(:,1); y0 = var(:,2); rho = varargin{2}; theta = varargin{3}; elseif length(varargin)==4 x0 = varargin{1}; y0 = varargin{2}; rho = varargin{3}; theta = varargin{4}; end point = [x0 + rho.*cos(theta) , y0+rho.*sin(theta)]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/hexagonalGrid.m0000644000000000000000000000013212676233417020124 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/hexagonalGrid.m0000644000175000017500000000757512676233417021321 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts} = } hexagonalGrid (@var{bounds}, @var{origin}, @var{size}) ## Generate hexagonal grid of points in the plane. ## ## usage ## PTS = hexagonalGrid(BOUNDS, ORIGIN, SIZE) ## generate points, lying in the window defined by BOUNDS (=[xmin ymin ## xmax ymax]), starting from origin with a constant step equal to size. ## SIZE is constant and is equals to the length of the sides of each ## hexagon. ## ## TODO: add possibility to use rotated grid ## @end deftypefn function varargout = hexagonalGrid(bounds, origin, size, varargin) size = size(1); dx = 3*size; dy = size*sqrt(3); # consider two square grids with different centers pts1 = squareGrid(bounds, origin + [0 0], [dx dy], varargin{:}); pts2 = squareGrid(bounds, origin + [dx/3 0], [dx dy], varargin{:}); pts3 = squareGrid(bounds, origin + [dx/2 dy/2], [dx dy], varargin{:}); pts4 = squareGrid(bounds, origin + [-dx/6 dy/2], [dx dy], varargin{:}); # gather points pts = [pts1;pts2;pts3;pts4]; # eventually compute also edges, clipped by bounds # TODO : manage generation of edges if nargout>1 edges = zeros([0 4]); x0 = origin(1); y0 = origin(2); # find all x coordinate x1 = bounds(1) + mod(x0-bounds(1), dx); x2 = bounds(3) - mod(bounds(3)-x0, dx); lx = (x1:dx:x2)'; # horizontal edges : first find y's y1 = bounds(2) + mod(y0-bounds(2), dy); y2 = bounds(4) - mod(bounds(4)-y0, dy); ly = (y1:dy:y2)'; # number of points in each coord, and total number of points ny = length(ly); nx = length(lx); if bounds(1)-x1+dx0 varargout{1} = pts; if nargout>1 varargout{2} = edges; end end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createDirectedCircle.m0000644000000000000000000000013212676233417021401 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createDirectedCircle.m0000644000175000017500000000622712676233417022567 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{circle} = } createDirectedCircle (@var{p1}, @var{p2}, @var{p3}) ## @deftypefnx {Function File} {@var{circle} = } createDirectedCircle (@var{p1}, @var{p2}) ## Create a circle from 2 or 3 points. ## ## Creates the circle passing through the 3 given points. ## C is a 1x4 array of the form: [XC YX R INV]. ## ## When two points are given, creates the circle whith center @var{p1} and passing ## throuh the point @var{p2}. ## ## Works also when input are point arrays the same size, in this case the ## result has as many lines as the point arrays. ## ## Example ## ## ## @seealso{circles2d, createCircle} ## @end deftypefn function circle = createDirectedCircle(varargin) if nargin == 2 # inputs are the center and a point on the circle p1 = varargin{1}; p2 = varargin{2}; x0 = (p1(:,1) + p2(:,1))/2; y0 = (p1(:,2) + p2(:,2))/2; r = hypot((p2(:,1)-p1(:,1)), (p2(:,2)-p1(:,2)))/2; # circle is direct by default d = 0; elseif nargin == 3 # inputs are three points on the circle p1 = varargin{1}; p2 = varargin{2}; p3 = varargin{3}; # compute circle center line1 = medianLine(p1, p2); line2 = medianLine(p1, p3); center = intersectLines(line1, line2); x0 = center(:, 1); y0 = center(:, 2); # circle radius r = hypot((p1(:,1)-x0), (p1(:,2)-y0)); # compute circle orientation angle = angle3Points(p1, center, p2) + angle3Points(p2, center, p3); d = angle>2*pi; end circle = [x0 y0 r d]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/reverseEdge.m0000644000000000000000000000013012676233417017606 xustar0029 mtime=1459173135.47313603 29 atime=1459173135.47313603 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/reverseEdge.m0000644000175000017500000000375212676233417020776 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{res} = } reverseEdge (@var{edge}) ## Intervert the source and target vertices of edge ## ## REV = reverseEdge(EDGE); ## Returns the opposite edge of EDGE. ## EDGE has the format [X1 Y1 X2 Y2]. The resulting edge REV has value ## [X2 Y2 X1 Y1]; ## ## @seealso{edges2d, createEdge, reverseLine} ## @end deftypefn function res = reverseEdge(edge) res = [edge(:,3:4) edge(:,1:2)]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/transforms2d.m0000644000000000000000000000013212676233417017774 xustar0030 mtime=1459173135.481132218 30 atime=1459173135.481132218 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/transforms2d.m0000644000175000017500000000444612676233417021163 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} transforms2d () ## Description of functions operating on transforms ## ## By 'transform' we mean an affine transform. A planar affine transform ## can be represented by a 3x3 matrix. ## ## Example ## ## @example ## # create a translation by the vector [10 20]: ## T = createTranslation([10 20]) ## T = ## 1 0 10 ## 0 1 20 ## 0 0 1 ##@end example ## ## @seealso{createTranslation, createRotation, createScaling, createBasisTransform, ## createHomothecy, createLineReflection, fitAffineTransform2d, ## transformPoint, transformVector, transformLine, transformEdge, ## rotateVector} ## @end deftypefn function transforms2d(varargin) help('transforms2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/projPointOnLine.m0000644000000000000000000000013212676233417020441 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.469137936 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/projPointOnLine.m0000644000175000017500000000542312676233417021624 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} = } projPointOnLine (@var{pt1}, @var{line}) ## Project of a point orthogonally onto a line ## ## Computes the (orthogonal) projection of point @var{pt1} onto the line @var{line}. ## ## Function works also for multiple points and lines. In this case, it ## returns multiple points. ## Point @var{pt1} is a [N*2] array, and @var{line} is a [N*4] array (see createLine ## for details). Result @var{point} is a [N*2] array, containing coordinates of ## orthogonal projections of @var{pt1} onto lines @var{line}. ## ## @seealso{lines2d, points2d, isPointOnLine, linePosition} ## @end deftypefn function point = projPointOnLine(point, line) # ensure input arguments have same size if size(line, 1)==1 && size(point, 1)>1 line = repmat(line, [size(point, 1) 1]); end if size(point, 1)==1 && size(line, 1)>1 point = repmat(point, [size(line, 1) 1]); end # slope of line dx = line(:, 3); dy = line(:, 4); # first find relative position of projection on the line, tp = ((point(:, 2) - line(:, 2)).*dy + (point(:, 1) - line(:, 1)).*dx) ./ (dx.*dx+dy.*dy); # convert position on line to cartesian coordinate point = line(:,1:2) + [tp tp].*[dx dy]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawEdge.m0000644000000000000000000000013212676233417017072 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawEdge.m0000644000175000017500000001212612676233417020253 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawEdge (@var{x1}, @var{y1}, @var{x2}, @var{y2}) ## @deftypefnx {Function File} {@var{h} = } drawEdge ([@var{x1} @var{y1} @var{x2} @var{y2}]) ## @deftypefnx {Function File} {@var{h} = } drawEdge ([@var{x1} @var{y1}], [@var{x2} @var{y2}]) ## @deftypefnx {Function File} {@var{h} = } drawEdge (@var{x1}, @var{y1}, @var{z1}, @var{x2}, @var{y2}, @var{z2}) ## @deftypefnx {Function File} {@var{h} = } drawEdge ([@var{x1} @var{y1} @var{z1} @var{x2} @var{y2} @var{z2}]) ## @deftypefnx {Function File} {@var{h} = } drawEdge ([@var{x1} @var{y1} @var{z1}], [@var{x2} @var{y2} @var{z2}]) ## @deftypefnx {Function File} {@var{h} = } drawEdge (@dots{}, @var{opt}) ## Draw an edge given by 2 points. ## ## Draw an edge between the points (x1 y1) and (x2 y2). Data can be bundled as an edge. ## The function supports 3D edges. ## Arguments can be single values or array of size [Nx1]. In this case, ## the function draws multiple edges. ## @var{opt}, being a set of pairwise options, can ## specify color, line width and so on. These are passed to function @code{line}. ## The function returns handle(s) to created edges(s). ## ## @seealso{edges2d, drawCenteredEdge, drawLine, line} ## @end deftypefn function varargout = drawEdge(varargin) # separate edge and optional arguments [edge options] = parseInputArguments(varargin{:}); # draw the edges if size(edge, 2)==4 h = drawEdge_2d(edge, options); else h = drawEdge_3d(edge, options); end # eventually return handle to created edges if nargout>0 varargout{1}=h; end endfunction function h = drawEdge_2d(edge, options) h = -1*ones(size(edge, 1), 1); for i=1:size(edge, 1) if isnan(edge(i,1)) continue; end h(i) = line(... [edge(i, 1) edge(i, 3)], ... [edge(i, 2) edge(i, 4)], options{:}); end endfunction function h = drawEdge_3d(edge, options) h = -1*ones(size(edge, 1), 1); for i=1:size(edge, 1) if isnan(edge(i,1)) continue; end h(i) = line( ... [edge(i, 1) edge(i, 4)], ... [edge(i, 2) edge(i, 5)], ... [edge(i, 3) edge(i, 6)], options{:}); end endfunction function [edge options] = parseInputArguments(varargin) # default values for parameters edge = []; # find the number of arguments defining edges nbVal=0; for i=1:nargin if isnumeric(varargin{i}) nbVal = nbVal+1; else # stop at the first non-numeric value break; end end # extract drawing options options = varargin(nbVal+1:end); # ensure drawing options have correct format if length(options)==1 options = [{'color'}, options]; end # extract edges characteristics if nbVal==1 # all parameters in a single array edge = varargin{1}; elseif nbVal==2 # parameters are two points, or two arrays of points, of size N*2. p1 = varargin{1}; p2 = varargin{2}; edge = [p1 p2]; elseif nbVal==4 # parameters are 4 parameters of the edge : x1 y1 x2 and y2 edge = [varargin{1} varargin{2} varargin{3} varargin{4}]; elseif nbVal==6 # parameters are 6 parameters of the edge : x1 y1 z1 x2 y2 and z2 edge = [varargin{1} varargin{2} varargin{3} varargin{4} varargin{5} varargin{6}]; end endfunction %!demo %! close %! points = rand(4,4); %! colorstr = 'rgbm'; %! for i=1:4 %! drawEdge (points(i,:),'color',colorstr(i),'linewidth',2); %! end %! axis tight; %!demo %! close %! drawEdge (rand(10,4),'linewidth',2); %! axis tight; geometry-2.1.1/inst/geom2d/PaxHeaders.5293/deg2rad.m0000644000000000000000000000013212676233417016660 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/deg2rad.m0000644000175000017500000000376212676233417020047 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{rad} =} deg2rad(@var{deg}) ## Convert angle from degrees to radians ## ## Usage: ## R = deg2rad(D) ## convert an angle in degrees to an angle in radians. ## ## Example ## deg2rad(180) # gives pi ## ans = ## 3.1416 ## deg2rad(60) # gives pi/3 ## ans = ## 1.0472 ## ## @seealso{angles2d, rad2deg} ## @end deftypefn function rad = deg2rad(deg) rad = deg*pi/180; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/rad2deg.m0000644000000000000000000000013212676233417016660 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.469137936 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/rad2deg.m0000644000175000017500000000367412676233417020051 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{deg} =} rad2deg(@var{rad}) # Convert angle from radians to degrees # # Usage: # R = rad2deg(D) # convert an angle in radians to angle in degrees # # Example: # rad2deg(pi) # ans = # 180 # rad2deg(pi/3) # ans = # 60 ## ## @seealso{angles2d, deg2rad} ## @end deftypefn function deg = rad2deg(rad) deg = rad*180/pi; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/reverseLine.m0000644000000000000000000000013212676233417017633 xustar0030 mtime=1459173135.477134124 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/reverseLine.m0000644000175000017500000000376212676233417021022 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} = } reverseLine (@var{line}) ## Return same line but with opposite orientation ## ## INVLINE = reverseLine(LINE); ## Returns the opposite line of LINE. ## LINE has the format [x0 y0 dx dy], then INVLINE will have following ## parameters: [x0 y0 -dx -dy]. ## ## @seealso{lines2d, createLine} ## @end deftypefn function line = reverseLine(line) line(:, 3:4) = -line(:, 3:4); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/cbezier2poly.m0000644000000000000000000000013212676233417017761 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/cbezier2poly.m0000644000175000017500000001242712676233417021146 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pp} =} cbezier2poly (@var{points}) ## @deftypefnx {Function File} {[@var{x} @var{y}] =} cbezier2poly (@var{points},@var{t}) ## Returns the polynomial representation of the cubic Bezier defined by the control points @var{points}. ## ## With only one input argument, calculates the polynomial @var{pp} of the cubic ## Bezier curve defined by the 4 control points stored in @var{points}. The first ## point is the inital point of the curve. The segment joining the first point ## with the second point (first center) defines the tangent of the curve at the initial point. ## The segment that joints the third point (second center) with the fourth defines the tanget at ## the end-point of the curve, which is defined in the fourth point. ## @var{points} is either a 4-by-2 array (vertical concatenation of point ## coordinates), or a 1-by-8 array (horizotnal concatenation of point ## coordinates). @var{pp} is a 2-by-3 array, 1st row is the polynomial for the ## x-coordinate and the 2nd row for the y-coordinate. Each row can be evaluated ## with @code{polyval}. The polynomial @var{pp}(t) is defined for t in [0,1]. ## ## When called with a second input argument @var{t}, it returns the coordinates ## @var{x} and @var{y} corresponding to the polynomial evaluated at @var{t} in ## [0,1]. ## ## @seealso{drawBezierCurve, polyval} ## @end deftypefn function varargout = cbezier2poly (points, ti=[]) # rename points if size(points, 2)==2 # case of points given as a 4-by-2 array p1 = points(1,:); c1 = points(2,:); c2 = points(3,:); p2 = points(4,:); elseif size(points,2) == 8 # case of points given as a 1-by-8 array, [X1 Y1 CX1 CX2..] p1 = points(1:2); c1 = points(3:4); c2 = points(5:6); p2 = points(7:8); else print_usage ; end # compute coefficients of Bezier Polynomial pp = zeros(2,4); pp(:,4) = [p1(1); ... p1(2)]; pp(:,3) = [3 * c1(1) - 3 * p1(1); ... 3 * c1(2) - 3 * p1(2)]; pp(:,2) = [3 * p1(1) - 6 * c1(1) + 3 * c2(1); ... 3 * p1(2) - 6 * c1(2) + 3 * c2(2)]; pp(:,1) = [p2(1) - 3 * c2(1) + 3 * c1(1) - p1(1); ... p2(2) - 3 * c2(2) + 3 * c1(2) - p1(2)]; if isempty (ti) varargout{1} = pp; else varargout{1} = polyval (pp(1,:), ti); varargout{2} = polyval (pp(2,:), ti); end endfunction %!demo %! points = [45.714286 483.79075; ... %! 241.65656 110.40445; ... %! 80.185847 741.77381; ... %! 537.14286 480.93361]; %! %! pp = cbezier2poly(points); %! t = linspace(0,1,64); %! x = polyval(pp(1,:),t); %! y = polyval(pp(2,:),t); %! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',... %! points([2 3],1),points([2 3],2),'o'); %! line(points([2 1],1),points([2 1],2),'color','r'); %! line(points([3 4],1),points([3 4],2),'color','r'); %!demo %! points = [0 0; ... %! 1 1; ... %! 1 1; ... %! 2 0]; %! %! t = linspace(0,1,64); %! [x y] = cbezier2poly(points,t); %! plot (x,y,'b-',points([1 4],1),points([1 4],2),'s',... %! points([2 3],1),points([2 3],2),'o'); %! line(points([2 1],1),points([2 1],2),'color','r'); %! line(points([3 4],1),points([3 4],2),'color','r'); %!test %! points = [0 0; ... %! 1 1; ... %! 1 1; ... %! 2 0]; %! t = linspace(0,1,64); %! %! [x y] = cbezier2poly(points,t); %! pp = cbezier2poly(points); %! x2 = polyval(pp(1,:),t); %! y2 = polyval(pp(2,:),t); %! assert(x,x2); %! assert(y,y2); %!test %! points = [0 0; ... %! 1 1; ... %! 1 1; ... %! 2 0]; %! t = linspace(0,1,64); %! %! p = reshape(points,1,8); %! [x y] = cbezier2poly(p,t); %! pp = cbezier2poly(p); %! x2 = polyval(pp(1,:),t); %! y2 = polyval(pp(2,:),t); %! assert(x,x2); %! assert(y,y2); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/findClosestPoint.m0000644000000000000000000000013212676233417020637 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/findClosestPoint.m0000644000175000017500000000524412676233417022023 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2015 David Legland ## Copyright (C) 2004-2015 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2016 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{index}, @var{mindist}] =} findClosestPoint (@var{point}, @var{pointarray}) ## Find index of closest point in an array and the distance between @var{point} and closest point in @var{pointarray}. ## ## Example: ##@example ## pts = rand(10, 2); ## findClosestPoint(pts(4, :), pts) ## ans = ## 4 ##@end example ## @seealso{points2d, minDistancePoints, distancePoints} ## @end deftypefn function [index, minDist] = findClosestPoint(coord, points) % number of point in first input to process np = size (coord, 1); % allocate memory for result index = zeros (np, 1); minDist = zeros (np, 1); for i = 1:np % compute squared distance between current point and all point in array dist = sumsq (coord(i,:) - points, 2); % keep index of closest point [minDist(i), index(i)] = min(dist); endfor endfunction %!demo %! pts = rand (10, 2); %! pt = rand (1, 2); %! [idx d] = findClosestPoint (pt, pts); %! printf ("Point (%g,%g).\n", pt); %! printf ("The %dth is the closest point (%g,%g).\n", idx, pts(idx,:)); %! printf ("The distance between them is %g.\n", d); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/enclosingCircle.m0000644000000000000000000000013212676233417020453 xustar0030 mtime=1459173135.369185589 30 atime=1459173135.369185589 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/enclosingCircle.m0000644000175000017500000000654512676233417021644 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{circle} = } enclosingCircle (@var{pts}) ## Find the minimum circle enclosing a set of points. ## ## CIRCLE = enclosingCircle(POINTS); ## compute cirlce CIRCLE=[xc yc r] which enclose all points POINTS given ## as an [Nx2] array. ## ## ## Rewritten from a file from ## Yazan Ahed ## which was rewritten from a Java applet by Shripad Thite : ## @url{http://heyoka.cs.uiuc.edu/~thite/mincircle/} ## ## @seealso{circles2d, points2d, boxes2d} ## @end deftypefn function circle = enclosingCircle(pts) # works on convex hull : it is faster pts = pts(convhull(pts(:,1), pts(:,2)), :); circle = recurseCircle(size(pts, 1), pts, 1, zeros(3, 2)); endfunction function circ = recurseCircle(n, p, m, b) # n: number of points given # m: an argument used by the function. Always use 1 for m. # bnry: an argument (3x2 array) used by the function to set the points that # determines the circle boundry. You have to be careful when choosing this # array's values. I think the values should be somewhere outside your points # boundary. For my case, for example, I know the (x,y) I have will be something # in between (-5,-5) and (5,5), so I use bnry as: # [-10 -10 # -10 -10 # -10 -10] if m==4 circ = createCircle(b(1,:), b(2,:), b(3,:)); return; end circ = [Inf Inf 0]; if m == 2 circ = [b(1,1:2) 0]; elseif m == 3 c = (b(1,:) + b(2,:))/2; circ = [c distancePoints(b(1,:), c)]; end for i = 1:n if distancePoints(p(i,:), circ(1:2)) > circ(3) if sum(b(:,1)==p(i,1) & b(:,2)==p(i,2)) == 0 b(m,:) = p(i,:); circ = recurseCircle(i, p, m+1, b); end end end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createRotation.m0000644000000000000000000000013212676233417020333 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createRotation.m0000644000175000017500000000717212676233417021521 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } createRotation (@var{theta}) ## @deftypefnx {Function File} {@var{T} = } createRotation (@var{point}, @var{theta}) ## @deftypefnx {Function File} {@var{T} = } createRotation (@var{x0}, @var{y0}, @var{theta}) ## Create the 3*3 matrix of a rotation. ## ## Returns the rotation corresponding to angle @var{theta} (in radians) ## The returned matrix has the form : ## [cos(theta) -sin(theta) 0] ## [sin(theta) cos(theta) 0] ## [0 0 1] ## ## @var{point} or (@var{x0},@var{y0}), specifies origin of rotation. The result is similar as performing ## translation(-@var{x0},-@var{y0}), rotation(@var{theta}), and translation(@var{x0},@var{y0}). ## ## ## @seealso{transforms2d, transformPoint, createTranslation, createScaling} ## @end deftypefn function trans = createRotation(varargin) # default values cx = 0; cy = 0; theta = 0; # get input values if length(varargin)==1 # only angle theta = varargin{1}; elseif length(varargin)==2 # origin point (as array) and angle var = varargin{1}; cx = var(1); cy = var(2); theta = varargin{2}; elseif length(varargin)==3 # origin (x and y) and angle cx = varargin{1}; cy = varargin{2}; theta = varargin{3}; end # compute coefs cot = cos(theta); sit = sin(theta); tx = cy*sit - cx*cot + cx; ty = -cy*cot - cx*sit + cy; # create transformation matrix trans = [cot -sit tx; sit cot ty; 0 0 1]; endfunction %!test %! trans = createRotation(0); %! assert (trans, [1 0 0;0 1 0;0 0 1], 1e-6); %!test %! trans = createRotation(pi/2); %! assert (trans, [0 -1 0; 1 0 0; 0 0 1], 1e-6); %!test %! trans = createRotation(pi); %! assert (trans, [-1 0 0;0 -1 0;0 0 1], 1e-6); %!test %! trans = createRotation(3*pi/2); %! assert (trans, [0 1 0; -1 0 0; 0 0 1], 1e-6); %!test %! p0 = [3 5]; %! theta = pi/3; %! trans1 = createRotation(p0, theta); %! t1 = createTranslation(-p0); %! rot = createRotation(theta); %! t2 = createTranslation(p0); %! trans2 = t2*rot*t1; %! assert (trans1, trans2, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/points2d.m0000644000000000000000000000013212676233417017112 xustar0030 mtime=1459173135.465139842 30 atime=1459173135.465139842 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/points2d.m0000644000175000017500000000433012676233417020271 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} points2d () ## Description of functions operating on points. ## ## A point is defined by its two cartesian coordinate, put into a row ## vector of 2 elements: ## P = [x y]; ## ## Several points are stores in a matrix with two columns, one for the ## x-coordinate, one for the y-coordinate. ## PTS = [x1 y1 ; x2 y2 ; x3 y3]; ## ## Example ## P = [5 6]; ## ## @seealso{centroid, midPoint, polarPoint, pointOnLine ## isCounterClockwise, angle2Points, angle3Points, angleSort ## distancePoints, minDistancePoints ## transformPoint, clipPoints, drawPoint} ## @end deftypefn function points2d help('points2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/transformVector.m0000644000000000000000000000013212676233417020546 xustar0030 mtime=1459173135.481132218 30 atime=1459173135.481132218 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/transformVector.m0000644000175000017500000000730112676233417021726 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{v2} = } transformVector (@var{v}, @var{T}) ## @deftypefnx {Function File} {[@var{x2} @var{y2}] = } transformVector (@var{x},@var{y}, @var{T}) ## Transform a vector with an affine transform ## ## @var{v} has the form [xv yv], and @var{T} is a [2x2], [2x3] or [3x3] ## matrix, returns the vector transformed with affine transform @var{T}. ## ## Format of @var{T} can be one of : ## @group ## [a b] , [a b c] , or [a b c] ## [d e] [d e f] [d e f] ## [0 0 1] ## @end group ## ## Also works when @var{v} is a [Nx2] array of double. In this case, @var{v2} has ## the same size as @var{v}. ## ## Also works when @var{x} and @var{y} are arrays the same size. The function ## transform each couple of (@var{x}, @var{y}), and return the result in ## (@var{x2}, @var{y2}), which is the same size as (@var{x}, @var{y}). ## ## @seealso{vectors2d, transforms2d, rotateVector, transformPoint} ## @end deftypefn function varargout = transformVector(varargin) if length(varargin)==2 var = varargin{1}; vx = var(:,1); vy = var(:,2); trans = varargin{2}; elseif length(varargin)==3 vx = varargin{1}; vy = varargin{2}; trans = varargin{3}; else error('wrong number of arguments in "transformVector"'); end # compute new position of vector vx2 = vx*trans(1,1) + vy*trans(1,2); vy2 = vx*trans(2,1) + vy*trans(2,2); if size(trans, 2) == 3 vx2 = vx2 + trans(1,3); vy2 = vy2 + trans(2,3); end # format output if nargout==0 || nargout==1 varargout{1} = [vx2 vy2]; elseif nargout==2 varargout{1} = vx2; varargout{2} = vy2; end endfunction %!demo %! t1 = [2 0 0; 0 2 0]; %! t2 = [1 0 1; 0 1 1]; %! t3 = [0.5 0 1; 0 0.5 1; 0 0 1]; %! %! triangle = [-0.5 -1/3; 0.5 -1/3; 0 2/3; -0.5 -1/3]; %! tr1 = transformVector(triangle,t1); %! tr2 = transformVector(triangle,t2); %! tr3 = transformVector(triangle,t3); %! %! plot(triangle(:,1),triangle(:,2),'k-', ... %! tr1(:,1),tr1(:,2),'g-;scaled up;', ... %! tr2(:,1),tr2(:,2),'m-;translated;', ... %! tr3(:,1),tr3(:,2),'b-;scaled down and translated;') geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawArrow.m0000644000000000000000000000013212676233417017320 xustar0030 mtime=1459173135.353193213 30 atime=1459173135.353193213 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawArrow.m0000644000175000017500000001253712676233417020507 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawArrow (@var{x1}, @var{y1}, @var{x2}, @var{y2}) ## @deftypefnx {Function File} {@var{h} = } drawArrow ([@var{ @var{x1}} @var{ @var{y1}} @var{x2} @var{y2}]) ## @deftypefnx {Function File} {@var{h} = } drawArrow (@dots{}, @var{L}, @var{W},@var{R},@var{TYPE}) ## Draw an arrow on the current axis. ## ## Draw an arrow between the points (@var{x1} @var{y1}) and (@var{x2} @var{y2}). ## The points can be given as a single array. @var{L}, @var{W} specify length ## and width of the arrow. ## ## The length wings of the arrow can be modified with @var{R}. By default ## @var{R} is 0.1, giving a wing legnth of 0.1*@var{L}. ## ## Also specify arrow type. @var{TYPE} can be one of the following : ## 0: draw only two strokes ## 1: fill a triangle ## .5: draw a half arrow (try it to see ...) ## ## Arguments can be single values or array of size [N*1]. In this case, ## the function draws multiple arrows. ## ## @end deftypefn function varargout = drawArrow(varargin) if isempty(varargin) error('should specify at least one argument'); end # parse arrow coordinate if size(varargin{1}, 2)==4 x1 = varargin{1}(:,1); y1 = varargin{1}(:,2); x2 = varargin{1}(:,3); y2 = varargin{1}(:,4); varargin = varargin(2:end); elseif length(varargin)>3 x1 = varargin{1}; y1 = varargin{2}; x2 = varargin{3}; y2 = varargin{4}; varargin = varargin(5:end); else error('wrong number of arguments, please read the doc'); end l = 10*size(size(x1)); w = 5*ones(size(x1)); h = zeros(size(x1)); # exctract length of arrow if ~isempty(varargin) l = varargin{1}; if length(x1)>length(l) l = l(1)*ones(size(x1)); end end # extract width of arrow if length(varargin)>1 w = varargin{2}; if length(x1)>length(w) w = w(1)*ones(size(x1)); end end # extract 'ratio' of arrow r = 0.1; if length(varargin)>2 r = varargin{3}; if length(x1)>length(r) r = r(1)*ones(size(x1)); end end # extract 'type' of arrow if length(varargin)>3 h = varargin{4}; if length(x1)>length(h) h = h(1)*ones(size(x1)); end end old_hold = ishold (gca); if ~old_hold hold on; end axis equal; # angle of the edge theta = atan2(y2-y1, x2-x1); # point on the 'left' xa1 = x2 - r.*l.*cos(theta) - w.*sin(theta)/2; ya1 = y2 - r.*l.*sin(theta) + w.*cos(theta)/2; # point on the 'right' xa2 = x2 - r.*l.*cos(theta) + w.*sin(theta)/2; ya2 = y2 - r.*l.*sin(theta) - w.*cos(theta)/2; # point on the middle of the arrow xa3 = x2 - l.*cos(theta).*h; ya3 = y2 - l.*sin(theta).*h; # draw main edge tmp = line([x1'; x2'], [y1'; y2'], 'color', [0 0 1]); handle.body = tmp; # draw only 2 wings ind = find(h==0); if !isempty (ind) tmp = line([xa1(ind)'; x2(ind)'], [ya1(ind)'; y2(ind)'], 'color', [0 0 1]); handle.wing(:,1) = tmp; tmp = line([xa2(ind)'; x2(ind)'], [ya2(ind)'; y2(ind)'], 'color', [0 0 1]); handle.wing(:,2) = tmp; end # draw a full arrow ind = find(h~=0); if !isempty (ind) tmp = patch([x2(ind) xa1(ind) xa3(ind) xa2(ind) x2(ind)]', ... [y2(ind) ya1(ind) ya3(ind) ya2(ind) y2(ind)]', [0 0 1]); handle.head = tmp; end if nargout>0 varargout{1} = handle; end if ~old_hold hold off end endfunction %!demo %! # Orthogonal projection respect to vector b %! dim = 2; %! b = 2*rand(dim,1); %! P = eye(dim) - (b*b')/(b'*b); %! v = 2*rand(dim,1)-1; %! Pv = P*v; %! %! # Draw the vectors %! clf; %! h = drawArrow ([zeros(3,dim) [b'; v'; Pv']],1,0.1); %! %! # Color them %! arrayfun(@(x,y)set(x,'color',y), [h.body; h.wing(:)],repmat(['rgb']',3,1)); %! # Name them %! legend (h.body, {'b','v','Pv'},'location','northoutside','orientation','horizontal'); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createVector.m0000644000000000000000000000013212676233417017776 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createVector.m0000644000175000017500000000434112676233417021157 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vect} = } createVector (@var{p1}, @var{p2}) ## Create a vector from two points. ## ## V12 = createVector(P1, P2) ## Creates the vector V12, defined as the difference between coordinates ## of points P1 and P2. ## P1 and P2 are row vectors with ND elements, ND being the space ## dimension. ## ## If one of the inputs is a N-by-Nd array, the other input is ## automatically repeated, and the result is N-by-Nd. ## ## If both inputs have the same size, the result also have the same size. ## ## @seealso{vectors2d, vectors3d, points2d} ## @end deftypefn function vect = createVector(p1, p2) vect = bsxfun(@minus, p2, p1); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/normalizeAngle.m0000644000000000000000000000013212676233417020317 xustar0030 mtime=1459173135.461141748 30 atime=1459173135.461141748 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/normalizeAngle.m0000644000175000017500000000654212676233417021505 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{alpha2} =} normalizeAngle (@var{alpha}) ## @deftypefnx {Function File} {@var{alpha2} =} normalizeAngle (@var{alpha}, @var{center}) ## Normalize an angle value within a 2*PI interval ## ## ALPHA2 = normalizeAngle(ALPHA); ## ALPHA2 is the same as ALPHA modulo 2*PI and is positive. ## ## ALPHA2 = normalizeAngle(ALPHA, CENTER); ## Specifies the center of the angle interval. ## If CENTER==0, the interval is [-pi ; +pi] ## If CENTER==PI, the interval is [0 ; 2*pi] (default). ## ## Example: ## # normalization between 0 and 2*pi (default) ## normalizeAngle(5*pi) ## ans = ## 3.1416 ## ## # normalization between -pi and +pi ## normalizeAngle(7*pi/2, 0) ## ans = ## -1.5708 ## ## References ## Follows the same convention as apache commons library, see: ## http://commons.apache.org/math/api-2.2/org/apache/commons/math/util/MathUtils.html## ## ## @seealso{vectorAngle, lineAngle} ## @end deftypefn function alpha = normalizeAngle(alpha, varargin) center = pi; if ~isempty(varargin) center = varargin{1}; end alpha = mod(alpha-center+pi, 2*pi) + center-pi; endfunction %!assert (pi/2, normalizeAngle (pi/2), 1e-6); %!assert (pi, normalizeAngle (pi), 1e-6); %!assert (3*pi/2, normalizeAngle (3*pi/2), 1e-6); %!assert (pi/2, normalizeAngle (pi/2, pi), 1e-6); %!assert (pi, normalizeAngle (pi, pi), 1e-6); %!assert (3*pi/2, normalizeAngle (3*pi/2, pi), 1e-6); %!test %! theta = linspace(0, 2*pi-.1, 100); %! assert(theta, normalizeAngle (theta), 1e-6); %!assert (0, normalizeAngle (0, 0), 1e-6); %!assert (pi/2, normalizeAngle (pi/2, 0), 1e-6); %!assert (-pi, normalizeAngle (-pi, 0), 1e-6); %!assert (-pi/2, normalizeAngle (7*pi/2, 0), 1e-6); %!test %! theta = linspace(-pi+.1, pi-.1, 100); %! assert(theta, normalizeAngle (theta, 0), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/distancePointLine.m0000644000000000000000000000013212676233417020764 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/distancePointLine.m0000644000175000017500000000542712676233417022153 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } distancePointLine (@var{point}, @var{line}) ## Minimum distance between a point and a line ## ## D = distancePointLine(POINT, LINE) ## Return the euclidean distance between line LINE and point POINT. ## ## LINE has the form : [x0 y0 dx dy], and POINT is [x y]. ## ## If LINE is N-by-4 array, result is N-by-1 array computes for each line. ## ## If POINT is N-by-2, then result is computed for each point. ## ## If both POINT and LINE are array, result is N-by-1, computed for each ## corresponding point and line. ## ## ## @seealso{lines2d, points2d, distancePoints, distancePointEdge} ## @end deftypefn function dist = distancePointLine (point, line) if size(line, 1)==1 && size(point, 1)>1 line = repmat(line, [size(point, 1) 1]); end if size(point, 1)==1 && size(line, 1)>1 point = repmat(point, [size(line, 1) 1]); end dx = line(:, 3); dy = line(:, 4); # compute position of points projected on line tp = ((point(:, 2) - line(:, 2)).*dy + (point(:, 1) - line(:, 1)).*dx) ./ (dx.*dx+dy.*dy); p0 = line(:, 1:2) + [tp tp].*[dx dy]; # compute distances between points and their projections dx = point - p0; dist = sqrt(sum(dx.*dx, 2)); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/edgeLength.m0000644000000000000000000000013212676233417017416 xustar0030 mtime=1459173135.365187495 30 atime=1459173135.365187495 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/edgeLength.m0000644000175000017500000000442512676233417020602 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{len} = } edgeLength (@var{edge}) ## Return length of an edge ## ## L = edgeLength(EDGE); ## Returns the length of an edge, with parametric representation: ## [x1 y1 x2 y2]. ## ## The function also works for several edges, in this case input is a ## [N*4] array, containing parametric representation of each edge, and ## output is a [N*1] array containing length of each edge. ## ## @seealso{edges2d, edgeAngle} ## @end deftypefn function len = edgeLength(varargin) # TODO : specify norm (euclidian, taxi, ...). nargs = length(varargin); if nargs == 1 edge = varargin{1}; len = sqrt(power(edge(:,3)-edge(:,1), 2) + power(edge(:,4)-edge(:,2), 2)); end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isParallel.m0000644000000000000000000000013212676233417017440 xustar0030 mtime=1459173135.445149373 30 atime=1459173135.445149373 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isParallel.m0000644000175000017500000000634112676233417020623 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isParallel (@var{v1}, @var{v2}) ## @deftypefnx {Function File} {@var{b} = } isParallel (@var{v1}, @var{v2},@var{tol}) ## Check parallelism of two vectors ## ## @var{v1} and @var{v2} are 2 row vectors of length Nd, Nd being the dimension, ## returns @code{true} if the vectors are parallel, and @code{false} otherwise. ## ## Also works when @var{v1} and @var{v2} are two [NxNd] arrays with same number of ## rows. In this case, return a [Nx1] array containing @code{true} at the positions ## of parallel vectors. ## ## @var{tol} specifies the accuracy of numerical computation. Default value is 1e-14. ## ## Example ## ## @example ## isParallel([1 2], [2 4]) ## ans = ## 1 ## isParallel([1 2], [1 3]) ## ans = ## 0 ## @end example ## ## @seealso{vectors2d, isPerpendicular, lines2d} ## @end deftypefn ## FIXME or erase me ## Also works when one of @var{v1} or @var{v2} is scalar and the other one is [NxNd] ## array, in this case return [Nx1] results. function b = isParallel(v1, v2, varargin) # default accuracy acc = 1e-14; if ~isempty(varargin) acc = abs(varargin{1}); end # adapt size of inputs if needed n1 = size(v1, 1); n2 = size(v2, 1); if n1 ~= n2 if n1 == 1 v1 = v1(ones(n2,1), :); elseif n2 == 1 v2 = v2(ones(n1,1), :); end end # performs computation if size(v1, 2) == 2 b = abs(v1(:, 1) .* v2(:, 2) - v1(:, 2) .* v2(:, 1)) < acc; else # computation in space b = vectorNorm(cross(v1, v2, 2)) < acc; end endfunction %!assert (isParallel ([1 2], [2 4])) %!assert (!isParallel ([1 2], [1 3])) %!error (isParallel (3, rand(4,2))) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/squareGrid.m0000644000000000000000000000013212676233417017456 xustar0030 mtime=1459173135.477134124 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/squareGrid.m0000644000175000017500000000545412676233417020645 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts} = } squaregrid (@var{bounds}, @var{origin}, @var{size}) ## Generate equally spaces points in plane. ## ## usage ## PTS = squareGrid(BOUNDS, ORIGIN, SIZE) ## generate points, lying in the window defined by BOUNDS (=[xmin ymin ## xmax ymax]), starting from origin with a constant step equal to size. ## ## Example ## PTS = squareGrid([0 0 10 10], [3 3], [4 2]) ## will return points : ## [3 1;7 1;3 3;7 3;3 5;7 5;3 7;7 7;3 9;7 9]; ## ## TODO: add possibility to use rotated grid ## ## @end deftypefn function varargout = squareGrid(bounds, origin, size) # find all x coordinate x1 = bounds(1) + mod(origin(1)-bounds(1), size(1)); x2 = bounds(3) - mod(bounds(3)-origin(1), size(1)); lx = (x1:size(1):x2)'; # find all y coordinate y1 = bounds(2) + mod(origin(2)-bounds(2), size(2)); y2 = bounds(4) - mod(bounds(4)-origin(2), size(2)); ly = (y1:size(2):y2)'; # number of points in each coord, and total number of points ny = length(ly); nx = length(lx); np = nx*ny; # create points pts = zeros(np, 2); for i=1:ny pts( (1:nx)'+(i-1)*nx, 1) = lx; pts( (1:nx)'+(i-1)*nx, 2) = ly(i); end # process output if nargout>0 varargout{1} = pts; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angle3Points.m0000644000000000000000000000013212676233417017716 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angle3Points.m0000644000175000017500000000552112676233417021100 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{alpha} =} angle3Points (@var{p1}, @var{p2}, @var{p3}) ## Computes the angle between the points @var{p1}, @var{p2} and @var{p3}. ## ## @var{p1}, @var{p2} and @var{p3} are either [1x2] arrays, or [Nx2] arrays, in this case ## @var{alpha} is a [Nx1] array. The angle computed is the directed angle between line ## (@var{p2}@var{p1}) and line (@var{p2}@var{p3}). ## ## Result is always given in radians, between 0 and 2*pi. ## ## @seealso{points2d, angles2d, angle2points} ## @end deftypefn function theta = angle3Points(varargin) if length(varargin)==3 p1 = varargin{1}; p2 = varargin{2}; p3 = varargin{3}; elseif length(varargin)==1 var = varargin{1}; p1 = var(1,:); p2 = var(2,:); p3 = var(3,:); end # angle line (P2 P1) theta = lineAngle(createLine(p2, p1), createLine(p2, p3)); endfunction %!test %! # all points inside window, possibly touching edges %! p1 = [10 0]; %! p2 = [0 0]; %! p3 = [0 10]; %! angle_ = angle3Points(p1, p2, p3); %! assert(pi/2, angle_,1e-6); %! angle_ = angle3Points([p1; p2; p3]); %! assert(pi/2, angle_, 1e-6); %!test %! p1 = [10 0; 20 0]; %! p2 = [0 0;0 0]; %! p3 = [0 10; 0 20]; %! angle_ = angle3Points(p1, p2, p3); %! assert(2, size(angle_, 1)); %! assert([pi/2;pi/2], angle_, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/readme.txt0000644000000000000000000000013012676233417017166 xustar0029 mtime=1459173135.47313603 29 atime=1459173135.47313603 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/readme.txt0000644000175000017500000000636412676233417020360 0ustar00juanpijuanpi00000000000000%% Copyright (c) 2011, INRA %% 2007-2011, David Legland %% 2011 Adapted to Octave by Juan Pablo Carbajal %% %% All rights reserved. %% (simplified BSD License) %% %% Redistribution and use in source and binary forms, with or without %% modification, are permitted provided that the following conditions are met: %% %% 1. Redistributions of source code must retain the above copyright notice, this %% list of conditions and the following disclaimer. %% %% 2. Redistributions in binary form must reproduce the above copyright notice, %% this list of conditions and the following disclaimer in the documentation %% and/or other materials provided with the distribution. %% %% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" %% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE %% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE %% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE %% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR %% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF %% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS %% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN %% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) %% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE %% POSSIBILITY OF SUCH DAMAGE. %% %% The views and conclusions contained in the software and documentation are %% those of the authors and should not be interpreted as representing official %% policies, either expressed or implied, of copyright holder. Description of the geom2d library. The aim of geom2d library is to handle and visualize geometric primitives such as points, lines, circles and ellipses, polylines and polygons... It provides low-level functions for manipulating geometrical primitives, making easier the development of more complex geometric algorithms. Some features of the library are: - creation of various shapes (points, circles, lines, ellipses, polylines, polygons...) through an intuitive syntax. Ex: createCircle(p1, p2, p3) to create a circle through 3 points. - derivation of new shapes: intersection between 2 lines, between line and circle, between polylines... or point on a curve from its parametrisation - functions for polylines and polygons: compute centroid and area, expand, self-intersections, clipping with half-plane... - manipulation of planar transformation. Ex.: ROT = createRotation(CENTER, THETA); P2 = transformPoint(P1, ROT); - direct drawing of shapes with specialized functions. Clipping is performed automatically for infinite shapes such as lines or rays. Ex: drawCircle([50 50 25]); % draw circle with radius 25 and center [50 50] drawLine([X0 Y0 DX DY]); % clip and draw straight line - measure distances (between points, a point and a line, a point and a group of points), angle (of a line, between 3 points), or test geometry (point on a line, on a circle). Additional help is provided in geom/Contents.m file, as well as summary files like 'points2d.m' or 'lines2d.m'. geometry-2.1.1/inst/geom2d/PaxHeaders.5293/boxes2d.m0000644000000000000000000000013212676233417016716 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/boxes2d.m0000644000175000017500000000407412676233417020102 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} boxes2d () ## Description of functions operating on bounding boxes. ## ## A box is represented as a set of limits in each direction: ## @example ## BOX = [XMIN XMAX YMIN YMAX]. ## @end example ## @noindent ## Boxes are used as result of computation for bounding boxes, and to clip ## shapes. ## ## @seealso{clipPoints, clipLine, clipEdge, clipRay, mergeBoxes, ## intersectBoxes, randomPointInBox, drawBox} ## @end deftypefn function boxes2d(varargin) help('boxes2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointInCircle.m0000644000000000000000000000013212676233417020406 xustar0030 mtime=1459173135.445149373 30 atime=1459173135.445149373 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointInCircle.m0000644000175000017500000000464612676233417021577 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointInCircle (@var{point}, @var{circle}) ## Test if a point is located inside a given circle ## ## B = isPointInCircle(POINT, CIRCLE) ## Returns true if point is located inside the circle, i.e. if distance to ## circle center is lower than the circle radius. ## ## B = isPointInCircle(POINT, CIRCLE, TOL) ## Specifies the tolerance value ## ## Example: ## isPointInCircle([1 0], [0 0 1]) ## isPointInCircle([0 0], [0 0 1]) ## returns true, whereas ## isPointInCircle([1 1], [0 0 1]) ## return false ## ## @seealso{circles2d, isPointOnCircle} ## @end deftypefn function b = isPointInCircle(point, circle, varargin) # extract computation tolerance tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end d = sqrt(sum(power(point - circle(:,1:2), 2), 2)); b = d-circle(:,3)<=tol; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/vectors2d.m0000644000000000000000000000013212676233417017263 xustar0030 mtime=1459173135.485130312 30 atime=1459173135.485130312 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/vectors2d.m0000644000175000017500000000420212676233417020440 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} vectors2d () ## Description of functions operating on plane vectors ## ## A vector is defined by its two cartesian coordinates, put into a row ## vector of 2 elements: ## @code{V = [vx vy];} ## ## Several vectors are stored in a matrix with two columns, one for the ## x-coordinate, one for the y-coordinate. ## @code{VS = [vx1 vy1 ; vx2 vy2 ; vx3 vy3];} ## ## @seealso{vectorNorm, vectorAngle, isPerpendicular, isParallel, ## normalizeVector, transformVector, rotateVector} ## @end deftypefn function vectors2d help('vectors2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/medianLine.m0000644000000000000000000000013212676233417017415 xustar0030 mtime=1459173135.457143654 30 atime=1459173135.457143654 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/medianLine.m0000644000175000017500000001102412676233417020572 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} = } medianLine (@var{p1}, @var{p2}) ## @deftypefnx {Function File} {@var{line} = } medianLine (@var{pts}) ## @deftypefnx {Function File} {@var{line} = } medianLine (@var{edge}) ## Create a median line between two points. ## ## Create the median line of points @var{p1} and @var{p2}, that is the line containing ## all points located at equal distance of @var{p1} and @var{p2}. ## ## Creates the median line of 2 points, given as a 2*2 array @var{pts}. Array has ## the form: ## [ [ x1 y1 ] ; [ x2 y2 ] ] ## ## Creates the median of the @var{edge}. @var{edge} is a 1*4 array, containing [X1 Y1] ## coordinates of first point, and [X2 Y2], the coordinates of the second ## point. ## ## Example ## ## @example ## # Draw the median line of two points ## P1 = [10 20]; ## P2 = [30 50]; ## med = medianLine(P1, P2); ## figure; axis square; axis([0 100 0 100]); ## drawEdge([P1 P2], 'linewidth', 2, 'color', 'k'); ## drawLine(med) ## ## # Draw the median line of an edge ## P1 = [50 60]; ## P2 = [80 30]; ## edge = createEdge(P1, P2); ## figure; axis square; axis([0 100 0 100]); ## drawEdge(edge, 'linewidth', 2) ## med = medianLine(edge); ## drawLine(med) ## @end example ## ## @seealso{lines2d, createLine, orthogonalLine} ## @end deftypefn function lin = medianLine(varargin) nargs = length(varargin); x0 = 0; y0 = 0; dx = 0; dy = 0; if nargs == 1 tab = varargin{1}; if size(tab, 2)==2 # input is an array of two points x0 = tab(1,1); y0 = tab(1,2); dx = tab(2,1)-x0; dy = tab(2,2)-y0; else # input is an edge x0 = tab(:, 1); y0 = tab(:, 2); dx = tab(:, 3) - tab(:, 1); dy = tab(:, 4) - tab(:, 2); end elseif nargs==2 # input is given as two points, or two point arrays p1 = varargin{1}; p2 = varargin{2}; x0 = p1(:, 1); y0 = p1(:, 2); dx = bsxfun(@minus, p2(:, 1), x0); dy = bsxfun(@minus, p2(:, 2), y0); else error('Too many input arguments'); end # compute median using middle point of the edge, and the direction vector # rotated by 90 degrees counter-clockwise lin = [bsxfun(@plus, x0, dx/2), bsxfun(@plus, y0, dy/2), -dy, dx]; endfunction %!shared privpath %! privpath = [fileparts(which('geom2d_Contents')) filesep() 'private']; %!test %! addpath (privpath,'-end') %! p1 = [0 0]; %! p2 = [10 0]; %! exp = [5 0 0 10]; %! lin = medianLine(p1, p2); %! assertElementsAlmostEqual(exp, lin); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! p1 = [0 0]; %! p2 = [10 0]; %! exp = [5 0 0 10]; %! lin = medianLine([p1 p2]); %! assertElementsAlmostEqual(exp, lin); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! p1 = [0 0; 10 10]; %! p2 = [10 0;10 20]; %! exp = [5 0 0 10; 10 15 -10 0]; %! lin = medianLine(p1, p2); %! assertElementsAlmostEqual(exp, lin); %! rmpath (privpath); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/midPoint.m0000644000000000000000000000013212676233417017133 xustar0030 mtime=1459173135.457143654 30 atime=1459173135.457143654 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/midPoint.m0000644000175000017500000001104612676233417020314 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{mid} = } midPoint (@var{p1}, @var{p2}) ## @deftypefnx {Function File} {@var{mid} = } midPoint (@var{edge}) ## @deftypefnx {Function File} {[@var{midx}, @var{midy}] = } midPoint (@var{edge}) ## Middle point of two points or of an edge ## ## Computes the middle point of the two points @var{p1} and @var{p2}. ## ## If an edge is given, computes the middle point of the edge given by @var{edge}. ## @var{edge} has the format: [X1 Y1 X2 Y2], and @var{mid} has the format [XMID YMID], ## with XMID = (X1+X2)/2, and YMID = (Y1+Y2)/2. ## ## If two output arguments are given, it returns the result as two separate variables or arrays. ## ## Works also when @var{edge} is a N-by-4 array, in this case the result is a ## N-by-2 array containing the midpoint of each edge. ## ## Example ## ## @example ## p1 = [10 20]; ## p2 = [30 40]; ## midPoint([p1 p2]) ## ans = ## 20 30 ## @end example ## ## @seealso{edges2d, points2d} ## @end deftypefn function varargout = midPoint(varargin) if nargin == 1 # input is an edge edge = varargin{1}; mid = [mean(edge(:, [1 3]), 2) mean(edge(:, [2 4]), 2)]; elseif nargin == 2 # input are two points p1 = varargin{1}; p2 = varargin{2}; # assert inputs are equal n1 = size(p1, 1); n2 = size(p2, 1); if n1 != n2 && min(n1, n2)>1 error('geom2d:midPoint', ... 'Inputs must have same size, or one must have length 1'); end # compute middle point mid = bsxfun(@plus, p1, p2) / 2; end # process output arguments if nargout<=1 varargout{1} = mid; else varargout = {mid(:,1), mid(:,2)}; end endfunction %!test %! p1 = [10 20]; %! p2 = [30 40]; %! exp = [20 30]; %! mid = midPoint(p1, p2); %! assert (mid, exp); %!test %! p1 = [ ... %! 10 20 ; ... %! 30 40 ; ... %! 50 60 ; ... %! ]; %! p2 = [ ... %! 30 40; ... %! 50 60; ... %! 70 80]; %! exp = [... %! 20 30; ... %! 40 50; ... %! 60 70]; %! mid = midPoint(p1, p2); %! assert (mid, exp); %!test %! p1 = [30 40]; %! p2 = [ ... %! 30 40; ... %! 50 60; ... %! 70 80]; %! exp = [... %! 30 40; ... %! 40 50; ... %! 50 60]; %! mid = midPoint(p1, p2); %! assert (mid, exp); %!test %! p1 = [ ... %! 10 20 ; ... %! 30 40 ; ... %! 50 60 ; ... %! ]; %! p2 = [30 40]; %! exp = [... %! 20 30; ... %! 30 40; ... %! 40 50]; %! mid = midPoint(p1, p2); %! assert (mid, exp); %!test %! p1 = [ ... %! 10 20 ; ... %! 30 40 ; ... %! 50 60 ; ... %! ]; %! p2 = [30 40]; %! expX = [20 ; 30 ; 40]; %! expY = [30 ; 40 ; 50]; %! [x y] = midPoint(p1, p2); %! assert (x, expX); %! assert (y, expY); %!test %! edge = [10 20 30 40]; %! exp = [20 30]; %! mid = midPoint(edge); %! assert (mid, exp); %! edge = [10 20 30 40; 30 40 50 60; 50 60 70 80]; %! exp = [20 30;40 50; 60 70]; %! mid = midPoint(edge); %! assert (mid, exp); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectBoxes.m0000644000000000000000000000013212676233417020351 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectBoxes.m0000644000175000017500000000506012676233417021531 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{box} =} intersectBoxes (@var{box1}, @var{box2}) ## Intersection of two bounding boxes. ## ## Example ## ## @example ## box1 = [5 20 5 30]; ## box2 = [0 15 0 15]; ## intersectBoxes(box1, box2) ## ans = ## 5 15 5 15 ## @end example ## ## @seealso{boxes2d, drawBox, mergeBoxes} ## @end deftypefn function bb = intersectBoxes(box1, box2) # unify sizes of data if size(box1,1) == 1 box1 = repmat(box1, size(box2,1), 1); elseif size(box2, 1) == 1 box2 = repmat(box2, size(box1,1), 1); elseif size(box1,1) != size(box2,1) error('geom2d:Error',"Bad size for inputs.\n"); end # compute extreme coords mini = min(box1(:,[2 4]), box2(:,[2 4])); maxi = max(box1(:,[1 3]), box2(:,[1 3])); # concatenate result into a new box structure bb = [maxi(:,1) mini(:,1) maxi(:,2) mini(:,2)]; endfunction %!test %! box1 = [5 20 10 25]; %! box2 = [0 15 15 20]; %! res = [5 15 15 20]; %! bb = intersectBoxes(box1, box2); %! assert (res, bb, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/centroid.m0000644000000000000000000000013212676233417017157 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/centroid.m0000644000175000017500000001010012676233417020326 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{c} = } centroid (@var{points}) ## @deftypefnx {Function File} {@var{c} = } centroid (@var{px}, @var{py}) ## @deftypefnx {Function File} {@var{c} = } centroid (@dots{}, @var{mass}) ## Compute centroid (center of mass) of a set of points. ## ## Computes the ND-dimensional centroid of a set of points. ## @var{points} is an array with as many rows as the number of points, and as ## many columns as the number of dimensions. ## @var{px} and @var{py} are two column vectors containing coordinates of the ## 2-dimensional points. ## The result @var{c} is a row vector with ND columns. ## ## If @var{mass} is given, computes center of mass of @var{points}, weighted by coefficient @var{mass}. ## @var{points} is a Np-by-Nd array, @var{mass} is Np-by-1 array, and @var{px} and @var{py} are ## also both Np-by-1 arrays. ## ## Example: ## ## @example ## pts = [2 2;6 1;6 5;2 4]; ## centroid(pts) ## ans = ## 4 3 ##@end example ## ## @seealso{points2d, polygonCentroid} ## @end deftypefn function center = centroid(varargin) ## extract input arguments # use empty mass by default mass = []; if nargin==1 # give only array of points pts = varargin{1}; elseif nargin==2 # either POINTS+MASS or PX+PY var = varargin{1}; if size(var, 2)>1 # arguments are POINTS, and MASS pts = var; mass = varargin{2}; else # arguments are PX and PY pts = [var varargin{2}]; end elseif nargin==3 # arguments are PX, PY, and MASS pts = [varargin{1} varargin{2}]; mass = varargin{3}; end ## compute centroid if isempty(mass) # no weight center = mean(pts); else # format mass to have sum equal to 1, and column format mass = mass(:)/sum(mass(:)); # compute weighted centroid center = sum(bsxfun(@times, pts, mass), 1); # equivalent to: # center = sum(pts .* mass(:, ones(1, size(pts, 2)))); end endfunction %!test %! points = [0 0;10 0;10 10;0 10]; %! centro = centroid(points); %! assert ([5 5], centro, 1e-6); %!test %! points = [0 0;10 0;10 10;0 10]; %! centro = centroid(points(:,1), points(:,2)); %! assert ([5 5], centro, 1e-6); %!test %! points = [0 0;30 0;30 30;0 30]; %! centro = centroid(points, [1;1;1;3]); %! assert ([10 20], centro, 1e-6); %!test %! points = [0 0;30 0;30 30;0 30]; %! centro = centroid(points(:,1), points(:,2), [1;1;1;3]); %! assert ([10 20], centro, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createLineReflection.m0000644000000000000000000000013212676233417021436 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createLineReflection.m0000644000175000017500000000471012676233417022617 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } function_name (@var{line}) ## Create the the 3x3 matrix of a line reflection. ## ## Where @var{line} is given as [x0 y0 dx dy], return the affine tansform ## corresponding to the desired line reflection. ## ## @seealso{lines2d, transforms2d, transformPoint, ## createTranslation, createHomothecy, createScaling} ## @end deftypefn function trans = createLineReflection(line) # extract line parameters x0 = line(:,1); y0 = line(:,2); dx = line(:,3); dy = line(:,4); # normalisation coefficient of line direction vector delta = dx*dx + dy*dy; # compute coefficients of transform m00 = (dx*dx - dy*dy)/delta; m01 = 2*dx*dy/delta; m02 = 2*dy*(dy*x0 - dx*y0)/delta; m10 = 2*dx*dy/delta; m11 = (dy*dy - dx*dx)/delta; m12 = 2*dx*(dx*y0 - dy*x0)/delta; # create transformation trans = [m00 m01 m02; m10 m11 m12; 0 0 1]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPerpendicular.m0000644000000000000000000000013212676233417020501 xustar0030 mtime=1459173135.445149373 30 atime=1459173135.445149373 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPerpendicular.m0000644000175000017500000000632312676233417021664 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPerpendicular (@var{v1}, @var{v2}) ## @deftypefnx {Function File} {@var{b} = } isPerpendicula (@var{v1}, @var{v2},@var{tol}) ## heck orthogonality of two vectors. ## ## @var{v1} and @var{v2} are 2 row vectors of length Nd, Nd being the dimension, ## returns @code{true} if the vectors are perpendicular, and @code{false} otherwise. ## ## Also works when @var{v1} and @var{v2} are two [NxNd] arrays with same number of ## rows. In this case, return a [Nx1] array containing @code{true} at the positions ## of parallel vectors. ## ## @var{tol} specifies the accuracy of numerical computation. Default value is 1e-14. ## ## Example ## ## @example # isPerpendicular([1 2 0], [0 0 2]) ## ans = ## 1 # isPerpendicular([1 2 1], [1 3 2]) ## ans = ## 0 ## @end example ## ## @seealso{vectors2d, isParallel, lines2d} ## @end deftypefn ## FIXME or erase me ## Also works when one of @var{v1} or @var{v2} is scalar and the other one is [NxNd] ## array, in this case return [Nx1] results. function b = isPerpendicular(v1, v2, varargin) # default accuracy acc = 1e-14; if ~isempty (varargin) acc = abs (varargin{1}); end # adapt size of inputs n1 = size (v1, 1); n2 = size (v2, 1); if n1~=n2 if n1==1 v1 = v1(ones (n2, 1), :); elseif n2==1 v2 = v2(ones (n1, 1), :); else error('Inputs must either have same size, or one must be scalar'); end end # performs test b = abs (dot (v1, v2, 2)) < acc; endfunction %!assert (isPerpendicular ([1 2 0], [0 0 2])) %!assert (!isPerpendicular([1 2 1], [1 3 2])) %!error (isPerpendicular(1, rand(4,3))) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/clipRay.m0000644000000000000000000000013212676233417016753 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/clipRay.m0000644000175000017500000001325012676233417020133 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{edge} @var{inside}] =} clipRay (@var{ray}, @var{box}) ## Clip a ray with a box. ## ## @var{ray} is a straight ray given as a 4 element row vector: [x0 y0 dx dy], ## with (x0 y0) being the origin of the ray and (dx dy) its direction ## vector, @var{box} is the clipping box, given by its extreme coordinates: ## [xmin xmax ymin ymax]. ## The result is given as an edge, defined by the coordinates of its 2 ## extreme points: [x1 y1 x2 y2]. ## If the ray does not intersect the box, [NaN NaN NaN NaN] is returned. ## ## Function works also if @var{ray} is a Nx4 array, if @var{box} is a Nx4 array, or ## if both @var{ray} and @var{box} are Nx4 arrays. In these cases, @var{edge} is a Nx4 ## array. ## ## @seealso{rays2d, boxes2d, edges2d, clipLine, drawRay} ## @end deftypefn function [edge isInside] = clipRay(ray, bb) # adjust size of two input arguments if size(ray, 1)==1 ray = repmat(ray, size(bb, 1), 1); elseif size(bb, 1)==1 bb = repmat(bb, size(ray, 1), 1); elseif size(ray, 1) != size(bb, 1) error('bad sizes for input'); end # first compute clipping of supporting line edge = clipLine(ray, bb); # detectes valid edges (edges outside box are all NaN) inds = find(isfinite(edge(:, 1))); # compute position of edge extremities relative to the ray pos1 = linePosition(edge(inds,1:2), ray(inds,:)); pos2 = linePosition(edge(inds,3:4), ray(inds,:)); # if first point is before ray origin, replace by origin edge(inds(pos1<0), 1:2) = ray(inds(pos1<0), 1:2); # if last point of edge is before origin, set all edge to NaN edge(inds(pos2<0), :) = NaN; # eventually returns result about inside or outside if nargout>1 isInside = isfinite(edge(:,1)); end endfunction %!shared bb %! bb = [0 100 0 100]; %!test # inside %! origin = [30 40]; %! direction = [10 0]; %! ray = [origin direction]; %! expected = [30 40 100 40]; %! assert (expected, clipRay(ray, bb), 1e-6); %!test # outside %! origin = [30 140]; %! direction = [10 0]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # line inside, but ray outside %! origin = [130 40]; %! direction = [10 0]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # inside %! origin = [30 40]; %! direction = [-10 0]; %! ray = [origin direction]; %! expected = [30 40 0 40]; %! assert (expected, clipRay(ray, bb), 1e-6); %!test # outside %! origin = [30 140]; %! direction = [-10 0]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # line inside, but ray outside %! origin = [-30 40]; %! direction = [-10 0]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # inside %! origin = [30 40]; %! direction = [0 10]; %! ray = [origin direction]; %! expected = [30 40 30 100]; %! assert (expected, clipRay(ray, bb), 1e-6); %!test # outside %! origin = [130 40]; %! direction = [0 10]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # line inside, but ray outside %! origin = [30 140]; %! direction = [0 10]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # inside %! origin = [30 40]; %! direction = [0 -10]; %! ray = [origin direction]; %! expected = [30 40 30 0]; %! assert (expected, clipRay(ray, bb), 1e-6); %!test # outside %! origin = [130 40]; %! direction = [0 -10]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test # line inside, but ray outside %! origin = [30 -40]; %! direction = [0 -10]; %! ray = [origin direction]; %! assert (sum(isnan(clipRay(ray, bb)))==4); %!test %! origins = [30 40;30 40;30 140;130 40]; %! directions = [10 0;0 10;10 0;0 10]; %! rays = [origins directions]; %! expected = [30 40 100 40;30 40 30 100;NaN NaN NaN NaN;NaN NaN NaN NaN]; %! clipped = clipRay(rays, bb); %! assert (expected, clipped, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/clipEdge.m0000644000000000000000000000013212676233417017064 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/clipEdge.m0000644000175000017500000001703612676233417020252 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{edge2} =} clipEdge (@var{edge}, @var{box}) ## Clip an edge with a rectangular box. ## ## @var{edge}: [x1 y1 x2 y2], ## @var{box} : [xmin xmax ; ymin ymax] or [xmin xmax ymin ymax]; ## return : ## @var{edge2} = [xc1 yc1 xc2 yc2]; ## ## If clipping is null, return [0 0 0 0]; ## ## if @var{edge} is a [nx4] array, return an [nx4] array, corresponding to each ## clipped edge. ## ## @seealso{edges2d, boxes2d, clipLine} ## @end deftypefn function edge2 = clipEdge(edge, bb) # process data input if size(bb, 1)==2 bb = bb'; end # get limits of window xmin = bb(1); xmax = bb(2); ymin = bb(3); ymax = bb(4); # convert window limits into lines lineX0 = [xmin ymin xmax-xmin 0]; lineX1 = [xmin ymax xmax-xmin 0]; lineY0 = [xmin ymin 0 ymax-ymin]; lineY1 = [xmax ymin 0 ymax-ymin]; # compute outcodes of each vertex p11 = edge(:,1)xmax; p22 = edge(:,3)>xmax; p13 = edge(:,2)ymax; p24 = edge(:,4)>ymax; out1 = [p11 p12 p13 p14]; out2 = [p21 p22 p23 p24]; # detect edges totally inside window -> no clip. inside = sum(out1 | out2, 2)==0; # detect edges totally outside window outside = sum(out1 & out2, 2)>0; # select edges not totally outside, and process separately edges totally # inside window ind = find(~(inside | outside)); edge2 = zeros(size(edge)); edge2(inside, :) = edge(inside, :); for i=1:length(ind) # current edge iedge = edge(ind(i), :); # compute intersection points with each line of bounding window px0 = intersectLineEdge(lineX0, iedge); px1 = intersectLineEdge(lineX1, iedge); py0 = intersectLineEdge(lineY0, iedge); py1 = intersectLineEdge(lineY1, iedge); # create array of points points = [px0; px1; py0; py1; iedge(1:2); iedge(3:4)]; # remove infinite points (edges parallel to box edges) points = points(all(isfinite(points), 2), :); # sort points by x then y points = sortrows(points); # get center positions between consecutive points centers = (points(2:end,:) + points(1:end-1,:))/2; # find the centers (if any) inside window inside = find( centers(:,1)>=xmin & centers(:,2)>=ymin & ... centers(:,1)<=xmax & centers(:,2)<=ymax); # if multiple segments are inside box, which can happen due to finite # resolution, only take the longest segment if length(inside)>1 # compute delta vectors of the segments dv = points(inside+1,:) - points(inside,:); # compute lengths of segments len = hypot(dv(:,1), dv(:,2)); # find index of longest segment [a, I] = max(len); ##ok inside = inside(I); end # if one of the center points is inside box, then the according edge # segment is indide box if length(inside)==1 # restore same direction of edge if iedge(1)>iedge(3) || (iedge(1)==iedge(3) && iedge(2)>iedge(4)) edge2(i, :) = [points(inside+1,:) points(inside,:)]; else edge2(i, :) = [points(inside,:) points(inside+1,:)]; end end end # end of loop of edges endfunction %!demo %! bb = [0 100 0 100]; %! edge = [-10 10 90 110]; %! ec = clipEdge (edge, bb); %! %! drawBox(bb,'color','k'); %! line(edge([1 3]),edge([2 4]),'color','b'); %! line(ec([1 3]),ec([2 4]),'color','r','linewidth',2); %! axis tight %! v = axis (); %! axis(v+[0 10 -10 0]) %!shared bb %! bb = [0 100 0 100]; %!assert (clipEdge([20 30 80 60], bb), [20 30 80 60],1e-6); %!assert (clipEdge([0 30 80 60], bb), [0 30 80 60],1e-6); %!assert (clipEdge([0 30 100 60], bb), [0 30 100 60],1e-6); %!assert (clipEdge([30 0 80 100], bb), [30 0 80 100],1e-6); %!assert (clipEdge([0 0 100 100], bb), [0 0 100 100],1e-6); %!assert (clipEdge([0 100 100 0], bb), [0 100 100 0],1e-6); %!assert (clipEdge([20 60 120 60], bb), [20 60 100 60],1e-6); %!assert (clipEdge([-20 60 80 60], bb), [0 60 80 60],1e-6); %!assert (clipEdge([20 60 20 160], bb), [20 60 20 100],1e-6); %!assert (clipEdge([20 -30 20 60], bb), [20 0 20 60],1e-6); %!assert (clipEdge([120 30 180 60], bb), [0 0 0 0],1e-6); %!assert (clipEdge([-20 30 -80 60], bb), [0 0 0 0],1e-6); %!assert (clipEdge([30 120 60 180], bb), [0 0 0 0],1e-6); %!assert (clipEdge([30 -20 60 -80], bb), [0 0 0 0],1e-6); %!assert (clipEdge([-120 110 190 150], bb), [0 0 0 0],1e-6); %!assert ([50 50 100 50], clipEdge([50 50 150 50], bb),1e-6); %!assert ([50 50 0 50], clipEdge([50 50 -50 50], bb),1e-6); %!assert ([50 50 50 100], clipEdge([50 50 50 150], bb),1e-6); %!assert ([50 50 50 0], clipEdge([50 50 50 -50], bb),1e-6); %!assert ([80 50 100 70], clipEdge([80 50 130 100], bb),1e-6); %!assert ([80 50 100 30], clipEdge([80 50 130 0], bb),1e-6); %!assert ([20 50 0 70], clipEdge([20 50 -30 100], bb),1e-6); %!assert ([20 50 0 30], clipEdge([20 50 -30 0], bb),1e-6); %!assert ([50 80 70 100], clipEdge([50 80 100 130], bb),1e-6); %!assert ([50 80 30 100], clipEdge([50 80 0 130], bb),1e-6); %!assert ([50 20 70 0], clipEdge([50 20 100 -30], bb),1e-6); %!assert ([50 20 30 0], clipEdge([50 20 0 -30], bb),1e-6); %!assert ([100 50 50 50], clipEdge([150 50 50 50], bb),1e-6); %!assert ([0 50 50 50], clipEdge([-50 50 50 50], bb),1e-6); %!assert ([50 100 50 50], clipEdge([50 150 50 50], bb),1e-6); %!assert ([50 0 50 50], clipEdge([50 -50 50 50], bb),1e-6); %!assert ([100 70 80 50], clipEdge([130 100 80 50], bb),1e-6); %!assert ([100 30 80 50], clipEdge([130 0 80 50], bb),1e-6); %!assert ([0 70 20 50], clipEdge([-30 100 20 50], bb),1e-6); %!assert ([0 30 20 50], clipEdge([-30 0 20 50], bb),1e-6); %!assert ([70 100 50 80], clipEdge([100 130 50 80], bb),1e-6); %!assert ([30 100 50 80], clipEdge([0 130 50 80], bb),1e-6); %!assert ([70 0 50 20], clipEdge([100 -30 50 20], bb),1e-6); %!assert ([30 0 50 20], clipEdge([0 -30 50 20], bb),1e-6); %!assert ([0 20 80 100], clipEdge([-10 10 90 110], bb),1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/rays2d.m0000644000000000000000000000013012676233417016552 xustar0029 mtime=1459173135.47313603 29 atime=1459173135.47313603 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/rays2d.m0000644000175000017500000000454612676233417017744 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} rays2d () ## Description of functions operating on planar rays ## ## A ray is defined by a point (its origin), and a vector (its ## direction). The different parameters are bundled into a row vector: ## @code{RAY = [x0 y0 dx dy];} ## ## The ray contains all the points (x,y) such that: ## x = x0 + t*dx ## y = y0 + t*dy; ## for all t>0 ## ## Contrary to a (straight) line, the points located before the origin do ## not belong to the ray. ## However, as rays and lines have the same representation, some functions ## working on lines are also working on rays (like @code{transformLine}). ## ## @seealso{points2d, vectors2d, lines2d, createRay, bisector, isPointOnRay, ## clipRay, drawRay} ## @end deftypefn function rays2d(varargin) help('rays2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawEllipseArc.m0000644000000000000000000000013212676233417020251 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawEllipseArc.m0000644000175000017500000001147312676233417021436 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawEllipseArc (@var{arc}) ## Draw an ellipse arc on the current axis. ## ## drawEllipseArc(ARC) ## draw ellipse arc specified by ARC. ARC has the format: ## ARC = [XC YC A B THETA T1 T2] ## or: ## ARC = [XC YC A B T1 T2] (isothetic ellipse) ## with center (XC, YC), main axis of half-length A, second axis of ## half-length B, and ellipse arc running from t1 to t2 (both in degrees, ## in Counter-Clockwise orientation). ## ## Parameters can also be arrays. In this case, all arrays are suposed to ## have the same size... ## ## @example ## # draw an ellipse arc: center = [10 20], radii = 50 and 30, theta = 45 ## arc = [10 20 50 30 45 -90 270]; ## figure; ## axis([-50 100 -50 100]); axis equal; ## hold on ## drawEllipseArc(arc, 'color', 'r') ## ## # draw another ellipse arc, between angles -60 and 70 ## arc = [10 20 50 30 45 -60 (60+70)]; ## figure; ## axis([-50 100 -50 100]); axis equal; ## hold on ## drawEllipseArc(arc, 'LineWidth', 2); ## ray1 = createRay([10 20], deg2rad(-60+45)); ## drawRay(ray1) ## ray2 = createRay([10 20], deg2rad(70+45)); ## drawRay(ray2) ## @end example ## ## @seealso{ellipses2d, drawEllipse, drawCircleArc} ## @end deftypefn function varargout = drawEllipseArc(varargin) ## Extract input arguments # extract dawing style strings styles = {}; for i = 1:length(varargin) if ischar(varargin{i}) styles = varargin(i:end); varargin(i:end) = []; break; end end if length(varargin)==1 ellipse = varargin{1}; x0 = ellipse(1); y0 = ellipse(2); a = ellipse(3); b = ellipse(4); if size(ellipse, 2)>6 theta = ellipse(5); start = ellipse(6); extent = ellipse(7); else theta = zeros(size(x0)); start = ellipse(5); extent = ellipse(6); end elseif length(varargin)>=6 x0 = varargin{1}; y0 = varargin{2}; a = varargin{3}; b = varargin{4}; if length(varargin)>6 theta = varargin{5}; start = varargin{6}; extent = varargin{7}; else theta = zeros(size(x0)); start = varargin{5}; extent = varargin{6}; end else error('drawellipse: please specify center x, center y and radii a and b'); end ## Drawing # allocate memory for handles h = zeros(size(x0)); for i = 1:length(x0) # start and end angles t1 = deg2rad(start); t2 = t1 + deg2rad(extent); # vertices of ellipse t = linspace(t1, t2, 60); # convert angles to ellipse parametrisation sup = cos(t) > 0; t(sup) = atan(a(i) / b(i) * tan(t(sup))); t(~sup) = atan2(a(i) / b(i) * tan(2*pi - t(~sup)), -1); t = mod(t, 2*pi); # precompute cos and sin of theta (given in degrees) cot = cosd(theta(i)); sit = sind(theta(i)); # compute position of points xt = x0(i) + a(i)*cos(t)*cot - b(i)*sin(t)*sit; yt = y0(i) + a(i)*cos(t)*sit + b(i)*sin(t)*cot; h(i) = plot(xt, yt, styles{:}); end ## Process output arguments if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createLine.m0000644000000000000000000000013212676233417017423 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createLine.m0000644000175000017500000001400412676233417020601 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} =} createLine(varargin) ## Create a straight line from 2 points, or from other inputs ## ## Line is represented in a parametric form : [x0 y0 dx dy] ## x = x0 + t*dx ## y = y0 + t*dy; ## ## ## L = createLine(p1, p2); ## Returns the line going through the two given points. ## ## L = createLine(x0, y0, dx, dy); ## Returns the line going through point (x0, y0) and with direction ## vector(dx, dy). ## ## L = createLine(LINE); ## where LINE is an array of 4 values, creates the line going through the ## point (LINE(1) LINE(2)), and with direction given by vector (LINE(3) ## LINE(4)). ## ## L = createLine(THETA); ## Create a polar line originated at (0,0) and with angle THETA. ## ## L = createLine(RHO, THETA); ## Create a polar line with normal theta, and with min distance to origin ## equal to rho. rho can be negative, in this case, the line is the same ## as with CREATELINE(-rho, theta+pi), but the orientation is different. ## ## ## Note: in all cases, parameters can be vertical arrays of the same ## dimension. The result is then an array of lines, of dimensions [N*4]. ## ## NOTE : A line can also be represented with a 1*5 array : ## [x0 y0 dx dy t]. ## whith 't' being one of the following : ## - t=0 : line is a singleton (x0,y0) ## - t=1 : line is an edge segment, between points (x0,y0) and (x0+dx, ## y0+dy). ## - t=Inf : line is a Ray, originated from (x0,y0) and going to infinity ## in the direction(dx,dy). ## - t=-Inf : line is a Ray, originated from (x0,y0) and going to infinity ## in the direction(-dx,-dy). ## - t=NaN : line is a real straight line, and contains all points ## verifying the above equation. ## This seems us a convenient way to represent uniformly all kind of lines ## (including edges, rays, and even point). ## ## NOTE2 : Any line object can be represented using a 1x6 array : ## [x0 y0 dx dy t0 t1] ## the first 4 parameters define the supporting line, ## t0 represent the position of the first point on the line, ## and t1 the position of the last point. ## * for edges : t0 = 0, and t1=1 ## * for straight lines : t0 = -inf, t1=inf ## * for rays : t0=0, t1=inf (or t0=-inf,t1=0 for inverted ray). ## I propose to call these objects 'lineArc' ## ## @seealso{lines2d, createEdge, createRay} ## @end deftypefn function line = createLine(varargin) if length(varargin)==1 # Only one input parameter. It can be : # - line angle # - array of four parameters # TODO : add control for arrays of lines. var = varargin{1}; if size(var, 2)==4 # 4 parameters of the line in a single array. line = var; elseif size(var, 2)==1 # 1 parameter : angle of the line, going through origin. line = [zeros(size(var)) zeros(size(var)) cos(var) sin(var)]; else error('wrong number of dimension for arg1 : can be 1 or 4'); end elseif length(varargin)==2 # 2 input parameters. They can be : # - line angle and signed distance to origin. # - 2 points, then 2 arrays of 1*2 double. v1 = varargin{1}; v2 = varargin{2}; if size(v1, 2)==1 # first param is angle of line, and second param is signed distance # to origin. line = [v1.*cos(v2) v1.*sin(v2) -sin(v2) cos(v2)]; else # first input parameter is first point, and second input is the # second point. line = [v1(:,1), v1(:,2), v2(:,1)-v1(:,1), v2(:,2)-v1(:,2)]; end elseif length(varargin)==3 # 3 input parameters : # first one is a point belonging to the line, # second and third ones are direction vector of the line (dx and dy). p = varargin{1}; line = [p(:,1) p(:,2) varargin{2} varargin{3}]; elseif length(varargin)==4 # 4 input parameters : # they are x0, y0 (point belongng to line) and dx, dy (direction vector # of the line). # All parameters should have the same size. line = [varargin{1} varargin{2} varargin{3} varargin{4}]; else error('Wrong number of arguments in ''createLine'' '); end endfunction %!test %! p1 = [1 1]; %! p2 = [2 3]; %! lin = createLine(p1, p2); %! assert (p1, lin(1,1:2), 1e-6); %! assert (p2-p1, lin(1,3:4), 1e-6); %!test %! p1 = [1 1;1 1]; %! p2 = [2 3;2 4]; %! lin = createLine(p1, p2); %! assert (2, size(lin, 1)); %! assert (p1, lin(:,1:2), 1e-6); %! assert (p2-p1, lin(:,3:4), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointOnRay.m0000644000000000000000000000013212676233417017746 xustar0030 mtime=1459173135.449147467 30 atime=1459173135.449147467 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointOnRay.m0000644000175000017500000000656212676233417021136 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointOnRay (@var{point}, @var{ray}) ## @deftypefnx {Function File} {@var{b} = } isPointOnRay (@var{point}, @var{ray}, @var{tol}) ## Test if a point belongs to a ray ## ## @var{b} = isPointOnRay(@var{point}, @var{ray}); ## Returns @code{true} if point @var{point} belongs to the ray @var{ray}. ## @var{point} is given by [x y] and RAY by [x0 y0 dx dy]. @var{tol} gives the ## tolerance for the calculations. ## ## @seealso{rays2d, points2d, isPointOnLine} ## @end deftypefn function b = isPointOnRay(point, ray, varargin) # extract computation tolerance tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end # number of rays and points Nr = size(ray, 1); Np = size(point, 1); # if several rays or several points, adapt sizes of arrays x0 = repmat(ray(:,1)', Np, 1); y0 = repmat(ray(:,2)', Np, 1); dx = repmat(ray(:,3)', Np, 1); dy = repmat(ray(:,4)', Np, 1); xp = repmat(point(:,1), 1, Nr); yp = repmat(point(:,2), 1, Nr); # test if points belongs to the supporting line b1 = abs ( (xp-x0).*dy - (yp-y0).*dx ) ./ hypot(dx, dy) < tol; # check if points lie the good direction on the rays ind = abs (dx) > abs (dy); t = zeros (size (b1)); t(ind) = (xp(ind)-x0(ind))./dx(ind); t(~ind) = (yp(~ind)-y0(~ind))./dy(~ind); # combine the two tests b = b1 & (t >= 0); endfunction %!shared ray %! p1 = [10 20]; %! p2 = [80 20]; %! ray = createRay (p1, p2); %!assert (isPointOnRay([10 20], ray)); %!assert (isPointOnRay([80 20], ray)); %!assert (isPointOnRay([50 20], ray)); %!assert (isPointOnRay([50 20+1e-3], ray,1e-2)); %!assert ( !isPointOnRay([50 20+1e-3], ray,1e-4)); %!assert ( !isPointOnRay([9.99 20], ray)); %!assert ( !isPointOnRay([80 20.01], ray)); %!assert ( !isPointOnRay([50 21], ray)); %!assert ( !isPointOnRay([79 19], ray)); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawRay.m0000644000000000000000000000013212676233417016761 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawRay.m0000644000175000017500000000463212676233417020145 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawRay (@var{ray}) ## @deftypefnx {Function File} {@var{h} = } drawRay (@var{ray}, @var{param}, @var{value}) ## Draw a ray on the current axis. ## ## With @var{ray} having the syntax: [x0 y0 dx dy], draws the ray starting from ## point (x0 y0) and going to direction (dx dy), clipped with the current ## window axis. @var{param}, @var{value} pairs are passed to function @code{line}. ## ## @seealso{rays2d, drawLine, line} ## @end deftypefn function varargout = drawRay(ray, varargin) # get bounding box limits bb = axis(gca); # compute clipped shapes [clipped isInside] = clipRay(ray, bb); # allocate memory for handle h = -ones(size(ray, 1), 1); # draw visible rays h(isInside) = drawEdge(clipped(isInside, :), varargin{:}); # process output if nargout>0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectLineCircle.m0000644000000000000000000000013212676233417021302 xustar0030 mtime=1459173135.441151279 30 atime=1459173135.441151279 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectLineCircle.m0000644000175000017500000000644112676233417022466 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{points} = } intersectLineCircle (@var{line}, @var{circle}) ## Intersection point(s) of a line and a circle ## ## INTERS = intersectLineCircle(LINE, CIRCLE); ## Returns a 2-by-2 array, containing on each row the coordinates of an ## intersection point. If the line and circle do not intersect, the result ## is filled with NaN. ## ## Example ## # base point ## center = [10 0]; ## # create vertical line ## l1 = [center 0 1]; ## # circle ## c1 = [center 5]; ## pts = intersectLineCircle(l1, c1) ## pts = ## 10 -5 ## 10 5 ## # draw the result ## figure; clf; hold on; ## axis([0 20 -10 10]); ## drawLine(l1); ## drawCircle(c1); ## drawPoint(pts, 'rx'); ## axis equal; ## ## @seealso{lines2d, circles2d, intersectLines, intersectCircles} ## @end deftypefn function points = intersectLineCircle(line, circle) # local precision eps = 1e-14; # center parameters center = circle(:, 1:2); radius = circle(:, 3); # line parameters dp = line(:, 1:2) - center; vl = line(:, 3:4); # coefficient of second order equation a = sum(line(:, 3:4).^2, 2); b = 2*sum(dp .* vl, 2); c = sum(dp.^2, 2) - radius.^2; # discriminant delta = b .^ 2 - 4 * a .* c; if delta > eps # find two roots of second order equation u1 = (-b - sqrt(delta)) / 2 ./ a; u2 = (-b + sqrt(delta)) / 2 ./ a; # convert into 2D coordinate points = [line(1:2) + u1 * line(3:4) ; line(1:2) + u2 * line(3:4)]; elseif abs(delta) < eps # find unique root, and convert to 2D coord. u = -b / 2 ./ a; points = line(1:2) + u*line(3:4); else # fill with NaN points = NaN * ones(2, 2); return; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/clipPoints.m0000644000000000000000000000013212676233417017474 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/clipPoints.m0000644000175000017500000000641412676233417020660 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{points2} =} clipPoints (@var{points}, @var{box}) ## Clip a set of points by a box. ## ## Returns the set @var{points2} which are located inside of the box @var{box}. ## ## @seealso{points2d, boxes2d, clipLine, drawPoint} ## @end deftypefn function points = clipPoints(points, bb) # get bounding box limits xmin = bb(1); xmax = bb(2); ymin = bb(3); ymax = bb(4); # compute indices of points inside visible area xOk = points(:,1)>=xmin & points(:,1)<=xmax; yOk = points(:,2)>=ymin & points(:,2)<=ymax; # keep only points inside box points = points(xOk & yOk, :); endfunction %!demo %! points = 2*rand(100,2)-1; %! bb = [-0.5 0.5 -0.25 0.25]; %! cpo = clipPoints (points, bb); %! %! plot(points(:,1),points(:,2),'xr') %! hold on %! drawBox(bb,'color','k') %! plot(cpo(:,1),cpo(:,2),'*g') %! hold off %!shared bb %! bb = [0 10 0 20]; %!test %! corners = [0 0;10 0;0 20;10 20]; %! cornersClipped = clipPoints(corners, bb); %! assert (4, size(cornersClipped, 1)); %! assert (corners, cornersClipped, 1e-6); %!test %! borders = [0 5;10 5;5 0;5 20]; %! bordersClipped = clipPoints(borders, bb); %! assert (4, size(bordersClipped, 1)); %! assert (borders, bordersClipped, 1e-6); %!test %! inside = [5 5;5 10;5 15]; %! insideClipped = clipPoints(inside, bb); %! assert (size(inside, 1), size(insideClipped, 1)); %! assert (inside, insideClipped); %!test %! points = [-1 0;11 0;-1 20;11 20;0 -1;0 21;10 -1;10 21]; %! pointsClipped = clipPoints(points, bb); %! assert (0, size(pointsClipped, 1)); %!test %! points = [-5 10;0 10;5 10;10 10; 15 10]; %! pointsClipped = clipPoints(points, bb); %! assert (3, size(pointsClipped, 1)); %! assert (points(2:4,:), pointsClipped, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawShape.m0000644000000000000000000000013212676233417017266 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawShape.m0000644000175000017500000000723412676233417020453 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012-2016 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawShape (@var{type}, @var{param}) ## @deftypefnx {Function File} drawShape (@dots{}, @var{option}) ## Draw various types of shapes (circles, polygons...). ## ## Draw the shape of type @var{type}, specified by given parameter @var{param}. ## @var{type} can be one of 'circle', 'ellipse', 'rect', 'polygon', 'curve' ## @var{param} depend on the type. For example, if @var{type} is 'circle', ## @var{param} will contain [x0 y0 R]. ## ## If @var{option} is 'fill', the shape will be filled. ## ## Examples : ## @example ## drawShape('circle', [20 10 30]); ## Draw circle centered on [20 10] with radius 10. ## drawShape('rect', [20 20 40 10 pi/3],'fill'); ## Draw rectangle centered on [20 20] with length 40 and width 10, and ## oriented pi/3 wrt axis Ox. ## @end example ## ## @end deftypefn function varargout = drawShape(type, param, option='draw') if ~iscell (type) type = {type}; end if ~iscell (param) tmp = cell (1, size (param, 1)); for i = 1:size (param, 1) tmp{i} = param(i,:); end param = tmp; end # transform each shape into a polygon shape = cell (1,length (type)); for i = 1:length (type) if strcmpi (type{i}, 'circle') shape{i} = circleAsPolygon (param{i}, 128); elseif strcmpi (type{i}, 'rect') shape{i} = rectAsPolygon (param{i}); elseif strcmpi (type{i}, 'polygon') shape{i} = param{i}; end end holded = false; if ~ishold (gca) hold on; holded = true; end h = zeros (length (shape), 1); if strcmp (option, 'draw') for i = 1:length (shape) h(i) = drawPolygon (shape{i}); end else for i = 1:length (shape) h(i) = fillPolygon (shape{i}); end end if holded hold off end if nargout>0 varargout{1}=h; end endfunction %!demo %! ## Draw circle centered on [20 10] with radius 10. %! drawShape ('circle', [20 10 30]); %! hold on %! ## Draw rectangle centered on [20 20] with length 40 and width 10, and %! ## oriented pi/3 wrt axis Ox. %! drawShape ('rect', [20 20 40 10 pi/3], "fill"); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawLine.m0000644000000000000000000000013212676233417017115 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawLine.m0000644000175000017500000001470612676233417020304 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawLine (@var{line}) ## @deftypefnx {Function File} {@var{h} =} drawLine (@var{line}, @var{param},@var{value}) ## Draw the line on the current axis. ## ## Draws the line LINE on the current axis, by using current axis to clip ## the line. Extra @var{param},@var{value} pairs are passed to the @code{line} function. ## Returns a handle to the created line object. If clipped line is not ## contained in the axis, the function returns -1. ## ## Example ## ## @example ## figure; hold on; axis equal; ## axis([0 100 0 100]); ## drawLine([30 40 10 20]); ## drawLine([30 40 20 -10], 'color', 'm', 'linewidth', 2); ## @end example ## ## @seealso{lines2d, createLine, drawEdge} ## @end deftypefn function varargout = drawLine(lin, varargin) # default style for drawing lines varargin = [{'color', 'b'}, varargin]; # extract bounding box of the current axis xlim = get(gca, 'xlim'); ylim = get(gca, 'ylim'); # clip lines with current axis box clip = clipLine(lin, [xlim ylim]); ok = isfinite(clip(:,1)); # initialize result array to invalide handles h = -1*ones(size(lin, 1), 1); # draw valid lines h(ok) = line(clip(ok, [1 3])', clip(ok, [2 4])', varargin{:}); # return line handle if needed if nargout>0 varargout{1}=h; end endfunction %!demo %! figure; hold on; axis equal; %! axis([0 100 0 100]); %! drawLine([30 40 10 20]); %! drawLine([30 40 20 -10], 'color', 'm', 'linewidth', 2); %!shared privpath %! privpath = [fileparts(which('geom2d_Contents')) filesep() 'private']; %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [30 40 10 0]; %! edge = [0 40 100 40]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [30 40 -10 0]; %! edge = [100 40 0 40]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [30 140 10 0]; %! hl = drawLine(line); %! assertEqual(-1, hl); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [30 40 0 10]; %! edge = [30 0 30 100]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [30 40 0 -10]; %! edge = [30 100 30 0]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [140 30 0 10]; %! hl = drawLine(line); %! assertEqual(-1, hl); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [80 30 10 10]; %! edge = [50 0 100 50]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [20 70 10 10]; %! edge = [0 50 50 100]; %! hl = drawLine(line); %! assertElementsAlmostEqual(edge([1 3]), get(hl, 'xdata')); %! assertElementsAlmostEqual(edge([2 4]), get(hl, 'ydata')); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [140 -30 10 10]; %! hl = drawLine(line); %! assertEqual(-1, hl); %! line = [-40 130 10 10]; %! hl = drawLine(line); %! assertEqual(-1, hl); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! box = [0 100 0 100]; %! hf = figure('visible','off'); %! axis(box); %! line = [... %! 80 30 10 10; ... %! 20 70 10 10; ... %! 140 -30 10 10; ... %! -40 130 10 10]; %! edge = [... %! 50 0 100 50; ... %! 0 50 50 100]; %! hl = drawLine(line); %! assertEqual(4, length(hl)); %! assertElementsAlmostEqual(edge(1, [1 3]), get(hl(1), 'xdata')); %! assertElementsAlmostEqual(edge(1, [2 4]), get(hl(1), 'ydata')); %! assertElementsAlmostEqual(edge(2, [1 3]), get(hl(2), 'xdata')); %! assertElementsAlmostEqual(edge(2, [2 4]), get(hl(2), 'ydata')); %! assertEqual(-1, hl(3)); %! assertEqual(-1, hl(4)); %! rmpath (privpath); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/vectorAngle.m0000644000000000000000000000013212676233417017621 xustar0030 mtime=1459173135.481132218 30 atime=1459173135.481132218 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/vectorAngle.m0000644000175000017500000001336012676233417021003 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{alpha} =} vectorAngle (@var{v1}) ## Angle of a vector, or between 2 vectors ## ## A = vectorAngle(V); ## Returns angle between Ox axis and vector direction, in Counter ## clockwise orientation. ## The result is normalised between 0 and 2*PI. ## ## A = vectorAngle(V1, V2); ## Returns the angle from vector V1 to vector V2, in counter-clockwise ## order, and in radians. ## ## A = vectorAngle(..., 'cutAngle', CUTANGLE); ## A = vectorAngle(..., CUTANGLE); # (deprecated syntax) ## Specifies convention for angle interval. CUTANGLE is the center of the ## 2*PI interval containing the result. See normalizeAngle for details. ## ## Example: ## rad2deg(vectorAngle([2 2])) ## ans = ## 45 ## rad2deg(vectorAngle([1 sqrt(3)])) ## ans = ## 60 ## rad2deg(vectorAngle([0 -1])) ## ans = ## 270 ## ## @seealso{vectors2d, angles2d, normalizeAngle} ## @end deftypefn function alpha = vectorAngle(v1, varargin) ## Initializations # default values v2 = []; cutAngle = pi; # process input arguments while ~isempty(varargin) var = varargin{1}; if isnumeric(var) && isscalar(var) # argument is normalization constant cutAngle = varargin{1}; varargin(1) = []; elseif isnumeric(var) && size(var, 2) == 2 # argument is second vector v2 = varargin{1}; varargin(1) = []; elseif ischar(var) && length(varargin) >= 2 # argument is option given as string + value if strcmpi(var, 'cutAngle') cutAngle = varargin{2}; varargin(1:2) = []; else error(['Unknown option: ' var]); end else error('Unable to parse inputs'); end end ## Case of one vector # If only one vector is provided, computes its angle if isempty(v2) # compute angle and format result in a 2*pi interval alpha = atan2(v1(:,2), v1(:,1)); # normalize within a 2*pi interval alpha = normalizeAngle(alpha + 2*pi, cutAngle); return; end ## Case of two vectors # compute angle of each vector alpha1 = atan2(v1(:,2), v1(:,1)); alpha2 = atan2(v2(:,2), v2(:,1)); # difference alpha = bsxfun(@minus, alpha2, alpha1); # normalize within a 2*pi interval alpha = normalizeAngle(alpha + 2*pi, cutAngle); endfunction %!test %! ang = vectorAngle([1 0]); %! assert(0, ang, 1e-6); %!test %! ang = vectorAngle([0 1]); %! assert(pi/2, ang, 1e-6); %!test %! ang = vectorAngle([-1 0]); %! assert(pi, ang, 1e-6); %!test %! ang = vectorAngle([0 -1]); %! assert(3*pi/2, ang, 1e-6); %!test %! ang = vectorAngle([-1 1]); %! assert(3*pi/4, ang, 1e-6); %!test %! ang = vectorAngle([1 0], pi); %! assert(0, ang, 1e-6); %!test %! ang = vectorAngle([0 1], pi); %! assert(pi/2, ang, 1e-6); %!test %! ang = vectorAngle([-1 0], pi); %! assert(pi, ang, 1e-6); %!test %! ang = vectorAngle([0 -1], pi); %! assert(3*pi/2, ang, 1e-6); %!test %! ang = vectorAngle([-1 1], pi); %! assert(3*pi/4, ang, 1e-6); %!test %! vecs = [1 0;0 1;-1 0;0 -1;1 1]; %! angs = [0;pi/2;pi;3*pi/2;pi/4]; %! assert(angs, vectorAngle(vecs)); %! assert(angs, vectorAngle(vecs, pi)); %!test %! ang = vectorAngle([1 0], 0); %! assert(0, ang, 1e-6); %!test %! ang = vectorAngle([0 1], 0); %! assert(pi/2, ang, 1e-6); %!test %! ang = vectorAngle([0 -1], 0); %! assert(-pi/2, ang, 1e-6); %!test %! ang = vectorAngle([-1 1], 0); %! assert(3*pi/4, ang, 1e-6); %!test %! vecs = [1 0;0 1;0 -1;1 1;1 -1]; %! angs = [0;pi/2;-pi/2;pi/4;-pi/4]; %! assert(angs, vectorAngle(vecs, 0), 1e-6); %!test %! v1 = [1 0]; %! v2 = [0 1]; %! ang = pi /2 ; %! assert(ang, vectorAngle(v1, v2), 1e-6); %!test %! v1 = [1 0]; %! v2 = [0 1; 0 1; 1 1; -1 1]; %! ang = [pi / 2 ;pi / 2 ;pi / 4 ; 3 * pi / 4]; %! assert(ang, vectorAngle(v1, v2), 1e-6); %!test %! v1 = [0 1; 0 1; 1 1; -1 1]; %! v2 = [-1 0]; %! ang = [pi / 2 ;pi / 2 ; 3 * pi / 4 ; pi / 4]; %! assert(ang, vectorAngle(v1, v2), 1e-6); %!test %! v1 = [1 0; 0 1; 1 1; -1 1]; %! v2 = [0 1; 1 0; -1 1; -1 0]; %! ang = [pi / 2 ;3 * pi / 2 ;pi / 2 ; pi / 4]; %! assert(ang, vectorAngle(v1, v2), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/ellipses2d.m0000644000000000000000000000013212676233417017416 xustar0030 mtime=1459173135.369185589 30 atime=1459173135.369185589 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/ellipses2d.m0000644000175000017500000000401012676233417020570 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} ellipses2d () ## Description of functions operating on ellipses. ## ## Ellipses are represented by their center, the length of their 2 ## semi-axes length, and their angle from the Ox direction (in degrees). ## E = [XC YC A B THETA]; ## ## @seealso{circles2d, inertiaEllipse, isPointInEllipse, ellipseAsPolygon ## drawEllipse, drawEllipseArc} ## @end deftypefn function ellipses2d(varargin) help('ellipses2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/clipLine.m0000644000000000000000000000013212676233417017107 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/clipLine.m0000644000175000017500000001541612676233417020275 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{edge} =} clipLine (@var{line}, @var{box}) ## Clip a line with a box. ## ## @var{line} is a straight line given as a 4 element row vector: [x0 y0 dx dy], ## with (x0 y0) being a point of the line and (dx dy) a direction vector, ## @var{box} is the clipping box, given by its extreme coordinates: ## [xmin xmax ymin ymax]. ## The result is given as an edge, defined by the coordinates of its 2 ## extreme points: [x1 y1 x2 y2]. ## If line does not intersect the box, [NaN NaN NaN NaN] is returned. ## ## Function works also if @var{line} is a Nx4 array, if @var{box} is a Nx4 array, or ## if both @var{line} and @var{box} are Nx4 arrays. In these cases, @var{edge} is a Nx4 ## array. ## ## Example: ## ## @example ## line = [30 40 10 0]; ## box = [0 100 0 100]; ## res = clipLine(line, box) ## res = ## 0 40 100 40 ## @end example ## ## @seealso{lines2d, boxes2d, edges2d, clipEdge, clipRay} ## @end deftypefn function edge = clipLine(lin, bb, varargin) # adjust size of two input arguments if size(lin, 1)==1 lin = repmat(lin, size(bb, 1), 1); elseif size(bb, 1)==1 bb = repmat(bb, size(lin, 1), 1); elseif size(lin, 1) ~= size(bb, 1) error('bad sizes for input'); end # allocate memory nbLines = size(lin, 1); edge = zeros(nbLines, 4); # main loop on lines for i=1:nbLines # extract limits of the box xmin = bb(i, 1); xmax = bb(i, 2); ymin = bb(i, 3); ymax = bb(i, 4); # use direction vector for box edges similar to direction vector of the # line in order to reduce computation errors delta = hypot(lin(i,3), lin(i,4)); # compute intersection with each edge of the box # lower edge px1 = intersectLines(lin(i,:), [xmin ymin delta 0]); # right edge px2 = intersectLines(lin(i,:), [xmax ymin 0 delta]); # upper edge py1 = intersectLines(lin(i,:), [xmax ymax -delta 0]); # left edge py2 = intersectLines(lin(i,:), [xmin ymax 0 -delta]); # remove undefined intersections (case of lines parallel to box edges) points = [px1 ; px2 ; py1 ; py2]; points = points(isfinite(points(:,1)), :); # sort points according to their position on the line pos = linePosition(points, lin(i,:)); [pos inds] = sort(pos); ##ok points = points(inds, :); # create clipped edge by using the two points in the middle ind = size(points, 1)/2; inter1 = points(ind,:); inter2 = points(ind+1,:); edge(i, 1:4) = [inter1 inter2]; # check that middle point of the edge is contained in the box midX = mean(edge(i, [1 3])); xOk = xmin <= midX && midX <= xmax; midY = mean(edge(i, [2 4])); yOk = ymin <= midY && midY <= ymax; # if one of the bounding condition is not met, set edge to NaN if ~(xOk && yOk) edge (i,:) = NaN; end end endfunction %!demo %! lin = [30 40 10 0]; %! bb = [0 100 0 100]; %! res = clipLine(lin, bb) %! %! drawBox(bb,'color','k'); %! line(lin([1 3]),lin([2 4]),'color','b'); %! line(res([1 3]),res([2 4]),'color','r','linewidth',2); %! axis tight %! v = axis (); %! axis(v+[0 10 -10 0]) %!test # inside, to the right # inside, to the left# outside %! bb = [0 100 0 100]; %! lin = [30 40 10 0]; %! edge = [0 40 100 40]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [30 40 -10 0]; %! edge = [100 40 0 40]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [30 140 10 0]; %! assert (sum(isnan(clipLine(lin, bb)))==4); %!test # inside, upward # inside, downward # outside %! bb = [0 100 0 100]; %! lin = [30 40 0 10]; %! edge = [30 0 30 100]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [30 40 0 -10]; %! edge = [30 100 30 0]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [140 30 0 10]; %! assert (sum(isnan(clipLine(lin, bb)))==4); %!test # inside, top right corner# inside, down right corner # outside %! bb = [0 100 0 100]; %! lin = [80 30 10 10]; %! edge = [50 0 100 50]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [20 70 10 10]; %! edge = [0 50 50 100]; %! assert (edge, clipLine(lin, bb), 1e-6); %! lin = [140 -30 10 10]; %! assert (sum(isnan(clipLine(lin, bb)))==4); %! lin = [-40 130 10 10]; %! assert (sum(isnan(clipLine(lin, bb)))==4); %!test #multilines # inside, top right corner %! bb = [0 100 0 100]; %! lin = [... %! 80 30 10 10; ... %! 20 70 10 10; ... %! 140 -30 10 10; ... %! -40 130 10 10]; %! edge = [... %! 50 0 100 50; ... %! 0 50 50 100; ... %! NaN NaN NaN NaN; ... %! NaN NaN NaN NaN; ... %! ]; %! clipped = clipLine(lin, bb); %! assert (4, size(clipped, 1)); %! assert (edge(1:2, :), clipped(1:2, :), 1e-6); %! assert (sum(isnan(clipped(3,:)))==4); %! assert (sum(isnan(clipped(4,:)))==4); %!test # test clipping of horizontal lines # inside, to the right %! bb = [-1 1 -1 1]*1e10; %! lin = [3 0 1 2]; %! D = 1e10; %! edge = [3-D/2 -D 3+D/2 D]; %! clipped = clipLine(lin, bb); %! assert (edge, clipped); %!test # inside, to the right %! bb = [-1 1 -1 1]*100; %! lin = [3 0 1*1e10 2*1e10]; %! D = 100; %! edge = [3-D/2 -D 3+D/2 D]; %! clipped = clipLine(lin, bb); %! assert (edge, clipped, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectEdges.m0000644000000000000000000000013212676233417020320 xustar0030 mtime=1459173135.441151279 30 atime=1459173135.441151279 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectEdges.m0000644000175000017500000001323212676233417021500 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} = } intersectEdges (@var{edge1}, @var{edge2}) ## Return all intersections between two set of edges ## ## P = intersectEdges(E1, E2); ## returns the intersection point of lines L1 and L2. E1 and E2 are 1-by-4 ## arrays, containing parametric representation of each edge (in the form ## [x1 y1 x2 y2], see 'createEdge' for details). ## ## In case of colinear edges, returns [Inf Inf]. ## In case of parallel but not colinear edges, returns [NaN NaN]. ## ## If each input is [N*4] array, the result is a [N*2] array containing ## intersections of each couple of edges. ## If one of the input has N rows and the other 1 row, the result is a ## [N*2] array. ## ## @seealso{edges2d, intersectLines} ## @end deftypefn function point = intersectEdges(edge1, edge2) ## Initialisations # ensure input arrays are same size N1 = size(edge1, 1); N2 = size(edge2, 1); # ensure input have same size if N1~=N2 if N1==1 edge1 = repmat(edge1, [N2 1]); N1 = N2; elseif N2==1 edge2 = repmat(edge2, [N1 1]); end end # tolerance for precision tol = 1e-14; # initialize result array x0 = zeros(N1, 1); y0 = zeros(N1, 1); ## Detect parallel and colinear cases # indices of parallel edges #par = abs(dx1.*dy2 - dx1.*dy2) return [NaN NaN] x0(par & ~col) = NaN; y0(par & ~col) = NaN; ## Process colinear edges # colinear edges may have 0, 1 or infinite intersection # Discrimnation based on position of edge2 vertices on edge1 if sum(col)>0 # array for storing results of colinear edges resCol = Inf*ones(size(col)); # compute position of edge2 vertices wrt edge1 t1 = edgePosition(edge2(col, 1:2), edge1(col, :)); t2 = edgePosition(edge2(col, 3:4), edge1(col, :)); # control location of vertices: we want t1t2 tmp = t1; t1 = t2; t2 = tmp; end # edge totally before first vertex or totally after last vertex resCol(col(t2<-eps)) = NaN; resCol(col(t1>1+eps)) = NaN; # set up result into point coordinate x0(col) = resCol; y0(col) = resCol; # touches on first point of first edge touch = col(abs(t2)<1e-14); x0(touch) = edge1(touch, 1); y0(touch) = edge1(touch, 2); # touches on second point of first edge touch = col(abs(t1-1)<1e-14); x0(touch) = edge1(touch, 3); y0(touch) = edge1(touch, 4); end ## Process non parallel cases # process intersecting edges whose interecting lines intersect i = find(~par); # use a test to avoid process empty arrays if sum(i)>0 # extract base parameters of supporting lines for non-parallel edges x1 = edge1(i,1); y1 = edge1(i,2); dx1 = edge1(i,3)-x1; dy1 = edge1(i,4)-y1; x2 = edge2(i,1); y2 = edge2(i,2); dx2 = edge2(i,3)-x2; dy2 = edge2(i,4)-y2; # compute intersection points of supporting lines delta = (dx2.*dy1-dx1.*dy2); x0(i) = ((y2-y1).*dx1.*dx2 + x1.*dy1.*dx2 - x2.*dy2.*dx1) ./ delta; y0(i) = ((x2-x1).*dy1.*dy2 + y1.*dx1.*dy2 - y2.*dx2.*dy1) ./ -delta; # compute position of intersection points on each edge # t1 is position on edge1, t2 is position on edge2 t1 = ((y0(i)-y1).*dy1 + (x0(i)-x1).*dx1) ./ (dx1.*dx1+dy1.*dy1); t2 = ((y0(i)-y2).*dy2 + (x0(i)-x2).*dx2) ./ (dx2.*dx2+dy2.*dy2); # check position of points on edges. # it should be comprised between 0 and 1 for both t1 and t2. # if not, the edges do not intersect out = t1<-tol | t1>1+tol | t2<-tol | t2>1+tol; x0(i(out)) = NaN; y0(i(out)) = NaN; end ## format output arguments point = [x0 y0]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawBezierCurve.m0000644000000000000000000000013212676233417020453 xustar0030 mtime=1459173135.353193213 30 atime=1459173135.353193213 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawBezierCurve.m0000644000175000017500000000777312676233417021650 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawBezierCurve (@var{points}) ## @deftypefnx {Function File} drawBezierCurve (@var{pp}) ## @deftypefnx {Function File} drawBezierCurve (@dots{}, @var{param}, @var{value}, @dots{}) ## @deftypefnx {Function File} {@var{h} =}drawBezierCurve (@dots{}) ## Draw a cubic bezier curve defined by the control points @var{points}. ## ## With only one input argument, draws the Bezier curve defined by the 4 control ## points stored in @var{points}. @var{points} is either a 4-by-2 array ## (vertical concatenation of point coordinates), or a 1-by-8 array (horizotnal ## concatenation of point coordinates). The curve could be described by its ## polynomial (output of @code{cbezier2poly}) @var{pp}, which should be a 2-by-4 ## array. ## ## The optional @var{param}, @var{value} pairs specify additional drawing ## parameters, see the @code{plot} function for details. The specific parameter ## 'discretization' with an integer associated value defines the amount of ## points used to plot the curve. If the output is requiered, the function ## returns the handle to the created graphic object. ## ## @seealso{cbezier2poly, plot} ## @end deftypefn function varargout = drawBezierCurve(points, varargin) # default number of discretization steps N = 64; # check if discretization step is specified if ~isempty(varargin) [tf idx] = ismember ({'discretization'},{varargin{1:2:end}}); if ~isempty(idx) N = varargin{idx+1}; varargin(idx:idx+1) = []; end end # parametrization variable for bezier (use N+1 points to have N edges) t = linspace(0, 1, N+1); if any(size(points) ~= [2 4]) [x y] = cbezier2poly(points,t); else # Got a polynomial description x = polyval(points(1,:),t); y = polyval(points(2,:),t); end # draw the curve h = plot(x, y, varargin{:}); # eventually return a handle to the created object if nargout > 0 varargout = {h}; end endfunction %!demo %! points = [0 0; 3 1; -2 1; 1 0]; %! drawBezierCurve(points); %! hold on %! plot(points([1 4],1),points([1 4],2),'go'); %! plot(points([2 3],1),points([2 3],2),'rs'); %! line(points([1 2],1),points([1 2],2),'color','k'); %! line(points([3 4],1),points([3 4],2),'color','k'); %! h = drawBezierCurve(points, 'discretization', 6, 'color','r'); %! hold off %!shared p %! p = [0 0; 3 1; -2 1; 1 0]; %!error(drawBezier()) %!error(drawBezier ('discretization')) %!error(drawBezier (p, 'discretization', 'a')) %!error(drawBezier (p(:))) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/edges2d.m0000644000000000000000000000013212676233417016665 xustar0030 mtime=1459173135.365187495 30 atime=1459173135.365187495 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/edges2d.m0000644000175000017500000000415212676233417020046 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} edges2d () ## Description of functions operating on planar edges # # An edge is represented by the corodinate of its end points: # EDGE = [X1 Y1 X2 Y2]; # # A set of edges is represented by a N*4 array, each row representing an # edge. # # # @seealso{lines2d, rays2d, points2d # createEdge, edgeAngle, edgeLength, edgeToLine, midPoint # intersectEdges, intersectLineEdge, isPointOnEdge # clipEdge, transformEdge # drawEdge, drawCenteredEdge} ## @end deftypefn function edges2d(varargin) help('edges2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/crackPattern2.m0000644000000000000000000000013212676233417020053 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/crackPattern2.m0000644000175000017500000001261712676233417021241 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{e} = } crackPattern2 (@var{box}, @var{points}, @var{alpha}) ## Create a (bounded) crack pattern tessellation ## ## E = crackPattern2(BOX, POINTS, ALPHA) ## create a crack propagation pattern wit following parameters : ## - pattern is bounded by area BOX which is a polygon. ## - each crack originates from points given in POINTS ## - directions of each crack is given by a [NxM] array ALPHA, where M is ## the number of rays emanating from each seed/ ## - a crack stop when it reaches another already created crack. ## - all cracks stop when they reach the border of the frame, given by box ## (a serie of 4 points). ## The result is a collection of edges, in the form [x1 y1 x2 y2]. ## ## E = crackPattern2(BOX, POINTS, ALPHA, SPEED) ## Also specify speed of propagation of each crack. ## ## ## See the result with : ## figure; ## drawEdge(E); ## ## @seealso{drawEdge} ## @end deftypefn function edges = crackPattern2(box, points, alpha, varargin) if ~isempty(varargin) speed = varargin{1}; else speed = ones(size(points, 1), 1); end # Compute line equations for each initial crack. # The 'Inf' at the end correspond to the position of the limit. # If an intersection point is found with another line, but whose position # is after this value, this means that another crack stopped it before it # reach the intersection point. NP = size(points, 1); lines = zeros(0, 5); for i=1:size(alpha, 2) lines = [lines; points speed.*cos(alpha(:,i)) speed.*sin(alpha(:,i)) Inf*ones(NP, 1)]; end NL = size(lines, 1); # initialize lines for borders, but assign a very high speed, to be sure # borders will stop all cracks. dx = (box([2 3 4 1],1)-box([1 2 3 4],1))*max(speed)*5; dy = (box([2 3 4 1],2)-box([1 2 3 4],2))*max(speed)*5; # add borders to the lines set lines = [lines ; createLine(box, dx, dy) Inf*ones(4,1)]; edges = zeros(0, 4); while true modif = 0; # try to update each line for i=1:NL # initialize first point of edge edges(i, 1:2) = lines(i, 1:2); # compute intersections with all other lines pi = intersectLines(lines(i,:), lines); # compute position of all intersection points on the current line pos = linePosition(pi, lines(i,:)); # consider points to the right (positive position), and sort them indr = find(pos>1e-12 & pos~=Inf); [posr, indr2] = sort(pos(indr)); # look for the closest intersection to the right for i2=1:length(indr2) # index of intersected line il = indr(indr2(i2)); # position of point relative to intersected line pos2 = linePosition(pi(il, :), lines(il, :)); # depending on the sign of position, tests if the line2 can # stop the current line, or if it was stopped before if pos2>0 if pos2 ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } createScaling (@var{s}) ## @deftypefnx {Function File} {@var{T} = } createScaling (@var{sx}, @var{sy}) ## Create the 3x3 matrix of a scaling in 2 dimensions. # # Assume scaling @var{s} is equal n all directions unless @var{sx} and @var{sy} are given. # Returns the matrix corresponding to scaling in the 2 main directions. # The returned matrix has the form: # [SX 0 0] # [0 SY 0] # [0 0 1] # # @seealso{transforms2d, transformPoint, createTranslation, createRotation} ## @end deftypefn function trans = createScaling(varargin) # defined default arguments sx = 1; sy = 1; cx = 0; cy = 0; # process input arguments if length(varargin)==1 # the argument is either the scaling factor in both direction, # or a 1x2 array containing scaling factor in each direction var = varargin{1}; sx = var(1); sy = var(1); if length(var)>1 sy = var(2); end elseif length(varargin)==2 # the 2 arguments are the scaling factors in each dimension sx = varargin{1}; sy = varargin{2}; elseif length(varargin)==3 # first argument is center, 2nd and 3d are scaling factors center = varargin{1}; cx = center(1); cy = center(2); sx = varargin{2}; sy = varargin{3}; end # create result matrix trans = [sx 0 cx*(1-sx); 0 sy cy*(1-sy); 0 0 1]; endfunction %!test %! trans = createScaling(2); %! assert (trans, [2 0 0;0 2 0;0 0 1], 1e-6); %!test %! trans = createScaling(2, 3); %! assert (trans, [2 0 0;0 3 0;0 0 1], 1e-6); %!test %! trans = createScaling([2 3]); %! assert (trans, [2 0 0;0 3 0;0 0 1], 1e-6); %!test %! sx = 2; %! sy = 3; %! p0 = [4 5]; %! trans1 = createScaling(p0, sx, sy); %! t1 = createTranslation(-p0); %! sca = createScaling(sx, sy); %! t2 = createTranslation(p0); %! trans2 = t2*sca*t1; %! assert (trans1, trans2, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/rotateVector.m0000644000000000000000000000013212676233417020031 xustar0030 mtime=1459173135.477134124 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/rotateVector.m0000644000175000017500000000435412676233417021216 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vr} = } rotateVector (@var{v}, @var{theta}) ## Rotate a vector by a given angle ## ## Rotate the vector @var{v} by an angle @var{theta}, given in radians. ## ## Example ## ## @example ## rotateVector([1 0], pi/2) ## ans = ## 0 1 ## @end example ## ## @seealso{vectors2d, transformVector, createRotation} ## @end deftypefn function vr = rotateVector(v, angle) # precomputes angles cot = cos(angle); sit = sin(angle); # compute rotated coordinates vr = [cot * v(:,1) - sit * v(:,2) , sit * v(:,1) + cot * v(:,2)]; endfunction %!assert ([0 1],rotateVector([1 0],pi/2), 1e-6) %!assert (sqrt([0.5 0.5]),rotateVector([1 0],pi/4), 1e-6) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/edgeToLine.m0000644000000000000000000000013212676233417017367 xustar0030 mtime=1459173135.365187495 30 atime=1459173135.365187495 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/edgeToLine.m0000644000175000017500000000412412676233417020547 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} = } edgeToLine (@var{edge}) ## Convert an edge to a straight line ## ## LINE = edgeToLine(EDGE); ## Returns the line containing the edge EDGE. ## ## Example ## edge = [2 3 4 5]; ## line = edgeToLine(edge); ## figure(1); hold on; axis([0 10 0 10]); ## drawLine(line, 'color', 'g') ## drawEdge(edge, 'linewidth', 2) ## ## @seealso{edges2d, lines2d} ## @end deftypefn function line = edgeToLine(edge) line = [edge(:, 1:2) edge(:, 3:4)-edge(:, 1:2)]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/private0000644000000000000000000000013212676233417016567 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/0000755000175000017500000000000012676233417020023 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/geom2d/private/PaxHeaders.5293/assertTrue.m0000644000000000000000000000013212676233417021163 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.469137936 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/assertTrue.m0000644000175000017500000000330312676233417022341 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} assertTrue () ## Wrapper. Not documented. ## ## @end deftypefn function assertTrue(a) assert(a); endfunction geometry-2.1.1/inst/geom2d/private/PaxHeaders.5293/assertElementsAlmostEqual.m0000644000000000000000000000013212676233417024170 xustar0030 mtime=1459173135.465139842 30 atime=1459173135.465139842 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/assertElementsAlmostEqual.m0000644000175000017500000000335212676233417025352 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} assertElementsAlmostEqual () ## Wrapper. Not documented. ## ## @end deftypefn function assertElementsAlmostEqual(a,b) assert(b,a,1e-6); endfunction geometry-2.1.1/inst/geom2d/private/PaxHeaders.5293/assertAlmostEqual.m0000644000000000000000000000013212676233417022473 xustar0030 mtime=1459173135.465139842 30 atime=1459173135.465139842 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/assertAlmostEqual.m0000644000175000017500000000333212676233417023653 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} assertAlmostEqual () ## Wrapper. Not documented. ## ## @end deftypefn function assertAlmostEqual(a,b) assert(b,a,1e-6); endfunction geometry-2.1.1/inst/geom2d/private/PaxHeaders.5293/assertEqual.m0000644000000000000000000000013212676233417021313 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.469137936 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/assertEqual.m0000644000175000017500000000331112676233417022470 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} assertEqual () ## Wrapper. Not documented. ## ## @end deftypefn function assertEqual(a,b) assert(b,a); endfunction geometry-2.1.1/inst/geom2d/private/PaxHeaders.5293/assertFalse.m0000644000000000000000000000013212676233417021276 xustar0030 mtime=1459173135.469137936 30 atime=1459173135.469137936 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/private/assertFalse.m0000644000175000017500000000330612676233417022457 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} assertFalse () ## Wrapper. Not documented. ## ## @end deftypefn function assertFalse(a) assert(!a); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawCircle.m0000644000000000000000000000013212676233417017427 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawCircle.m0000644000175000017500000001020012676233417020577 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawCircle (@var{x0}, @var{y0}, @var{r}) ## @deftypefnx {Function File} {@var{h} = } drawCircle (@var{circle}) ## @deftypefnx {Function File} {@var{h} = } drawCircle (@var{center}, @var{radius}) ## @deftypefnx {Function File} {@var{h} = } drawCircle (@dots{}, @var{nstep}) ## @deftypefnx {Function File} {@var{h} = } drawCircle (@dots{}, @var{name}, @var{value}) ## Draw a circle on the current axis ## ## drawCircle(X0, Y0, R); ## Draw the circle with center (X0,Y0) and the radius R. If X0, Y0 and R ## are column vectors of the same length, draw each circle successively. ## ## drawCircle(CIRCLE); ## Concatenate all parameters in a Nx3 array, where N is the number of ## circles to draw. ## ## drawCircle(CENTER, RADIUS); ## Specify CENTER as Nx2 array, and radius as a Nx1 array. ## ## drawCircle(..., NSTEP); ## Specify the number of edges that will be used to draw the circle. ## Default value is 72, creating an approximation of one point for each 5 ## degrees. ## ## drawCircle(..., NAME, VALUE); ## Specifies plotting options as pair of parameters name/value. See plot ## documentation for details. ## ## ## H = drawCircle(...); ## return handles to each created curve. ## ## @seealso{circles2d, drawCircleArc, drawEllipse} ## @end deftypefn function varargout = drawCircle(varargin) # process input parameters var = varargin{1}; if size(var, 2) == 1 x0 = varargin{1}; y0 = varargin{2}; r = varargin{3}; varargin(1:3) = []; elseif size(var, 2) == 2 x0 = var(:,1); y0 = var(:,2); r = varargin{2}; varargin(1:2) = []; elseif size(var, 2) == 3 x0 = var(:,1); y0 = var(:,2); r = var(:,3); varargin(1) = []; else error('bad format for input in drawCircle'); end # ensure each parameter is column vector x0 = x0(:); y0 = y0(:); r = r(:); # default number of discretization steps N = 72; # check if discretization step is specified if ~isempty(varargin) var = varargin{1}; if length(var)==1 && isnumeric(var) N = round(var); varargin(1) = []; end end # parametrization variable for circle (use N+1 as first point counts twice) t = linspace(0, 2*pi, N+1); cot = cos(t); sit = sin(t); # empty array for graphic handles h = zeros(size(x0)); # compute discretization of each circle for i = 1:length(x0) xt = x0(i) + r(i) * cot; yt = y0(i) + r(i) * sit; h(i) = plot(xt, yt, varargin{:}); end if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectCircles.m0000644000000000000000000000013212676233417020655 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectCircles.m0000644000175000017500000001054212676233417022036 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{points} = } intersectCircles (@var{circle1}, @var{circle2}) ## Intersection points of two circles. ## ## POINTS = intersectCircles(CIRCLE1, CIRCLE2) ## Computes the intersetion point of the two circles CIRCLE1 and CIRCLE1. ## Both circles are given with format: [XC YC R], with (XC,YC) being the ## coordinates of the center and R being the radius. ## POINTS is a 2-by-2 array, containing coordinate of an intersection ## point on each row. ## In the case of tangent circles, the intersection is returned twice. It ## can be simplified by using the 'unique' function. ## ## Example ## # intersection points of two distant circles ## c1 = [0 0 10]; ## c2 = [10 0 10]; ## pts = intersectCircles(c1, c2) ## pts = ## 5 -8.6603 ## 5 8.6603 ## ## # intersection points of two tangent circles ## c1 = [0 0 10]; ## c2 = [20 0 10]; ## pts = intersectCircles(c1, c2) ## pts = ## 10 0 ## 10 0 ## pts2 = unique(pts, 'rows') ## pts2 = ## 10 0 ## ## References ## http://local.wasp.uwa.edu.au/~pbourke/geometry/2circle/ ## http://mathworld.wolfram.com/Circle-CircleIntersection.html ## ## @seealso{circles2d, intersectLineCircle, radicalAxis} ## @end deftypefn function points = intersectCircles(circle1, circle2) # adapt sizes of inputs n1 = size(circle1, 1); n2 = size(circle2, 1); if n1 ~= n2 if n1 > 1 && n2 == 1 circle2 = repmat(circle2, n1, 1); elseif n2 > 1 && n1 == 1 circle1 = repmat(circle1, n2, 1); else error('Both input should have same number of rows'); end end # extract center and radius of each circle center1 = circle1(:, 1:2); center2 = circle2(:, 1:2); r1 = circle1(:,3); r2 = circle2(:,3); # allocate memory for result nPoints = length(r1); points = NaN * ones(2*nPoints, 2); # distance between circle centers d12 = distancePoints(center1, center2, 'diag'); # get indices of circle couples with intersections inds = d12 >= abs(r1 - r2) & d12 <= (r1 + r2); if sum(inds) == 0 return; end # angle of line from center1 to center2 angle = angle2Points(center1(inds,:), center2(inds,:)); # position of intermediate point, located at the intersection of the # radical axis with the line joining circle centers d1m = d12(inds) / 2 + (r1(inds).^2 - r2(inds).^2) ./ (2 * d12(inds)); tmp = polarPoint(center1(inds, :), d1m, angle); # distance between intermediate point and each intersection point h = sqrt(r1(inds).^2 - d1m.^2); # indices of valid intersections inds2 = find(inds)*2; inds1 = inds2 - 1; # create intersection points points(inds1, :) = polarPoint(tmp, h, angle - pi/2); points(inds2, :) = polarPoint(tmp, h, angle + pi/2); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/closed_path.m0000644000000000000000000000013212676233417017635 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/closed_path.m0000644000175000017500000000720512676233417021020 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{y} =} polygon (@var{x}) ## Returns a simple closed path that passes through all the points in @var{x}. ## @var{x} is a vector containing 2D coordinates of the points. ## ## @end deftypefn ## Author: Simeon Simeonov function y = closed_path(x) if(size(x,1) > 1 && size(x,1) < size(x,2)) x = x'; end N = size(x,1); # Number of points idx = zeros(N, 1); # ind contains the indices of the sorted coordinates a = find(x(:,2)==min(x(:,2))); if(size(a,1) > 1) [~, i] = sort(x(a,1)); a = a(i(1)); end x_1 = x(x(:,2)==x(a,2),:); # find all x with the same y coordinate if(x(a,1) == min(x(:,1))) x_2 = x(x(:,1)==x(a,1),:); # find all x with the same x coordinate else x_2 = x(a,:); end if(size(x_1,1) > 1 || size(x_2,1) > 1) if(size(x_1,1) > 1) x_1 = sort(x_1); # Sort by x coordinate y(1,:) = x(a,:); # original starting point end if (size(x_2,1) > 1) x_2 = sort(x_2, 'descend'); end x_not = [x_1; x_2]; i = ismember(x,x_not,'rows'); x(i, :) = []; x = [x_1(size(x_1,1),:); x]; x_1(size(x_1, 1),:) = []; N = size(x,1); a = 1; else x_1 = []; x_2 = x(a,:); end d = x - repmat(x(a,:), N, 1); th = d(:,2)./(d(:,1) + d(:,2)); [~, idx0] = ismember(sort(th(th==0)), th); [~, idx1] = ismember(sort(th(th>0)), th); [~, idx2] = ismember(sort(th(th<0)), th); idx = [a; idx0; idx1; idx2]; # I contains the indices of idx in a sorted order. [v i] = sort(idx) then # i==I. [~,I,J]= unique(idx); if(size(I,1) ~= size(J,1)) R = histc(J, 1:size(I,1)); # R(1) will always be 1? idx_sorted = idx(I); r = find(R>1); for ri = r' idx_repeated = idx_sorted(ri); idx(idx==idx_repeated) = find(th==th(idx_sorted(ri))); end end y = [x_1; x(idx,:); x_2;]; endfunction %!demo %! maxInt = 100; %! N = 25; %! figure (); %! for i = 1:4 %! subplot (2,2,i); %! x = randi(maxInt, N, 2); %! y = closed_path(x); %! plot(y(:,1), y(:,2), '-*'); %! end geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawCenteredEdge.m0000644000000000000000000000013212676233417020544 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawCenteredEdge.m0000644000175000017500000001065712676233417021734 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawCenteredEdge (@var{center}, @var{L}, @var{theta}) ## @deftypefnx {Function File} {@var{h} =} drawCenteredEdge (@var{edge}) ## @deftypefnx {Function File} {@var{h} =} drawCenteredEdge (@dots{}, @var{name},@var{value}) ## Draw an edge centered on a point. ## ## drawCenteredEdge(CENTER, L, THETA) ## Draws an edge centered on point CENTER, with length L, and orientation ## THETA (given in degrees). Input arguments can also be arrays, that must ## all have the same number odf rows. ## ## drawCenteredEdge(EDGE) ## Concatenates edge parameters into a single N-by-4 array, containing: ## [XC YV L THETA]. ## ## drawCenteredEdge(..., NAME, VALUE) ## Also specifies drawing options by using one or several parameter name - ## value pairs (see doc of plot function for details). ## ## H = drawCenteredEdge(...) ## Returns handle(s) to the created edges(s). ## ## @example ## # Draw an ellipse with its two axes ## figure(1); clf; ## center = [50 40]; ## r1 = 30; r2 = 10; ## theta = 20; ## elli = [center r1 r2 theta]; ## drawEllipse(elli, 'linewidth', 2); ## axis([0 100 0 100]); axis equal; ## hold on; ## edges = [center 2*r1 theta ; center 2*r2 theta+90]; ## drawCenteredEdge(edges, 'linewidth', 2, 'color', 'g'); ## @end example ## ## @seealso{edges2d, drawEdge} ## @end deftypefn function varargout = drawCenteredEdge(center, len, theta, varargin) ## process input variables if size(center, 2) == 4 # manage edge in single parameter varargin = [{len, theta}, varargin]; len = center(:, 3); theta = center(:, 4); center = center(:, 1:2); N = size(center, 1); else # parameters given in different arguments # size of data NP = size(center, 1); NL = size(len, 1); ND = size(theta, 1); N = max([NP NL ND]); # ensure all data have same size if N > 1 if NP == 1, center = repmat(center, [N 1]); end if NL == 1, len = repmat(len, [N 1]); end if ND == 1, theta = repmat(theta, [N 1]); end end end # extract drawing options options = varargin(:); ## Draw edges # coordinates of center point xc = center(:, 1); yc = center(:, 2); # convert angle to radians theta = theta * pi / 180; # computation shortcuts cot = cos(theta); sit = sin(theta); # compute starting and ending points x1 = xc - len .* cot / 2; x2 = xc + len .* cot / 2; y1 = yc - len .* sit / 2; y2 = yc + len .* sit / 2; # draw the edges h = zeros(N, 1); for i = 1:N h(i) = plot([x1(i) x2(i)], [y1(i) y2(i)]); end # apply style to edges if ~isempty(options) > 0 for i = 1:N set(h(i), options{:}); end end ## Format output # process output arguments if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angleSort.m0000644000000000000000000000013212676233417017306 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angleSort.m0000644000175000017500000000627312676233417020475 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {varargout =} angleSort (@var{pts}, varargin) ## Sort points in the plane according to their angle to origin ## ## ## PTS2 = angleSort(PTS); ## Computes angle of points with origin, and sort points with increasing ## angles in Counter-Clockwise direction. ## ## PTS2 = angleSort(PTS, PTS0); ## Computes angles between each point of PTS and PT0, which can be ## different from origin. ## ## PTS2 = angleSort(..., THETA0); ## Specifies the starting angle for sorting. ## ## [PTS2, I] = angleSort(...); ## Also returns in I the indices of PTS, such that PTS2 = PTS(I, :); ## ## @seealso{points2d, angles2d, angle2points, normalizeAngle} ## @end deftypefn function varargout = angleSort(pts, varargin) # default values pt0 = [0 0]; theta0 = 0; if length(varargin)==1 var = varargin{1}; if size(var, 2)==1 # specify angle theta0 = var; else pt0 = var; end elseif length(varargin)==2 pt0 = varargin{1}; theta0 = varargin{2}; end n = size(pts, 1); pts2 = pts - repmat(pt0, [n 1]); angle = lineAngle([zeros(n, 2) pts2]); angle = mod(angle - theta0 + 2*pi, 2*pi); [dummy, I] = sort(angle); # format output if nargout<2 varargout{1} = pts(I, :); elseif nargout==2 varargout{1} = pts(I, :); varargout{2} = I; end endfunction %!shared p1,p2,p3,p4,pts,center %! p1 = [0 0]; %! p2 = [10 0]; %! p3 = [10 10]; %! p4 = [0 10]; %! pts = [p1;p2;p3;p4]; %! center = [5 5]; %!test %! expected = pts([3 4 1 2], :); %! assert (expected, angleSort (pts, center), 1e-6); %!assert (pts, angleSort (pts, center, -pi), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/changelog.txt0000644000000000000000000000013212676233417017662 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/changelog.txt0000644000175000017500000001274612676233417021053 0ustar00juanpijuanpi00000000000000%% Copyright (c) 2011, INRA %% 2007-2011, David Legland %% 2011 Adapted to Octave by Juan Pablo Carbajal %% %% All rights reserved. %% (simplified BSD License) %% %% Redistribution and use in source and binary forms, with or without %% modification, are permitted provided that the following conditions are met: %% %% 1. Redistributions of source code must retain the above copyright notice, this %% list of conditions and the following disclaimer. %% %% 2. Redistributions in binary form must reproduce the above copyright notice, %% this list of conditions and the following disclaimer in the documentation %% and/or other materials provided with the distribution. %% %% THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" %% AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE %% IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE %% ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE %% LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR %% CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF %% SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS %% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN %% CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) %% ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE %% POSSIBILITY OF SUCH DAMAGE. %% %% The views and conclusions contained in the software and documentation are %% those of the authors and should not be interpreted as representing official %% policies, either expressed or implied, of copyright holder. change log for geom2d geom2d, release 2011.??.?? ========================== New functions - added angleDiff and angleAbsDiff various doc updates geom2d, release 2011.06.30 ========================== New functions - added function rotateVector - added function randomPointInBox Changes - Shape orientation is now represented using degrees - function vectorAngle can now compute the angle between two vectors Bug fixes - enhanced function distancePointEdge - enhanced function isPointOnEdge - enhanced function isParallel - fixed bugs intersectLineCircle geom2d, release 2011.03.21 ========================== New functions - added functions intersectLineCircle and intersectCircles - added functions inertiaEllipse, isPointInEllipse - added function drawBezierCurve - added functions intersectBoxes and mergeBoxes Changes - re-organized the library in three sub-directories: geom2d, polygons2d, and polynomialCurves2d - cleanup of code and doc Bug fixes - several bugs fixed in clipEdge, isPointOnEdge geom2d, release 2010.08.06 ========================== New functions - polygonToRow and rowToPolygon, to convert polygon to a row vector - midPoint, to compute middle points of either 2 points or an edge - added rad2deg and deg2rad, for angle conversions Changes - createCircle and createdirectedCircle are now vectorized, and use different convention for 2 input variables (center + point and circle) - median line has been vectorized Bug fixes - fix bugs in intersectEdges - fix bugs in clipLine - rewrite drawLine using clipLine geom2d, release 2010.07.19 ========================== new functions - isCounterClockwise - intersectRayPolygon - clipRay - reverseEdge - drawBox - fitAffineTransform2d Changes - updated inertiaEllipse - fixed bugs in intersectEdges.m, isParallel.m and isPerpendicular.m - vectorized intersectLinePolygon - fixed precision bug in isPointOnEdge - renamed formatAngle to normalizeAngle - created help file 'angles2d' - fixed bug in weighted centroid computation various bug fixes, and doc updates. geom2d, release 2009.07.22 ========================== new features - new functions for polygons: polygonPoint, polygonSubcurve, polygonLoops, distancePointPolygon, distancePolygons, expandPolygon, polygonSelfIntersections, projPointOnPolygon, isPointInPolygon, reveresPolygon - new functions for polylines: intersectPolylines, polylineSelfIntersections, distancePolylines, isPointOnPolyline, reveresPolyline - projPointOnPolyline can also return the distance of the point to the polyline - function 'edgeToLine' converts an edge to its supporting line Changes - Renamed functions + subcurve -> polylineSubCurve + curveCentroid -> polylineCentroid + invertLine -> reverseLine - Compatibility considerations + parallelLine: changed convention for signed distance various bug fixes, and doc updates. geom2d, release 2009.06.15 ========================== * new features - radicalAxis from 2 circles: - moment of a curve (polyline): curveMoment, curveCMoment, curveCSMoment - new functions for polylines distancePointPolyline, drawPolyline, polylineLength, polylinePoint, polylineSubcurve, projPointOnPolyline * changes - changed some function names to avoid potential name conflicts, and to make function names more explicit: + rotation -> createRotation + scaling -> createScaling + translation -> createRotation + homothecy -> createHomothecy + lineSymmetry -> createLineReflection + inCircle -> isPointInCircle + onCircle -> isPointOnCircle + onEdge -> isPointOnEdge + onLine -> isPointOnLine + onRay -> isPointOnRay + normalize -> normalizeVector * bug fixes - fixed bug in intersectEdges many updates in doc. geometry-2.1.1/inst/geom2d/PaxHeaders.5293/cartesianLine.m0000644000000000000000000000013212676233417020131 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/cartesianLine.m0000644000175000017500000000442612676233417021316 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} = } cartesianLine (@var{A}, @var{B},@var{C}) ## Create a straight line from cartesian equation coefficients. ## ## Create a line verifying the Cartesian equation: ## @var{A}*x + @var{B}*x + @var{C} = 0; ## ## @seealso{lines2d, createLine} ## @end deftypefn function line = cartesianLine(varargin) if length(varargin)==1 var = varargin{1}; a = var(:,1); b = var(:,2); c = var(:,3); elseif length(varargin)==3 a = varargin{1}; b = varargin{2}; c = varargin{3}; end # normalisation factor d = a.*a + b.*b; x0 = -a.*c./d; y0 = -b.*c./d; theta = atan2(-a, b); dx = cos(theta); dy = sin(theta); line = [x0 y0 dx dy]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/transformLine.m0000644000000000000000000000013212676233417020173 xustar0030 mtime=1459173135.477134124 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/transformLine.m0000644000175000017500000000475412676233417021364 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line2} = } transformLine (@var{line1}, @var{T}) ## Transform a line with an affine transform. ## ## Returns the line @var{line1} transformed with affine transform @var{T}. ## @var{line1} has the form [x0 y0 dx dy], and @var{T} is a transformation ## matrix. ## ## Format of @var{T} can be one of : ## [a b] , [a b c] , or [a b c] ## [d e] [d e f] [d e f] ## [0 0 1] ## ## Also works when @var{line1} is a [Nx4] array of double. In this case, @var{line2} ## has the same size as @var{line1}. ## ## @seealso{lines2d, transforms2d, transformPoint} ## @end deftypefn function dest = transformLine(line, trans) # isolate points points1 = line(:, 1:2); points2 = line(:, 1:2) + line(:, 3:4); # transform points points1 = transformPoint(points1, trans); points2 = transformPoint(points2, trans); dest = createLine(points1, points2); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angleDiff.m0000644000000000000000000000013212676233417017227 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angleDiff.m0000644000175000017500000000502712676233417020412 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dif} =} angleDiff (@var{angle1}, @var{angle2}) ## Difference between two angles ## ## Computes the signed angular difference between two angles in radians. ## The result is comprised between -PI and +PI. ## ## Example ## A = angleDiff(-pi/4, pi/4) ## A = ## 1.5708 # equal to pi/2 ## A = angleDiff(pi/4, -pi/4) ## A = ## -1.5708 # equal to -pi/2 ## ## @seealso{angles2d, angleAbsDiff} ## @end deftypefn function dif = angleDiff(angle1, angle2) # first, normalization angle1 = normalizeAngle(angle1); angle2 = normalizeAngle(angle2); # compute difference and normalize in [-pi pi] dif = normalizeAngle(angle2 - angle1, 0); endfunction %!test %! dif = angleDiff(0, pi/2); %! assert (pi/2, dif, 1e-6); %!test %! dif = angleDiff(pi/2, 0); %! assert (-pi/2, dif, 1e-6); %!test %! dif = angleDiff(0, 3*pi/2); %! assert (-pi/2, dif, 1e-6); %!test %! dif = angleDiff(3*pi/2, 0); %! assert (pi/2, dif, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/ellipse2cov.m0000644000000000000000000000013212676233417017577 xustar0030 mtime=1459173135.369185589 30 atime=1459173135.369185589 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/ellipse2cov.m0000644000175000017500000000652712676233417020770 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{K} = } ellipse2cov (@var{elli}) ## @deftypefnx {Function File} {@var{K} = } ellipse2cov (@var{ra}, @var{rb}) ## @deftypefnx {Function File} {@var{K} = } ellipse2cov (@dots{}, @var{theta}) ## Calculates covariance matrix from ellipse. ## ## If only one input is given, @var{elli} must define an ellipse as described in ## @command{ellipses2d}. ## If two inputs are given, @var{ra} and @var{rb} define the half-lenght of the ## axes. ## If a third input is given, @var{theta} must be the angle of rotation of the ## ellipse in radians, and in counter-clockwise direction. ## ## The output @var{K} contains the covariance matrix define by the ellipse. ## ## Run @code{demo ellipse2cov} to see an example. ## ## @seealso{ellipses2d, cov2ellipse, drawEllipse} ## @end deftypefn function K = ellipse2cov (elli, varargin); ra = 1; rb = 1; theta = 0; switch numel (varargin) case 0 ## ellipse format if numel (elli) != 5 print_usage (); end ra = elli(1,3); rb = elli(1,4); theta = elli(1,5)*pi/180; case 2 ## ra,rb if numel (elli) != 1 print_usage (); end ra = elli; rb = varargin{1}; case 3 ## ra,rb, theta if numel (elli) != 1 print_usage (); end ra = elli; rb = varargin{1}; theta = varargin{2}; otherwise print_usage (); end T = createRotation (theta)(1:2,1:2); K = T*diag([ra rb])*T'; endfunction %!demo %! elli = [0 0 1 3 -45]; %! %! # Create 2D normal random variables with covarinace defined by elli. %! K = ellipse2cov (elli) %! L = chol(K,'lower'); %! u = randn(1e3,2)*L'; %! %! Kn = cov (u) %! %! figure(1) %! plot(u(:,1),u(:,2),'.r'); %! hold on; %! drawEllipse(elli,'linewidth',2); %! hold off %! axis tight geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawEllipse.m0000644000000000000000000000013212676233417017623 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawEllipse.m0000644000175000017500000001123312676233417021002 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawEllipse (@var{elli}) ## @deftypefnx {Function File} {@var{h} = } drawEllipse (@var{xc}, @var{yc}, @var{ra}, @var{rb}) ## @deftypefnx {Function File} {@var{h} = } drawEllipse (@var{xc}, @var{yc}, @var{ra}, @var{rb}, @var{theta}) ## @deftypefnx {Function File} {@var{h} = } drawEllipse (@dots{}, @var{param}, @var{value}) ## Draw an ellipse on the current axis. ## ## drawEllipse(ELLI); ## Draws the ellipse ELLI in the form [XC YC RA RB THETA], with center ## (XC, YC), with main axis of half-length RA and RB, and orientation ## THETA in degrees counted counter-clockwise. ## Puts all parameters into one single array. ## ## drawEllipse(XC, YC, RA, RB); ## drawEllipse(XC, YC, RA, RB, THETA); ## Specifies ellipse parameters as separate arguments (old syntax). ## ## drawEllipse(..., NAME, VALUE); ## Specifies drawing style of ellipse, see the help of plot function. ## ## H = drawEllipse(...); ## Also returns handles to the created line objects. ## ## -> Parameters can also be arrays. In this case, all arrays are supposed ## to have the same size. ## ## Example: ## @example ## # Draw an ellipse centered in [50 50], with semi major axis length of ## # 40, semi minor axis length of 20, and rotated by 30 degrees. ## figure(1); clf; hold on; ## drawEllipse([50 50 40 20 30]); ## axis equal; ## @end example ## ## @seealso{ellipses2d, drawCircle, drawEllipseArc, ellipseAsPolygon} ## @end deftypefn function varargout = drawEllipse(varargin) # extract dawing style strings styles = {}; for i = 1:length(varargin) if ischar(varargin{i}) styles = varargin(i:end); varargin(i:end) = []; break; end end # extract ellipse parameters if length(varargin)==1 # ellipse is given in a single array ellipse = varargin{1}; x0 = ellipse(:, 1); y0 = ellipse(:, 2); a = ellipse(:, 3); b = ellipse(:, 4); if length(ellipse)>4 theta = ellipse(:, 5); else theta = zeros(size(x0)); end elseif length(varargin)>=4 # ellipse parameters given as separate arrays x0 = varargin{1}; y0 = varargin{2}; a = varargin{3}; b = varargin{4}; if length(varargin)>4 theta = varargin{5}; else theta = zeros(size(x0)); end else error('drawEllipse: incorrect input arguments'); end ## Process drawing of a set of ellipses # angular positions of vertices t = linspace(0, 2*pi, 145); # compute position of points to draw each ellipse h = zeros(length(x0), 1); for i = 1:length(x0) # pre-compute rotation angles (given in degrees) cot = cosd(theta(i)); sit = sind(theta(i)); # compute position of points used to draw current ellipse xt = x0(i) + a(i) * cos(t) * cot - b(i) * sin(t) * sit; yt = y0(i) + a(i) * cos(t) * sit + b(i) * sin(t) * cot; # stores handle to graphic object h(i) = plot(xt, yt, styles{:}); end # return handles if required if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/distancePointEdge.m0000644000000000000000000000013212676233417020741 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/distancePointEdge.m0000644000175000017500000001166612676233417022132 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } distancePointEdge (@var{point}, @var{edge}) ## @deftypefnx {Function File} {@var{dist} = } distancePointEdge (@dots{}, @var{opt}) ## @deftypefnx {Function File} {[@var{dist} @var{pos}]= } distancePointEdge (@dots{}) ## Minimum distance between a point and an edge ## ## Return the euclidean distance between edge @var{edge} and point @var{point}. ## @var{edge} has the form: [x1 y1 x2 y2], and @var{point} is [x y]. ## If @var{edge} is Ne-by-4 and @var{point} is Np-by-2, then @var{dist} is ## Np-by-Ne, where each row contains the distance of each point to all the edges. ## ## If @var{opt} is true (or equivalent), the optput is cmpatible with the original function: ## @table @samp ## @item 1 ## If @var{point} is 1-by-2 array, the result is Ne-by-1 array computed for each edge. ## @item 2 ## If @var{edge} is a 1-by-4 array, the result is Np-by-1 computed for each point. ## @item 3 ## If both @var{point} and @var{edge} are array, they must have the same number of ## rows, and the result is computed for each couple @code{@var{point}(i,:),@var{edge}(i,:)}. ## @end table ## ## If the the second output argument @var{pos} is requested, the function also ## returns the position of closest point on the edge. @var{pos} is comprised ## between 0 (first point) and 1 (last point). ## ## @seealso{edges2d, points2d, distancePoints, distancePointLine} ## @end deftypefn ## Rewritten to accept different numbers of points and edges. ## 2012 - Juan Pablo Carbajal function [dist, tp] = distancePointEdge(point, edge, opt=[]) Np = size (point,1); Ne = size (edge,1); edge = edge.'; # direction vector of each edge dx = edge(3,:) - edge(1,:); dy = edge(4,:) - edge(2,:); # compute position of points projected on the supporting line # (Size of tp is the max number of edges or points) delta = dx .* dx + dy .* dy; mask = delta < eps; delta(mask) = 1; warning ('off', 'Octave:broadcast','local'); tp = ((point(:, 1) - edge(1, :)) .* dx + ... (point(:, 2) - edge(2, :)) .* dy) ./ delta; tp(:,mask) = 0; # change position to ensure projected point is located on the edge tp(tp < 0) = 0; tp(tp > 1) = 1; # coordinates of projected point p0x = (edge(1,:) + tp .* dx); p0y = (edge(2,:) + tp .* dy); # compute distance between point and its projection on the edge dist = sqrt ((point(:,1) - p0x) .^ 2 + (point(:,2) - p0y) .^ 2); warning ('on', 'Octave:broadcast','local'); ## backwards compatibility if opt if Np != Ne && (Ne != 1 && Np !=1) error ("geometry:InvalidArgument", ... "Sizes must be equal or one of the inputs must be 1-by-N array."); end if Np == Ne dist = diag(dist)(:); tp = diag(tp)(:); elseif Np == 1 dist = dist.'; tp = tp.'; end end endfunction ## Original code ##tp = ((point(:, 1) - edge(:, 1)) .* dx + (point(:, 2) - edge(:, 2)) .* dy) ./ delta; ### ensure degenerated edges are correclty processed (consider the first ### vertex is the closest) ##if Ne > 1 ## tp(delta < eps) = 0; ##elseif delta < eps ## tp(:) = 0; ##end ### change position to ensure projected point is located on the edge ##tp(tp < 0) = 0; ##tp(tp > 1) = 1; ### coordinates of projected point ##p0 = [edge(:,1) + tp .* dx, edge(:,2) + tp .* dy]; ### compute distance between point and its projection on the edge ##dist = sqrt((point(:,1) - p0(:,1)) .^ 2 + (point(:,2) - p0(:,2)) .^ 2); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angleAbsDiff.m0000644000000000000000000000013212676233417017655 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angleAbsDiff.m0000644000175000017500000000460312676233417021037 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dif} =} angleAbsDiff (@var{angle1}, @var{angle2}) ## Computes the absolute angular difference between two angles in radians. ## The result is comprised between 0 and pi. ## ## @example ## A = angleAbsDiff(pi/2, pi/3) ## A = ## 0.5236 # equal to pi/6 ## @end example ## ## @seealso{angles2d, angleDiff} ## @end deftypefn function dif = angleAbsDiff(angle1, angle2) # first, normalization angle1 = normalizeAngle(angle1); angle2 = normalizeAngle(angle2); # compute difference and normalize dif = normalizeAngle(angle1 - angle2); dif = min(dif, 2*pi - dif); endfunction %!shared xp %! xp = pi/2; %!assert (xp, angleAbsDiff (pi/2, 0), 1e-6); %!assert (xp, angleAbsDiff (0, pi/2), 1e-6); %!assert (xp, angleAbsDiff (0, 3*pi/2), 1e-6); %!assert (xp, angleAbsDiff (3*pi/2, 0), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createRay.m0000644000000000000000000000013212676233417017267 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createRay.m0000644000175000017500000000666112676233417020457 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} { @var{ray} = } createRay (@var{point}, @var{angle}) ## @deftypefnx {Function File} { @var{ray} = } createRay (@var{x0},@var{y0}, @var{angle}) ## @deftypefnx {Function File} { @var{ray} = } createRay (@var{p1}, @var{p2}) ## Create a ray (half-line), from various inputs. ## ## A Ray is represented in a parametric form: [x0 y0 dx dy]. ## x = x0 + t*dx ## y = y0 + t*dy; ## for all t>0. ## ## @var{point} is a Nx2 array giving the starting point of the ray, and @var{angle} is the ## orientation of the ray respect to the positive x-axis. The ray origin can be specified with 2 input arguments @var{x0},@var{y0}. ## ## If two points @var{p1}, @var{p2} are given, creates a ray starting from point @var{p1} and going in the direction of point ## @var{p2}. ## ## Example ## @example ## origin = [3 4]; ## theta = pi/6; ## ray = createRay(origin, theta); ## axis([0 10 0 10]); ## drawRay(ray); ## @end example ## ## @seealso{rays2d, createLine, points2d} ## @end deftypefn function ray = createRay(varargin) if length(varargin)==2 p0 = varargin{1}; arg = varargin{2}; if size(arg, 2)==1 # second input is the ray angle ray = [p0 cos(arg) sin(arg)]; else # second input is another point ray = [p0 arg-p0]; end elseif length(varargin)==3 x = varargin{1}; y = varargin{2}; theta = varargin{3}; ray = [x y cos(theta) sin(theta)]; else error("Wrong number of arguments in 'createRay'. "); end endfunction %!shared p1,p2,ray %! p1 = [1 1]; %! p2 = [2 3]; %! ray = createRay(p1, p2); %!assert (p1, ray(1,1:2), 1e-6); %!assert (p2-p1, ray(1,3:4), 1e-6); %!shared p1,p2,ray %! p1 = [1 1;1 1]; %! p2 = [2 3;2 4]; %! ray = createRay(p1, p2); %!assert (2, size(ray, 1)); %!assert (p1, ray(:,1:2), 1e-6); %!assert (p2-p1, ray(:,3:4), 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointOnLine.m0000644000000000000000000000013212676233417020102 xustar0030 mtime=1459173135.449147467 30 atime=1459173135.449147467 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointOnLine.m0000644000175000017500000000516212676233417021265 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointOnLine (@var{point}, @var{line}) ## Test if a point belongs to a line ## ## B = isPointOnLine(POINT, LINE) ## with POINT being [xp yp], and LINE being [x0 y0 dx dy]. ## Returns 1 if point lies on the line, 0 otherwise. ## ## If POINT is an N*2 array of points, B is a N*1 array of booleans. ## ## If LINE is a N*4 array of line, B is a 1*N array of booleans. ## ## @seealso {lines2d, points2d, isPointOnEdge, isPointOnRay, angle3Points} ## @end deftypefn function b = isPointOnLine(point, line, varargin) # extract computation tolerance tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end # number of lines and of points Nl = size(line, 1); Np = size(point, 1); # adapt the size of inputs x0 = repmat(line(:,1)', Np, 1); y0 = repmat(line(:,2)', Np, 1); dx = repmat(line(:,3)', Np, 1); dy = repmat(line(:,4)', Np, 1); xp = repmat(point(:,1), 1, Nl); yp = repmat(point(:,2), 1, Nl); # test if lines are colinear b = abs((xp-x0).*dy-(yp-y0).*dx)./hypot(dx, dy) < tol; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/randomPointInBox.m0000644000000000000000000000013012676233417020600 xustar0029 mtime=1459173135.47313603 29 atime=1459173135.47313603 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/randomPointInBox.m0000644000175000017500000000545412676233417021771 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{points} =} randomPointInBox (@var{box}) ## @deftypefnx {Function File} {@var{points} =} randomPointInBox (@var{box}, @var{n}) ## Generate random points within a box. ## ## Generate a random point within the box @var{box}. The result is a 1-by-2 row ## vector. If @var{n} is given, generates @var{n} points. The result is a ## @var{n}-by-2 array. ## ## Example ## ## @example ## # draw points within a box ## box = [10 80 20 60]; ## pts = randomPointInBox(box, 500); ## figure(1); clf; hold on; ## drawBox(box); ## drawPoint(pts, '.'); ## axis('equal'); ## axis([0 100 0 100]); ## @end example ## ## @seealso{edges2d, boxes2d, clipLine} ## @end deftypefn function points = randomPointInBox(box, N=1, varargin) # extract box bounds xmin = box(1); xmax = box(2); ymin = box(3); ymax = box(4); # compute size of box dx = xmax - xmin; dy = ymax - ymin; # compute point coordinates points = [rand(N, 1)*dx+xmin , rand(N, 1)*dy+ymin]; endfunction %!demo %! # draw points within a box %! bb = [10 80 20 60]; %! pts = randomPointInBox(bb, 500); %! figure(1); clf; hold on; %! drawBox(bb); %! drawPoint(pts, '.'); %! axis equal %! axis([0 100 0 100]); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/ellipseAsPolygon.m0000644000000000000000000000013212676233417020641 xustar0030 mtime=1459173135.369185589 30 atime=1459173135.369185589 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/ellipseAsPolygon.m0000644000175000017500000000605612676233417022027 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} = } ellipseAsPolygon (@var{ell}, @var{n}) ## Convert an ellipse into a series of points ## ## P = ellipseAsPolygon(ELL, N); ## converts ELL given as [x0 y0 a b] or [x0 y0 a b theta] into a polygon ## with N edges. The result P is (N+1)-by-2 array containing coordinates ## of the N+1 vertices of the polygon. ## The resulting polygon is closed, i.e. the last point is the same as the ## first one. ## ## P = ellipseAsPolygon(ELL); ## Use a default number of edges equal to 72. This result in one piont for ## each 5 degrees. ## ## [X Y] = ellipseAsPolygon(...); ## Return the coordinates o fvertices in two separate arrays. ## ## @seealso{ellipses2d, circleAsPolygon, rectAsPolygon, drawEllipse} ## @end deftypefn function varargout = ellipseAsPolygon(ellipse, N) # default value for N if nargin < 2 N = 72; end # angle of ellipse theta = 0; if size(ellipse, 2) > 4 theta = ellipse(:,5); end # get ellipse parameters xc = ellipse(:,1); yc = ellipse(:,2); a = ellipse(:,3); b = ellipse(:,4); # create time basis t = linspace(0, 2*pi, N+1)'; # pre-compute trig functions (angles is in degrees) cot = cosd(theta); sit = sind(theta); # position of points x = xc + a * cos(t) * cot - b * sin(t) * sit; y = yc + a * cos(t) * sit + b * sin(t) * cot; # format output depending on number of a param. if nargout == 1 varargout = {[x y]}; elseif nargout == 2 varargout = {x, y}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/beltproblem.m0000644000000000000000000000013212676233417017657 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/beltproblem.m0000644000175000017500000001157212676233417021044 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{tangent},@var{inner}] = } beltproblem (@var{c}, @var{r}) ## Finds the four lines tangent to two circles with given centers and radii. ## ## The function solves the belt problem in 2D for circles with center @var{c} and ## radii @var{r}. ## ## @strong{INPUT} ## @table @var ## @item c ## 2-by-2 matrix containig coordinates of the centers of the circles; one row per circle. ## @item r ## 2-by-1 vector with the radii of the circles. ##@end table ## ## @strong{OUPUT} ## @table @var ## @item tangent ## 4-by-4 matrix with the points of tangency. Each row describes a segment(edge). ## @item inner ## 4-by-2 vector with the point of intersection of the inner tangents (crossed belts) ## with the segment that joins the centers of the two circles. If ## the i-th edge is not an inner tangent then @code{inner(i,:)=[NaN,NaN]}. ## @end table ## ## Example: ## ## @example ## c = [0 0;1 3]; ## r = [1 0.5]; ## [T inner] = beltproblem(c,r) ## @result{} T = ## -0.68516 0.72839 1.34258 2.63581 ## 0.98516 0.17161 0.50742 2.91419 ## 0.98675 -0.16225 1.49338 2.91888 ## -0.88675 0.46225 0.55663 3.23112 ## ## @result{} inner = ## 0.66667 2.00000 ## 0.66667 2.00000 ## NaN NaN ## NaN NaN ## ## @end example ## ## @seealso{edges2d} ## @end deftypefn function [edgeTan inner] = beltproblem(c,r) x0 = [c(1,1) c(1,2) c(2,1) c(2,2)]; r0 = r([1 1 2 2]); middleEdge = createEdge(c(1,:),c(2,:)); ind0 = [1 0 1 0; 0 1 1 0; 1 1 1 0; -1 0 1 0; 0 -1 1 0; -1 -1 1 0;... 1 0 0 1; 0 1 0 1; 1 1 0 1; -1 0 0 1; 0 -1 0 1; -1 -1 0 1;... 1 0 1 1; 0 1 1 1; 1 1 1 1; -1 0 1 1; 0 -1 1 1; -1 -1 1 1;... 1 0 -1 0; 0 1 -1 0; 1 1 -1 0; -1 0 -1 0; 0 -1 -1 0; -1 -1 -1 0;... 1 0 0 -1; 0 1 0 -1; 1 1 0 -1; -1 0 0 -1; 0 -1 0 -1; -1 -1 0 -1;... 1 0 -1 -1; 0 1 -1 -1; 1 1 -1 -1; -1 0 -1 -1; 0 -1 -1 -1; -1 -1 -1 -1]; nInit = size(ind0,1); ir = randperm(nInit); edgeTan = zeros(4,4); inner = zeros(4,2); nSol = 0; i=1; ## Solve for 2 different lines while nSol<4 && i 1e-6); end if all(notequal) nSol = nSol+1; edgeTan(nSol,:) = createEdge(sol(1:2),sol(3:4)); # Find innerTangent inner(nSol,:) = intersectEdges(middleEdge,edgeTan(nSol,:)); end i = i+1; end endfunction function res = belt(x,c,r) res = zeros(4,1); res(1,1) = (x(3:4) - c(2,1:2))*(x(3:4) - x(1:2))'; res(2,1) = (x(1:2) - c(1,1:2))*(x(3:4) - x(1:2))'; res(3,1) = sumsq(x(1:2) - c(1,1:2)) - r(1)^2; res(4,1) = sumsq(x(3:4) - c(2,1:2)) - r(2)^2; end %!demo %! c = [0 0;1 3]; %! r = [1 0.5]; %! [T inner] = beltproblem(c,r) %! %! figure(1) %! clf %! h = drawEdge(T); %! set(h(find(~isnan(inner(:,1)))),'color','r'); %! set(h,'linewidth',2); %! hold on %! drawCircle([c(1,:) r(1); c(2,:) r(2)],'linewidth',2); %! axis tight %! axis equal %! %! # ------------------------------------------------------------------- %! # The circles with the tangents edges are plotted. The solution with %! # crossed belts (inner tangets) is shown in red. geometry-2.1.1/inst/geom2d/PaxHeaders.5293/inertiaEllipse.m0000644000000000000000000000013212676233417020321 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/inertiaEllipse.m0000644000175000017500000000646012676233417021506 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{ell} = } inertiaEllipse (@var{pts}) ## Inertia ellipse of a set of points ## ## ELL = inertiaEllipse(PTS); ## where PTS is a N*2 array containing coordinates of N points, computes ## the inertia ellispe of the set of points. ## ## The result has the form: ## ELL = [XC YC A B THETA], ## with XC and YC being the center of mass of the point set, A and B are ## the lengths of the inertia ellipse (see below), and THETA is the angle ## of the main inertia axis with the horizontal (counted in degrees ## between 0 and 180). ## A and B are the standard deviations of the point coordinates when ## ellipse is aligned with the inertia axes. ## ## @example ## pts = randn(100, 2); ## pts = transformPoint(pts, createScaling(5, 2)); ## pts = transformPoint(pts, createRotation(pi/6)); ## pts = transformPoint(pts, createTranslation(3, 4)); ## ell = inertiaEllipse(pts); ## figure(1); clf; hold on; ## drawPoint(pts); ## drawEllipse(ell, 'linewidth', 2, 'color', 'r'); ## @end example ## ## @seealso{ellipses2d, drawEllipse} ## @end deftypefn function ell = inertiaEllipse(points) # ellipse center xc = mean(points(:,1)); yc = mean(points(:,2)); # recenter points x = points(:,1) - xc; y = points(:,2) - yc; # number of points n = size(points, 1); # inertia parameters Ixx = sum(x.^2) / n; Iyy = sum(y.^2) / n; Ixy = sum(x.*y) / n; # compute ellipse semi-axis lengths common = sqrt( (Ixx - Iyy)^2 + 4 * Ixy^2); ra = sqrt(2) * sqrt(Ixx + Iyy + common); rb = sqrt(2) * sqrt(Ixx + Iyy - common); # compute ellipse angle in degrees theta = atan2(2 * Ixy, Ixx - Iyy) / 2; theta = rad2deg(theta); # create the resulting inertia ellipse ell = [xc yc ra rb theta]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/triangleGrid.m0000644000000000000000000000013212676233417017763 xustar0030 mtime=1459173135.481132218 30 atime=1459173135.481132218 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/triangleGrid.m0000644000175000017500000000474612676233417021155 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts} = } triangleGrid (@var{bounds}, @var{origin}, @var{size}) ## Generate triangular grid of points in the plane. ## ## usage ## PTS = triangleGrid(BOUNDS, ORIGIN, SIZE) ## generate points, lying in the window defined by BOUNDS, given in form ## [xmin ymin xmax ymax], starting from origin with a constant step equal ## to size. ## SIZE is constant and is equals to the length of the sides of each ## triangles. ## ## TODO: add possibility to use rotated grid ## ## @end deftypefn function varargout = triangleGrid(bounds, origin, size, varargin) dx = size(1); dy = size(1)*sqrt(3); # consider two square grids with different centers pts1 = squareGrid(bounds, origin, [dx dy], varargin{:}); pts2 = squareGrid(bounds, origin + [dx dy]/2, [dx dy], varargin{:}); # gather points pts = [pts1;pts2]; # process output if nargout>0 varargout{1} = pts; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createTranslation.m0000644000000000000000000000013212676233417021032 xustar0030 mtime=1459173135.349195119 30 atime=1459173135.349195119 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createTranslation.m0000644000175000017500000000502612676233417022214 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } createTranslation (@var{vector}) ## @deftypefnx {Function File} {@var{T} = } createTranslation (@var{dx},@var{dy}) ## Create the 3*3 matrix of a translation. ## ## Returns the matrix corresponding to a translation by the vector [@var{dx} @var{dy}]. ## The components can be given as two arguments. ## The returned matrix has the form : ## [1 0 TX] ## [0 1 TY] ## [0 0 1] ## ## @seealso{transforms2d, transformPoint, createRotation, createScaling} ## @end deftypefn function trans = createTranslation(varargin) # process input arguments if isempty(varargin) tx = 0; ty = 0; elseif length(varargin)==1 var = varargin{1}; tx = var(1); ty = var(2); else tx = varargin{1}; ty = varargin{2}; end # create the matrix representing the translation trans = [1 0 tx ; 0 1 ty ; 0 0 1]; endfunction %!test %! trans = createTranslation(2, 3); %! assert (trans, [1 0 2;0 1 3;0 0 1], 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isLeftOriented.m0000644000000000000000000000013212676233417020270 xustar0030 mtime=1459173135.445149373 30 atime=1459173135.445149373 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isLeftOriented.m0000644000175000017500000000441212676233417021450 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isLeftOriented (@var{point}, @var{line}) ## Test if a point is on the left side of a line ## ## B = isLeftOriented(POINT, LINE); ## Returns TRUE if the point lies on the left side of the line with ## respect to the line direction. ## ## @seealso{lines2d, points2d, isCounterClockwise, isPointOnLine, distancePointLine} ## @end deftypefn function b = isLeftOriented(point, line) Nl = size(line, 1); Np = size(point, 1); x0 = repmat(line(:,1)', Np, 1); y0 = repmat(line(:,2)', Np, 1); dx = repmat(line(:,3)', Np, 1); dy = repmat(line(:,4)', Np, 1); xp = repmat(point(:,1), 1, Nl); yp = repmat(point(:,2), 1, Nl); b = (xp-x0).*dy-(yp-y0).*dx < 0; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/lines2d.m0000644000000000000000000000013212676233417016710 xustar0030 mtime=1459173135.457143654 30 atime=1459173135.457143654 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/lines2d.m0000644000175000017500000000512612676233417020073 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} lines2d () ## Description of functions operating on planar lines. # # The term 'line' refers to a planar straight line, which is an unbounded # curve. Line segments defined between 2 points, which are bounded, are # called 'edge', and are presented in file 'edges2d'. # # A straight line is defined by a point (its origin), and a vector (its # direction). The different parameters are bundled into a row vector: # LINE = [x0 y0 dx dy]; # # A line contains all points (x,y) such that: # x = x0 + t*dx # y = y0 + t*dy; # for all t between -infinity and +infinity. # # @seealso{points2d, vectors2d, edges2d, rays2d # createLine, cartesianLine, medianLine, edgeToLine # orthogonalLine, parallelLine, bisector, radicalAxis # lineAngle, linePosition, projPointOnLine # isPointOnLine, distancePointLine, isLeftOriented # intersectLines, intersectLineEdge, clipLine # invertLine, transformLine, drawLine # lineFit} ## @end deftypefn function lines2d(varargin) help('lines2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/orthogonalLine.m0000644000000000000000000000013212676233417020334 xustar0030 mtime=1459173135.461141748 30 atime=1459173135.461141748 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/orthogonalLine.m0000644000175000017500000000446412676233417021523 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{perp} = } orthogonalLine (@var{line}, @var{point}) ## Create a line orthogonal to another one. # # Returns the line orthogonal to the line @var{line} and going through the # point given by @var{point}. Directed angle from @var{line} to @var{perp} is pi/2. # @var{line} is given as [x0 y0 dx dy] and @var{point} is [xp yp]. # # @seealso{lines2d, parallelLine} ## @end deftypefn function res = orthogonalLine(line, point) N = max(size(point, 1), size(line, 1)); if size(point, 1)>1 res = point; else res = ones(N, 1)*point; end if size(line, 1)>1 res(:,3) = -line(:,4); res(:,4) = line(:,3); else res(:,3) = -ones(N,1)*line(4); res(:,4) = ones(N,1)*line(3); end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createEdge.m0000644000000000000000000000013212676233417017400 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createEdge.m0000644000175000017500000001151412676233417020561 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{edge} = } createEdge (@var{p1}, @var{p2}) ## @deftypefnx {Function File} {@var{edge} = } createEdge (@var{x0}, @var{y0}, @var{dx}, @var{dy}) ## @deftypefnx {Function File} {@var{edge} = } createEdge (@var{param}) ## @deftypefnx {Function File} {@var{edge} = } createEdge (@var{line}, @var{d}) ## Create an edge between two points, or from a line. ## ## The internal format for edge representation is given by coordinates of ## two points : [x1 y1 x2 y2]. ## This function can serve as a line to edge converter. ## ## ## Returns the edge between the two given points @var{p1} and @var{p2}. ## ## Returns the edge going through point (@var{x0}, @var{y0}) and with direction ## vector (@var{dx},@var{dy}). ## ## When @var{param} is an array of 4 values, creates the edge going through the ## point (param(1) param(2)), and with direction vector given by ## (param(3) param(4)). ## ## When @var{line} is given, creates the edge contained in @var{line}, with same ## direction and start point, but with length given by @var{d}. ## ## ## Note: in all cases, parameters can be vertical arrays of the same ## dimension. The result is then an array of edges, of dimensions [N*4]. ## ## @seealso{edges2d, lines2d, drawEdge, clipEdge} ## @end deftypefn function edge = createEdge(varargin) if length(varargin)==1 # Only one input parameter. It can be : # - line angle # - array of four parameters # TODO : add control for arrays of lines. var = varargin{1}; if size(var, 2)==4 # 4 parameters of the line in a single array. #edge = var; edge = zeros(size(var)); edge(:, 1:2) = var(:,1:2); edge(:, 3:4) = edge(:, 1:2)+var(:,3:4); elseif size(var, 2)==1 # 1 parameter : angle of the line, going through origin. edge = [zeros(size(var,1)) zeros(size(var,1)) cos(var) sin(var)]; else error('wrong number of dimension for arg1 : can be 1 or 4'); end elseif length(varargin)==2 # 2 input parameters. They can be : # - 2 points, then 2 arrays of 1*2 double, # - a line, and a distance. v1 = varargin{1}; v2 = varargin{2}; if size(v1, 2)==2 # first input parameter is first point, and second input is the # second point. #edge = [v1(:,1), v1(:,2), v2(:,1), v2(:,2)]; edge = [v1 v2]; else # first input parameter is a line, and second one a distance. angle = atan2(v1(:,4), v1(:,3)); edge = [v1(:,1), v1(:,2), v1(:,1)+v2.*cos(angle), v1(:,2)+v2.*sin(angle)]; end elseif length(varargin)==3 # 3 input parameters : # first one is a point belonging to the line, # second and third ones are direction vector of the line (dx and dy). p = varargin{1}; edge = [p(:,1) p(:,2) p(:,1)+varargin{2} p(:,2)+varargin{3}]; elseif length(varargin)==4 # 4 input parameters : # they are x0, y0 (point belonging to line) and dx, dy (direction # vector of the line). # All parameters should have the same size. edge = [varargin{1} varargin{2} varargin{1}+varargin{3} varargin{2}+varargin{4}]; else error('Wrong number of arguments in ''createLine'' '); end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawCircleArc.m0000644000000000000000000000013212676233417020055 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawCircleArc.m0000644000175000017500000000745712676233417021251 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawCircleArc (@var{xc}, @var{yc}, @var{r}, @var{start}, @var{end}) ## @deftypefnx {Function File} {@var{h} = } drawCircleArc (@var{arc}) ## @deftypefnx {Function File} {@var{h} = } drawCircleArc (@dots{}, @var{param}, @var{value}) ## Draw a circle arc on the current axis ## ## drawCircleArc(XC, YC, R, START, EXTENT); ## Draws circle with center (XC, YC), with radius R, starting from angle ## START, and with angular extent given by EXTENT. START and EXTENT angles ## are given in degrees. ## ## drawCircleArc(ARC); ## Puts all parameters into one single array. ## ## drawCircleArc(..., PARAM, VALUE); ## specifies plot properties by using one or several parameter name-value ## pairs. ## ## H = drawCircleArc(...); ## Returns a handle to the created line object. ## ## @example ## # Draw a red thick circle arc ## arc = [10 20 30 -120 240]; ## figure; ## axis([-50 100 -50 100]); ## hold on ## drawCircleArc(arc, 'LineWidth', 3, 'Color', 'r') ## @end example ## ## @seealso{circles2d, drawCircle, drawEllipse} ## @end deftypefn function varargout = drawCircleArc(varargin) if nargin == 0 error('Need to specify circle arc'); end circle = varargin{1}; if size(circle, 2) == 5 x0 = circle(:,1); y0 = circle(:,2); r = circle(:,3); start = circle(:,4); extent = circle(:,5); varargin(1) = []; elseif length(varargin) >= 5 x0 = varargin{1}; y0 = varargin{2}; r = varargin{3}; start = varargin{4}; extent = varargin{5}; varargin(1:5) = []; else error('drawCircleArc: please specify center, radius and angles of circle arc'); end # convert angles in radians t0 = deg2rad(start); t1 = t0 + deg2rad(extent); # number of line segments N = 60; # initialize handles vector h = zeros(length(x0), 1); # draw each circle arc individually for i = 1:length(x0) # compute basis t = linspace(t0(i), t1(i), N+1)'; # compute vertices coordinates xt = x0(i) + r(i)*cos(t); yt = y0(i) + r(i)*sin(t); # draw the circle arc h(i) = plot(xt, yt, varargin{:}); end if nargout > 0 varargout = {h}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/normalizeVector.m0000644000000000000000000000013212676233417020533 xustar0030 mtime=1459173135.461141748 30 atime=1459173135.461141748 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/normalizeVector.m0000644000175000017500000000461212676233417021715 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{vn} = } normalizeVector (@var{v}) ## Normalize a vector to have norm equal to 1 ## ## Returns the normalization of vector @var{v}, such that ||@var{v}|| = 1. ## @var{v} can be either a row or a column vector. ## ## When @var{v} is a MxN array, normalization is performed for each row of the ## array. ## ## Example: ## ## @example ## vn = normalizeVector([3 4]) ## vn = ## 0.6000 0.8000 ## vectorNorm(vn) ## ans = ## 1 ## @end example ## ## @seealso{vectors2d, vectorNorm} ## @end deftypefn function vn = normalizeVector(v) dim = size(v); if dim(1)==1 || dim(2)==1 vn = v / sqrt(sum(v.^2)); else #same as: vn = v./repmat(sqrt(sum(v.*v, 2)), [1 dim(2)]); vn = bsxfun(@rdivide, v, sqrt(sum(v.^2, 2))); end endfunction %!assert (1,vectorNorm (normalizeVector ([3 4]))) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angles2d.m0000644000000000000000000000013212676233417017047 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angles2d.m0000644000175000017500000000436112676233417020232 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} angles2d () ## Description of functions for manipulating angles ## ## Angles are normalized in an interval of width 2*PI. Most geom2d ## functions return results in the [0 2*pi] interval, but it can be ## convenient to consider the [-pi pi] interval as well. See the ## normalizeAngle function to switch between conventions. ## ## Angles are usually oriented. The default orientation is the CCW ## (Counter-Clockwise) orientation. ## ## @seealso{angle2Points, angle3Points, angleAbsDiff, normalizeAngle, vectorAngle, ## angleDiff, angleSort, lineAngle, edgeAngle, deg2rad, rad2deg} ## @end deftypefn function angles2d help('angles2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/parallelLine.m0000644000000000000000000000013212676233417017754 xustar0030 mtime=1459173135.461141748 30 atime=1459173135.461141748 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/parallelLine.m0000644000175000017500000000517212676233417021140 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{res} = } parallelLine (@var{line}, @var{point}) ## @deftypefnx {Function File} {@var{res} = } parallelLine (@var{line}, @var{dist}) ## Create a line parallel to another one. ## ## Returns the line with same direction vector than @var{line} and going through ## the point given by @var{point}. ## @var{line} is given as [x0 y0 dx dy] and @var{point} is [xp yp]. ## ## Uses relative distance to specify position. The new line will be ## located at distance @var{dist}, counted positive in the right side of @var{line} ## and negative in the left side. ## ## @seealso{lines2d, orthogonalLine, distancePointLine} ## @end deftypefn function res = parallelLine(line, point) if size(point, 1)==1 # use a distance. Compute position of point located at distance DIST on # the line orthogonal to the first one. point = pointOnLine([line(:,1) line(:,2) line(:,4) -line(:,3)], point); end # normal case: compute line through a point with given direction res = zeros(1, 4); res(1:2) = point; res(3:4) = line(3:4); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/cov2ellipse.m0000644000000000000000000000013212676233417017577 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/cov2ellipse.m0000644000175000017500000000614612676233417020765 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{ellipse} = } cov2ellipse (@var{K}) ## @deftypefnx {Function File} {[@var{ra} @var{rb} @var{theta}] = } cov2ellipse (@var{K}) ## @deftypefnx {Function File} {@dots{} = } cov2ellipse (@dots{}, @samp{tol},@var{tol}) ## Calculates ellipse parameters from covariance matrix. ## ## @var{K} must be symmetric positive (semi)definite. The optional argument ## @samp{tol} sets the tolerance for the verification of the ## positive-(semi)definiteness of the matrix @var{K} (see @command{isdefinite}). ## ## If only one output argument is supplied a vector defining a ellipse is returned ## as defined in @command{ellipses2d}. Otherwise the angle @var{theta} is given ## in radians. ## ## Run @code{demo cov2ellipse} to see an example. ## ## @seealso{ellipses2d, cov2ellipse, drawEllipse} ## @end deftypefn function varargout = cov2ellipse (K, varargin); parser = inputParser (); parser.FunctionName = "cov2ellipse"; parser.addParamValue ('Tol', 100*eps*norm (K, "fro"), @(x)x>0); parser.parse(varargin{:}); if isdefinite (K,parser.Results.Tol) == -1 print_usage end [R S W] = svd (K); theta = atan2 (R(2,1), R(1,1)); v = sqrt (diag(S))'; if nargout == 1 varargout{1} = [0 0 v theta*180/pi]; elseif nargout == 3 varargout{1} = v(1); varargout{2} = v(2); varargout{3} = theta; end endfunction %!demo %! K = [2 1; 1 2]; %! L = chol(K,'lower'); %! u = randn(1e3,2)*L'; %! %! elli = cov2ellipse (K) %! %! figure(1) %! plot(u(:,1),u(:,2),'.r'); %! hold on; %! drawEllipse(elli,'linewidth',2); %! hold off %! axis tight geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointOnEdge.m0000644000000000000000000000013212676233417020057 xustar0030 mtime=1459173135.449147467 30 atime=1459173135.449147467 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointOnEdge.m0000644000175000017500000002170412676233417021242 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edge}) ## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edge}, @var{tol}) ## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{point}, @var{edgearray}) ## @deftypefnx {Function File} {@var{b} = } isPointOnEdge (@var{pointarray}, @var{edgearray}) ## Test if a point belongs to an edge. # # with @var{point} being [xp yp], and @var{edge} being [x1 y1 x2 y2], returns TRUE if # the point is located on the edge, and FALSE otherwise. # # Specify an optilonal tolerance value @var{tol}. The tolerance is given as a # fraction of the norm of the edge direction vector. Default is 1e-14. # # When one of the inputs has several rows, return the result of the test # for each element of the array tested against the single parameter. # # When both @var{pointarray} and @var{edgearray} have the same number of rows, # returns a column vector with the same number of rows. # When the number of rows are different and both greater than 1, returns # a Np-by-Ne matrix of booleans, containing the result for each couple of # point and edge. # # @seealso{edges2d, points2d, isPointOnLine} ## @end deftypefn function b = isPointOnEdge(point, edge, varargin) # extract computation tolerance tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end # number of edges and of points Np = size(point, 1); Ne = size(edge, 1); # adapt size of inputs if needed, and extract elements for computation if Np == Ne # When the number of points and edges is the same, the one-to-one test # will be computed, so there is no need to repeat matrices dx = edge(:,3) - edge(:,1); dy = edge(:,4) - edge(:,2); lx = point(:,1) - edge(:,1); ly = point(:,2) - edge(:,2); elseif Np == 1 # one point, several edges dx = edge(:, 3) - edge(:, 1); dy = edge(:, 4) - edge(:, 2); lx = point(ones(Ne, 1), 1) - edge(:, 1); ly = point(ones(Ne, 1), 2) - edge(:, 2); elseif Ne == 1 # several points, one edge dx = (edge(3) - edge(1)) * ones(Np, 1); dy = (edge(4) - edge(2)) * ones(Np, 1); lx = point(:, 1) - edge(1); ly = point(:, 2) - edge(2); else # Np points and Ne edges: # Create an array for each parameter, so that the result will be a # Np-by-Ne matrix of booleans (requires more memory, and uses repmat) x0 = repmat(edge(:, 1)', Np, 1); y0 = repmat(edge(:, 2)', Np, 1); dx = repmat(edge(:,3)', Np, 1) - x0; dy = repmat(edge(:,4)', Np, 1) - y0; lx = repmat(point(:, 1), 1, Ne) - x0; ly = repmat(point(:, 2), 1, Ne) - y0; end # test if point is located on supporting line b1 = (abs(lx.*dy - ly.*dx) ./ hypot(dx, dy)) < tol; # compute position of point with respect to edge bounds # use different tests depending on line angle ind = abs(dx) > abs(dy); t = zeros(size(dx)); t(ind) = lx( ind) ./ dx( ind); t(~ind) = ly(~ind) ./ dy(~ind); # check if point is located between edge bounds b = t >- tol & t-1 < tol & b1; endfunction %!shared points, vertices, edges %!demo %! # create a point array %! points = [10 10;15 10; 30 10]; %! # create an edge array %! vertices = [10 10;20 10;20 20;10 20]; %! edges = [vertices vertices([2:end 1], :)]; %! %! # Test one point and one edge %! isPointOnEdge(points(1,:), edges(1,:)) %! isPointOnEdge(points(3,:), edges(1,:)) %!demo %! # create a point array %! points = [10 10;15 10; 30 10]; %! # create an edge array %! vertices = [10 10;20 10;20 20;10 20]; %! edges = [vertices vertices([2:end 1], :)]; %! %! # Test one point and several edges %! isPointOnEdge(points(1,:), edges)' %!demo %! # create a point array %! points = [10 10;15 10; 30 10]; %! # create an edge array %! vertices = [10 10;20 10;20 20;10 20]; %! edges = [vertices vertices([2:end 1], :)]; %! %! # Test several points and one edge %! isPointOnEdge(points, edges(1,:))' %!demo %! # create a point array %! points = [10 10;15 10; 30 10]; %! # create an edge array %! vertices = [10 10;20 10;20 20;10 20]; %! edges = [vertices vertices([2:end 1], :)]; %! %! # Test N points and N edges %! isPointOnEdge(points, edges(1:3,:))' %!demo %! # create a point array %! points = [10 10;15 10; 30 10]; %! # create an edge array %! vertices = [10 10;20 10;20 20;10 20]; %! edges = [vertices vertices([2:end 1], :)]; %! %! # Test NP points and NE edges %! isPointOnEdge(points, edges) %!test %! p1 = [10 20]; %! p2 = [80 20]; %! edge = [p1 p2]; %! p0 = [10 20]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [80 20]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [50 20]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [9.99 20]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [80.01 20]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [50 21]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [79 19]; %! assert (!isPointOnEdge(p0, edge)); %!test %! p1 = [20 10]; %! p2 = [20 80]; %! edge = [p1 p2]; %! p0 = [20 10]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [20 80]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [20 50]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [20 9.99]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [20 80.01]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [21 50]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [19 79]; %! assert (!isPointOnEdge(p0, edge)); %!test %! p1 = [10 20]; %! p2 = [60 70]; %! edge = [p1 p2]; %! assert (isPointOnEdge(p1, edge)); %! assert (isPointOnEdge(p2, edge)); %! p0 = [11 21]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [59 69]; %! assert (isPointOnEdge(p0, edge)); %! p0 = [9.99 19.99]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [60.01 70.01]; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [30 50.01]; %! assert (!isPointOnEdge(p0, edge)); %!test %! edge = [10 20 80 20; 20 10 20 80; 20 10 60 70]; %! p0 = [20 20]; %! assert ([true ; true ; false], isPointOnEdge(p0, edge)); %!test %! k = 1e15; %! p1 = [10 20]*k; %! p2 = [60 70]*k; %! edge = [p1 p2]; %! assert (isPointOnEdge(p1, edge)); %! assert (isPointOnEdge(p2, edge)); %! p0 = [11 21]*k; %! assert (isPointOnEdge(p0, edge)); %! p0 = [59 69]*k; %! assert (isPointOnEdge(p0, edge)); %! p0 = [9.99 19.99]*k; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [60.01 70.01]*k; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [30 50.01]*k; %! assert (!isPointOnEdge(p0, edge)); %!test %! k = 1e-10; %! p1 = [10 20]*k; %! p2 = [60 70]*k; %! edge = [p1 p2]; %! assert (isPointOnEdge(p1, edge)); %! assert (isPointOnEdge(p2, edge)); %! p0 = [11 21]*k; %! assert (isPointOnEdge(p0, edge)); %! p0 = [59 69]*k; %! assert (isPointOnEdge(p0, edge)); %! p0 = [9.99 19.99]*k; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [60.01 70.01]*k; %! assert (!isPointOnEdge(p0, edge)); %! p0 = [30 50.01]*k; %! assert (!isPointOnEdge(p0, edge)); %!test %! p1 = [10 20]; %! p2 = [80 20]; %! edge = [p1 p2]; %! p0 = [10 20; 80 20; 50 20;50 21]; %! exp = [true;true;true;false]; %! assert (exp, isPointOnEdge(p0, edge)); %!test %! p1 = [10 20]; %! p2 = [80 20]; %! edge = [p1 p2]; %! p0 = [40 20]; %! exp = [true;true;true;true]; %! assert (exp, isPointOnEdge(p0, [edge;edge;edge;edge])); %!test %! edge1 = [10 20 80 20]; %! edge2 = [30 10 30 80]; %! edges = [edge1; edge2]; %! p0 = [40 20;30 90]; %! exp = [true;false]; %! assert (exp, isPointOnEdge(p0, edges)); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/circleArcAsCurve.m0000644000000000000000000000013212676233417020530 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/circleArcAsCurve.m0000644000175000017500000000543212676233417021713 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} = } circleArcAsCurve (@var{arc}, @var{N}) ## Convert a circle arc into a series of points ## ## P = circleArcAsCurve(ARC, N); ## convert the circle ARC into a series of N points. ## ARC is given in the format: [XC YC R THETA1 DTHETA] ## where XC and YC define the center of the circle, R its radius, THETA1 ## is the start of the arc and DTHETA is the angle extent of the arc. Both ## angles are given in degrees. ## N is the number of vertices of the resulting polyline, default is 65. ## ## The result is a N-by-2 array containing coordinates of the N points. ## ## [X Y] = circleArcAsCurve(ARC, N); ## Return the result in two separate arrays with N lines and 1 column. ## ## ## @seealso{circles2d, circleAsPolygon, drawCircle, drawPolygon} ## @end deftypefn function varargout = circleArcAsCurve(arc, N) # default value for N if nargin < 2 N = 65; end # vector of positions t0 = deg2rad(arc(4)); t1 = t0 + deg2rad(arc(5)); t = linspace(t0, t1, N)'; # compute coordinates of vertices x = arc(1) + arc(3) * cos(t); y = arc(2) + arc(3) * sin(t); # format output if nargout <= 1 varargout = {[x y]}; else varargout = {x, y}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createHomothecy.m0000644000000000000000000000013212676233417020473 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createHomothecy.m0000644000175000017500000000426412676233417021660 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } createHomothecy (@var{point}, @var{ratio}) ## Create the the 3x3 matrix of an homothetic transform. # # @var{point} is the center of the homothecy, @var{ratio} is its factor. # # @seealso{transforms2d, transformPoint, createTranslation} ## @end deftypefn function trans = createHomothecy(point, ratio) # extract coordinate of center x0 = point(:,1); y0 = point(:,2); # compute coefficients of the matrix m00 = ratio; m01 = 0; m02 = x0*(1-ratio); m10 = 0; m11 = ratio; m12 = y0*(1-ratio); # create transformation trans = [m00 m01 m02; m10 m11 m12; 0 0 1]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/pointOnLine.m0000644000000000000000000000013212676233417017606 xustar0030 mtime=1459173135.465139842 30 atime=1459173135.465139842 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/pointOnLine.m0000644000175000017500000000432212676233417020766 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} = } pointOnLine (@var{line}, @var{d}) ## Create a point on a line at a given position on the line. ## ## Creates the point belonging to the line @var{line}, and located at the ## distance @var{d} from the line origin. ## @var{line} has the form [x0 y0 dx dy]. ## @var{line} and @var{d} should have the same number N of rows. The result will have ## N rows and 2 column (x and y positions). ## ## @seealso{lines2d, points2d, onLine, onLine, linePosition} ## @end deftypefn function point = pointOnLine(lin, pos) ang = lineAngle(lin); point = [lin(:,1) + pos .* cos(ang), lin(:,2) + pos .* sin(ang)]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectLines.m0000644000000000000000000000013212676233417020343 xustar0030 mtime=1459173135.441151279 30 atime=1459173135.441151279 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectLines.m0000644000175000017500000001350712676233417021530 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} =} intersectLines (@var{line1}, @var{line2}) ## @deftypefnx {Function File} {@var{point} =} intersectLines (@var{line1}, @var{line2},@var{eps}) ## Return all intersection points of N lines in 2D. ## ## Returns the intersection point of lines @var{line1} and @var{line2}. ## @var{line1} and @var{line2} are [1*4] ## arrays, containing parametric representation of each line (in the form ## [x0 y0 dx dy], see @code{createLine} for details). ## ## In case of colinear lines, returns [Inf Inf]. ## In case of parallel but not colinear lines, returns [NaN NaN]. ## ## If each input is [N*4] array, the result is a [N*2] array containing ## intersections of each couple of lines. ## If one of the input has N rows and the other 1 row, the result is a ## [N*2] array. ## ## A third input argument specifies the tolerance for detecting parallel lines. ## Default is 1e-14. ## ## Example ## ## @example ## line1 = createLine([0 0], [10 10]); ## line2 = createLine([0 10], [10 0]); ## point = intersectLines(line1, line2) ## point = ## 5 5 ## @end example ## ## @seealso{lines2d, edges2d, intersectEdges, intersectLineEdge, intersectLineCircle} ## @end deftypefn function point = intersectLines(line1, line2, varargin) # extreact tolerance tol = 1e-14; if !isempty(varargin) tol = varargin{1}; end x1 = line1(:,1); y1 = line1(:,2); dx1 = line1(:,3); dy1 = line1(:,4); x2 = line2(:,1); y2 = line2(:,2); dx2 = line2(:,3); dy2 = line2(:,4); N1 = length(x1); N2 = length(x2); # indices of parallel lines par = abs(dx1.*dy2 - dx2.*dy1) < tol; # indices of colinear lines col = abs((x2-x1) .* dy1 - (y2-y1) .* dx1) < tol & par ; x0(col) = Inf; y0(col) = Inf; x0(par & !col) = NaN; y0(par & !col) = NaN; i = !par; # compute intersection points if N1==N2 x0(i) = ((y2(i)-y1(i)).*dx1(i).*dx2(i) + x1(i).*dy1(i).*dx2(i) - x2(i).*dy2(i).*dx1(i)) ./ ... (dx2(i).*dy1(i)-dx1(i).*dy2(i)) ; y0(i) = ((x2(i)-x1(i)).*dy1(i).*dy2(i) + y1(i).*dx1(i).*dy2(i) - y2(i).*dx2(i).*dy1(i)) ./ ... (dx1(i).*dy2(i)-dx2(i).*dy1(i)) ; elseif N1==1 x0(i) = ((y2(i)-y1).*dx1.*dx2(i) + x1.*dy1.*dx2(i) - x2(i).*dy2(i).*dx1) ./ ... (dx2(i).*dy1-dx1.*dy2(i)) ; y0(i) = ((x2(i)-x1).*dy1.*dy2(i) + y1.*dx1.*dy2(i) - y2(i).*dx2(i).*dy1) ./ ... (dx1.*dy2(i)-dx2(i).*dy1) ; elseif N2==1 x0(i) = ((y2-y1(i)).*dx1(i).*dx2 + x1(i).*dy1(i).*dx2 - x2.*dy2.*dx1(i)) ./ ... (dx2.*dy1(i)-dx1(i).*dy2) ; y0(i) = ((x2-x1(i)).*dy1(i).*dy2 + y1(i).*dx1(i).*dy2 - y2.*dx2.*dy1(i)) ./ ... (dx1(i).*dy2-dx2.*dy1(i)) ; else # formattage a rajouter x0(i) = ((y2(i)-y1(i)).*dx1(i).*dx2(i) + x1(i).*dy1(i).*dx2(i) - x2(i).*dy2(i).*dx1(i)) ./ ... (dx2(i).*dy1(i)-dx1(i).*dy2(i)) ; y0(i) = ((x2(i)-x1(i)).*dy1(i).*dy2(i) + y1(i).*dx1(i).*dy2(i) - y2(i).*dx2(i).*dy1(i)) ./ ... (dx1(i).*dy2(i)-dx2(i).*dy1(i)) ; end # concatenate result point = [x0' y0']; endfunction %!test # basic test with two orthogonal lines %! line1 = [3 1 0 1]; %! line2 = [1 4 1 0]; %! assert (intersectLines(line1, line2), [3 4], 1e-6); %!test # orthognal diagonal lines %! line1 = [0 0 3 2]; %! line2 = [5 -1 4 -6]; %! assert (intersectLines(line1, line2), [3 2], 1e-6); %!test # one diagonal and one horizontal line %! line1 = [10 2 25 0]; %! line2 = [5 -1 4 -6]; %! assert (intersectLines(line1, line2), [3 2], 1e-6); %!test # check for dx and dy very big compared to other line %! line1 = [3 1 0 1000]; %! line2 = [1 4 -14 0]; %! assert (intersectLines(line1, line2), [3 4], 1e-6); %!test %! line1 = [2 0 20000 30000]; %! line2 = [1 6 1 -1]; %! assert (intersectLines(line1, line2), [4 3], 1e-6); %!test %! line1 = [3 1 0 1]; %! line2 = repmat([1 4 1 0], 5, 1); %! res = repmat([3 4], 5, 1); %! inters = intersectLines(line1, line2); %! assert (res, inters, 1e-6); %!test %! line1 = repmat([3 1 0 1], 5, 1); %! line2 = [1 4 1 0]; %! res = repmat([3 4], 5, 1); %! inters = intersectLines(line1, line2); %! assert (res, inters, 1e-6); %!test %! line1 = repmat([3 1 0 1], 5, 1); %! line2 = repmat([1 4 1 0], 5, 1); %! res = repmat([3 4], 5, 1); %! inters = intersectLines(line1, line2); %! assert (res, inters, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/intersectLineEdge.m0000644000000000000000000000013212676233417020745 xustar0030 mtime=1459173135.441151279 30 atime=1459173135.441151279 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/intersectLineEdge.m0000644000175000017500000000770512676233417022135 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} = } intersecLineEdge (@var{line}, @var{edge}) ## Return intersection between a line and an edge. ## ## Returns the intersection point of lines @var{line} and edge @var{edge}. ## @var{line} is a 1x4 array containing parametric representation of the line ## (in the form [x0 y0 dx dy], see @code{createLine} for details). ## @var{edge} is a 1x4 array containing coordinates of first and second point ## (in the form [x1 y1 x2 y2], see @code{createEdge} for details). ## ## In case of colinear line and edge, returns [Inf Inf]. ## If line does not intersect edge, returns [NaN NaN]. ## ## If each input is [N*4] array, the result is a [N*2] array containing ## intersections for each couple of edge and line. ## If one of the input has N rows and the other 1 row, the result is a ## [N*2] array. ## ## @seealso{lines2d, edges2d, intersectEdges, intersectLine} ## @end deftypefn function point = intersectLineEdge(lin, edge) x0 = lin(:,1); y0 = lin(:,2); dx1 = lin(:,3); dy1 = lin(:,4); x1 = edge(:,1); y1 = edge(:,2); x2 = edge(:,3); y2 = edge(:,4); dx2 = x2-x1; dy2 = y2-y1; N1 = length(x0); N2 = length(x1); # indices of parallel lines par = abs(dx1.*dy2-dx2.*dy1)<1e-14; # indices of colinear lines col = abs((x1-x0).*dy1-(y1-y0).*dx1)<1e-14 & par ; xi(col) = Inf; yi(col) = Inf; xi(par & ~col) = NaN; yi(par & ~col) = NaN; i = ~par; # compute intersection points if N1==N2 xi(i) = ((y1(i)-y0(i)).*dx1(i).*dx2(i) + x0(i).*dy1(i).*dx2(i) - x1(i).*dy2(i).*dx1(i)) ./ ... (dx2(i).*dy1(i)-dx1(i).*dy2(i)) ; yi(i) = ((x1(i)-x0(i)).*dy1(i).*dy2(i) + y0(i).*dx1(i).*dy2(i) - y1(i).*dx2(i).*dy1(i)) ./ ... (dx1(i).*dy2(i)-dx2(i).*dy1(i)) ; elseif N1==1 xi(i) = ((y1(i)-y0).*dx1.*dx2(i) + x0.*dy1.*dx2(i) - x1(i).*dy2(i).*dx1) ./ ... (dx2(i).*dy1-dx1.*dy2(i)) ; yi(i) = ((x1(i)-x0).*dy1.*dy2(i) + y0.*dx1.*dy2(i) - y1(i).*dx2(i).*dy1) ./ ... (dx1.*dy2(i)-dx2(i).*dy1) ; elseif N2==1 xi(i) = ((y1-y0(i)).*dx1(i).*dx2 + x0(i).*dy1(i).*dx2 - x1(i).*dy2.*dx1(i)) ./ ... (dx2.*dy1(i)-dx1(i).*dy2) ; yi(i) = ((x1-x0(i)).*dy1(i).*dy2 + y0(i).*dx1(i).*dy2 - y1(i).*dx2.*dy1(i)) ./ ... (dx1(i).*dy2-dx2.*dy1(i)) ; end point = [xi' yi']; out = find(~isPointOnEdge(point, edge)); point(out, :) = repmat([NaN NaN], [length(out) 1]); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/crackPattern.m0000644000000000000000000000013212676233417017771 xustar0030 mtime=1459173135.341198932 30 atime=1459173135.341198932 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/crackPattern.m0000644000175000017500000001616412676233417021160 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{e} = } crackPattern (@var{box}, @var{points}, @var{alpha}) ## Create a (bounded) crack pattern tessellation ## ## E = crackPattern2(BOX, POINTS, ALPHA) ## create a crack propagation pattern wit following parameters : ## - pattern is bounded by area BOX which is a polygon. ## - each crack originates from points given in POINTS ## - directions of each crack is given by a [NxM] array ALPHA, where M is ## the number of rays emanating from each seed/ ## - a crack stop when it reaches another already created crack. ## - all cracks stop when they reach the border of the frame, given by box ## (a serie of 4 points). ## The result is a collection of edges, in the form [x1 y1 x2 y2]. ## ## E = crackPattern2(BOX, POINTS, ALPHA, SPEED) ## Also specify speed of propagation of each crack. ## ## ## See the result with : ## figure; ## drawEdge(E); ## ## @seealso{drawEdge} ## @end deftypefn function edges = crackPattern(box, points, alpha, varargin) if ~isempty(varargin) speed = varargin{1}; else speed = ones(size(points, 1), 1); end # Compute line equations for each initial crack. # The two 'Inf' at the end correspond to the position of the limit. # If an intersection point is found with another line, but whose position # is after this value, this means that another crack stopped it before it # reach the intersection point. # There is one 'end position' for each side of the crack. lines = [points speed.*cos(alpha) speed.*sin(alpha) Inf*ones(size(points, 1), 2)]; # initialize lines for borders, but assign a very high speed, to be sure # borders will stop all cracks. dx = (box([2 3 4 1],1)-box([1 2 3 4],1))*max(speed)*5; dy = (box([2 3 4 1],2)-box([1 2 3 4],2))*max(speed)*5; # add borders to the lines set lines = [lines ; createLine(box, dx, dy) Inf*ones(4,2)]; edges = zeros(0, 4); while true modif = 0; # try to update each line for i=1:size(points, 1) # compute intersections with all other lines pi = intersectLines(lines(i,:), lines); # compute position of all intersection points on the current line pos = linePosition(pi, lines(i,:)); # consider points to the right (positive position), and sort them indr = find(pos>=0 & pos~=Inf); [posr, indr2] = sort(pos(indr)); # look for the closest intersection to the right for i2=1:length(indr2) # index of intersected line il = indr(indr2(i2)); # position of point relative to intersected line pos2 = linePosition(pi(il, :), lines(il, :)); # depending on the sign of position, tests if the line2 can # stop the current line, or if it was stopped before if pos2>0 if pos20 if pos2 ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{d} = } edgePosition (@var{point}, @var{edge}) ## Return position of a point on an edge ## ## POS = edgePosition(POINT, EDGE); ## Computes position of point POINT on the edge EDGE, relative to the ## position of edge vertices. ## EDGE has the form [x1 y1 x2 y2], ## POINT has the form [x y], and is assumed to belong to edge. ## The position POS has meaning: ## POS<0: POINT is located before the first vertex ## POS=0: POINT is located on the first vertex ## 0 ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pos} =} linePosition (@var{point}, @var{line}) ## Position of a point on a line. ## ## Computes position of point @var{point} on the line @var{line}, relative to origin ## point and direction vector of the line. ## @var{line} has the form [x0 y0 dx dy], ## @var{point} has the form [x y], and is assumed to belong to line. ## ## If @var{line} is an array of NL lines, return NL positions, corresponding to ## each line. ## ## If @var{point} is an array of NP points, return NP positions, corresponding ## to each point. ## ## If @var{point} is an array of NP points and @var{line}S is an array of NL lines, ## return an array of [NP NL] position, corresponding to each couple ## point-line. ## ## Example ## ## @example ## line = createLine([10 30], [30 90]); ## linePosition([20 60], line) ## ans = ## .5 ## @end example ## ## @seealso{lines2d, createLine, projPointOnLine, isPointOnLine} ## @end deftypefn function d = linePosition(point, lin) # number of inputs Nl = size(lin, 1); Np = size(point, 1); if Np == Nl # if both inputs have the same size, no problem dxl = lin(:, 3); dyl = lin(:, 4); dxp = point(:, 1) - lin(:, 1); dyp = point(:, 2) - lin(:, 2); elseif Np == 1 # one point, several lines dxl = lin(:, 3); dyl = lin(:, 4); dxp = point(ones(Nl, 1), 1) - lin(:, 1); dyp = point(ones(Nl, 1), 2) - lin(:, 2); elseif Nl == 1 # one lin, several points dxl = lin(ones(Np, 1), 3); dyl = lin(ones(Np, 1), 4); dxp = point(:, 1) - lin(1); dyp = point(:, 2) - lin(2); else # expand one of the array to have the same size dxl = repmat(lin(:,3)', Np, 1); dyl = repmat(lin(:,4)', Np, 1); dxp = repmat(point(:,1), 1, Nl) - repmat(lin(:,1)', Np, 1); dyp = repmat(point(:,2), 1, Nl) - repmat(lin(:,2)', Np, 1); end # compute position d = (dxp.*dxl + dyp.*dyl) ./ (dxl.^2 + dyl.^2); endfunction %!demo %! point = [20 60;10 30;25 75]; %! lin = createLine([10 30], [30 90]); %! pos = linePosition(point, lin) %! %! plot(point(:,1),point(:,2),'ok'); %! hold on %! drawLine(lin,'color','r'); %! plot(lin(1)+lin(3)*pos,lin(2)+lin(4)*pos,'xb') %! hold off %!test %! point = [20 60]; %! lin = createLine([10 30], [30 90]); %! res = .5; %! pos = linePosition(point, lin); %! assert (res, pos); %!test %! point = [20 60;10 30;25 75]; %! lin = createLine([10 30], [30 90]); %! res = [.5; 0; .75]; %! pos = linePosition(point, lin); %! assert (res, pos); %!test %! point = [20 60]; %! lin1 = createLine([10 30], [30 90]); %! lin2 = createLine([0 0], [20 60]); %! lin3 = createLine([20 60], [40 120]); %! lines = [lin1;lin2;lin3]; %! res = [.5; 1; 0]; %! pos = linePosition(point, lines); %! assert (res, pos); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/radicalAxis.m0000644000000000000000000000013012676233417017572 xustar0029 mtime=1459173135.47313603 29 atime=1459173135.47313603 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/radicalAxis.m0000644000175000017500000000553712676233417020765 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{line} = } radicalAxis (@var{circle1}, @var{circle2}) ## Compute the radical axis (or radical line) of 2 circles ## ## L = radicalAxis(C1, C2) ## Computes the radical axis of 2 circles. ## ## Example ## C1 = [10 10 5]; ## C2 = [60 50 30]; ## L = radicalAxis(C1, C2); ## hold on; axis equal;axis([0 100 0 100]); ## drawCircle(C1);drawCircle(C2);drawLine(L); ## ## Ref: ## http://mathworld.wolfram.com/RadicalLine.html ## http://en.wikipedia.org/wiki/Radical_axis ## ## @seealso{lines2d, circles2d, createCircle} ## ## @end deftypefn function line = radicalAxis(circle1, circle2) # extract circles parameters x1 = circle1(:,1); x2 = circle2(:,1); y1 = circle1(:,2); y2 = circle2(:,2); r1 = circle1(:,3); r2 = circle2(:,3); # distance between each couple of centers dist = sqrt((x2-x1).^2 + (y2-y1).^2); # relative position of intersection point of # the radical line with the line joining circle centers d = (dist.^2 + r1.^2 - r2.^2) * .5 ./ dist; # compute angle of radical axis angle = lineAngle(createLine([x1 y1], [x2 y2])); cot = cos(angle); sit = sin(angle); # parameters of the line x0 = x1 + d*cot; y0 = y1 + d*sit; dx = -sit; dy = cot; # concatenate into one structure line = [x0 y0 dx dy]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointOnCircle.m0000644000000000000000000000013212676233417020414 xustar0030 mtime=1459173135.449147467 30 atime=1459173135.449147467 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointOnCircle.m0000644000175000017500000000455512676233417021604 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointOnCircle (@var{point}, @var{circle}) ## Test if a point is located on a given circle. ## ## B = isPointOnCircle(POINT, CIRCLE) ## return true if point is located on the circle, i.e. if the distance to ## the circle center equals the radius up to an epsilon value. ## ## B = isPointOnCircle(POINT, CIRCLE, TOL) ## Specifies the tolerance value. ## ## Example: ## isPointOnCircle([1 0], [0 0 1]) ## returns true, whereas ## isPointOnCircle([1 1], [0 0 1]) ## return false ## ## @seealso{circles2d, isPointInCircle} ## @end deftypefn function b = isPointOnCircle(point, circle, varargin) tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end d = sqrt(sum(power(point - circle(:,1:2), 2), 2)); b = abs(d-circle(:,3)) ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawPoint (@var{x}, @var{y}) ## @deftypefnx {Function File} {@var{h} = } drawPoint (@var{coord}) ## @deftypefnx {Function File} {@var{h} = } drawPoint (@dots{}, @var{opt}) ## Draw the point on the axis. # # Draws points defined by coordinates @var{x} and @var{y}. # @var{x} and @var{y} should be array the same size. Coordinates can be # packed coordinates in a single [N*2] array @var{coord}. Options @var{opt} # are passed to the @code{plot} function. # # @seealso{points2d, clipPoints} # ## @end deftypefn function varargout = drawPoint(varargin) # process input arguments var = varargin{1}; if size(var, 2)==1 # points stored in separate arrays px = varargin{1}; py = varargin{2}; varargin(1:2) = []; else # points packed in one array px = var(:, 1); py = var(:, 2); varargin(1) = []; end # ensure we have column vectors px = px(:); py = py(:); # default drawing options, but keep specified options if it has the form of # a bundled string if length(varargin)~=1 varargin = [{'linestyle', 'none', 'marker', 'o', 'color', 'b'}, varargin]; end # plot the points, using specified drawing options h = plot(px(:), py(:), varargin{:}); # process output arguments if nargout>0 varargout{1}=h; end endfunction %!demo %! drawPoint(10, 10); %!demo %! t = linspace(0, 2*pi, 20)'; %! drawPoint([5*cos(t)+10 3*sin(t)+10], 'r+'); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/bisector.m0000644000000000000000000000013212676233417017162 xustar0030 mtime=1459173135.333202744 30 atime=1459173135.333202744 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/bisector.m0000644000175000017500000000760312676233417020347 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{ray} = } bisector (@var{line1}, @var{line2}) ## @deftypefnx {Function File} {@var{ray} = } bisector (@var{p1}, @var{p2}, @var{p3}) ## Return the bisector of two lines, or 3 points. ## ## Creates the bisector of the two lines, given as [x0 y0 dx dy]. ## ## create the bisector of lines (@var{p2} @var{p1}) and (@var{p2} @var{p3}). ## ## The result has the form [x0 y0 dx dy], with [x0 y0] being the origin ## point ans [dx dy] being the direction vector, normalized to have unit ## norm. ## ## @seealso{lines2d, rays2d} ## @end deftypefn function ray = bisector(varargin) if length(varargin)==2 # two lines line1 = varargin{1}; line2 = varargin{2}; point = intersectLines(line1, line2); elseif length(varargin)==3 # three points p1 = varargin{1}; p2 = varargin{2}; p3 = varargin{3}; line1 = createLine(p2, p1); line2 = createLine(p2, p3); point = p2; elseif length(varargin)==1 # three points, given in one array var = varargin{1}; p1 = var(1, :); p2 = var(2, :); p3 = var(3, :); line1 = createLine(p2, p1); line2 = createLine(p2, p3); point = p2; end # compute line angles a1 = lineAngle(line1); a2 = lineAngle(line2); # compute bisector angle (angle of first line + half angle between lines) angle = mod(a1 + mod(a2-a1+2*pi, 2*pi)/2, pi*2); # create the resulting ray ray = [point cos(angle) sin(angle)]; endfunction %!shared privpath %! privpath = [fileparts(which('geom2d_Contents')) filesep() 'private']; %!test %! addpath (privpath,'-end') %! p0 = [0 0]; %! p1 = [10 0]; %! p2 = [0 10]; %! line1 = createLine(p0, p1); %! line2 = createLine(p0, p2); %! ray = bisector(line1, line2); %! assertElementsAlmostEqual([0 0], ray(1,1:2)); %! assertAlmostEqual(pi/4, lineAngle(ray)); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! p0 = [0 0]; %! p1 = [10 0]; %! p2 = [0 10]; %! ray = bisector(p1, p0, p2); %! assertElementsAlmostEqual([0 0], ray(1,1:2)); %! assertAlmostEqual(pi/4, lineAngle(ray)); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! p0 = [0 0]; %! p1 = [10 0]; %! p2 = [0 10]; %! ray = bisector([p1; p0; p2]); %! assertElementsAlmostEqual([0 0], ray(1,1:2)); %! assertAlmostEqual(pi/4, lineAngle(ray)); %! rmpath (privpath); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/geom2d_Contents.m0000644000000000000000000000013212676233417020402 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/geom2d_Contents.m0000644000175000017500000002677412676233417021601 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} geom2d_Contents () ## Geometry 2D Toolbox ## Version 1.2.0 21-Oct-2011 . ## ## Library to handle and visualize geometric primitives such as points, ## lines, circles and ellipses, polygons... ## ## The goal is to provide a low-level library for manipulating geometrical ## primitives, making easier the development of more complex geometric ## algorithms. ## ## Most functions works for planar shapes, but some ones have been ## extended to 3D or to any dimension. ## ## Points ## points2d - Description of functions operating on points ## clipPoints - Clip a set of points by a box ## centroid - Compute centroid (center of mass) of a set of points ## midPoint - Middle point of two points or of an edge ## isCounterClockwise - Compute relative orientation of 3 points ## polarPoint - Create a point from polar coordinates (rho + theta) ## angle2Points - Compute horizontal angle between 2 points ## angle3Points - Compute oriented angle made by 3 points ## angleSort - Sort points in the plane according to their angle to origin ## distancePoints - Compute distance between two points ## minDistancePoints - Minimal distance between several points ## transformPoint - Transform a point with an affine transform ## drawPoint - Draw the point on the axis. ## ## Vectors ## vectors2d - Description of functions operating on plane vectors ## createVector - Create a vector from two points ## vectorNorm - Compute norm of a vector, or of a set of vectors ## vectorAngle - Angle of a vector, or between 2 vectors ## normalizeVector - Normalize a vector to have norm equal to 1 ## isPerpendicular - Check orthogonality of two vectors ## isParallel - Check parallelism of two vectors ## transformVector - Transform a vector with an affine transform ## rotateVector - Rotate a vector by a given angle ## ## Straight lines ## lines2d - Description of functions operating on planar lines ## createLine - Create a straight line from 2 points, or from other inputs ## medianLine - Create a median line between two points ## cartesianLine - Create a straight line from cartesian equation coefficients ## orthogonalLine - Create a line orthogonal to another one. ## parallelLine - Create a line parallel to another one. ## intersectLines - Return all intersection points of N lines in 2D ## lineAngle - Computes angle between two straight lines ## linePosition - Position of a point on a line ## lineFit - Fit a straight line to a set of points ## clipLine - Clip a line with a box ## reverseLine - Return same line but with opposite orientation ## transformLine - Transform a line with an affine transform ## drawLine - Draw the line on the current axis ## ## Edges (line segments between 2 points) ## edges2d - Description of functions operating on planar edges ## createEdge - Create an edge between two points, or from a line ## edgeToLine - Convert an edge to a straight line ## edgeAngle - Return angle of edge ## edgeLength - Return length of an edge ## midPoint - Middle point of two points or of an edge ## edgePosition - Return position of a point on an edge ## clipEdge - Clip an edge with a rectangular box ## reverseEdge - Intervert the source and target vertices of edge ## intersectEdges - Return all intersections between two set of edges ## intersectLineEdge - Return intersection between a line and an edge ## transformEdge - Transform an edge with an affine transform ## drawEdge - Draw an edge given by 2 points ## drawCenteredEdge - Draw an edge centered on a point ## ## Rays ## rays2d - Description of functions operating on planar rays ## createRay - Create a ray (half-line), from various inputs ## bisector - Return the bisector of two lines, or 3 points ## clipRay - Clip a ray with a box ## drawRay - Draw a ray on the current axis ## ## Relations between points and lines ## distancePointEdge - Minimum distance between a point and an edge ## distancePointLine - Minimum distance between a point and a line ## projPointOnLine - Project of a point orthogonally onto a line ## pointOnLine - Create a point on a line at a given position on the line ## isPointOnLine - Test if a point belongs to a line ## isPointOnEdge - Test if a point belongs to an edge ## isPointOnRay - Test if a point belongs to a ray ## isLeftOriented - Test if a point is on the left side of a line ## ## Circles ## circles2d - Description of functions operating on circles ## createCircle - Create a circle from 2 or 3 points ## createDirectedCircle - Create a directed circle ## intersectCircles - Intersection points of two circles ## intersectLineCircle - Intersection point(s) of a line and a circle ## circleAsPolygon - Convert a circle into a series of points ## circleArcAsCurve - Convert a circle arc into a series of points ## isPointInCircle - Test if a point is located inside a given circle ## isPointOnCircle - Test if a point is located on a given circle. ## enclosingCircle - Find the minimum circle enclosing a set of points. ## radicalAxis - Compute the radical axis (or radical line) of 2 circles ## drawCircle - Draw a circle on the current axis ## drawCircleArc - Draw a circle arc on the current axis ## ## Ellipses ## ellipses2d - Description of functions operating on ellipses ## inertiaEllipse - Inertia ellipse of a set of points ## isPointInEllipse - Check if a point is located inside a given ellipse ## ellipseAsPolygon - Convert an ellipse into a series of points ## drawEllipse - Draw an ellipse on the current axis ## drawEllipseArc - Draw an ellipse arc on the current axis ## ## Geometric transforms ## transforms2d - Description of functions operating on transforms ## createTranslation - Create the 3*3 matrix of a translation ## createRotation - Create the 3*3 matrix of a rotation ## createScaling - Create the 3*3 matrix of a scaling in 2 dimensions ## createHomothecy - Create the the 3x3 matrix of an homothetic transform ## createBasisTransform - Compute matrix for transforming a basis into another basis ## createLineReflection - Create the the 3x3 matrix of a line reflection ## fitAffineTransform2d - Fit an affine transform using two point sets ## ## Angles ## angles2d - Description of functions for manipulating angles ## normalizeAngle - Normalize an angle value within a 2*PI interval ## angleAbsDiff - Absolute difference between two angles ## angleDiff - Difference between two angles ## deg2rad - Convert angle from degrees to radians ## rad2deg - Convert angle from radians to degrees ## ## Boxes ## boxes2d - Description of functions operating on bounding boxes ## intersectBoxes - Intersection of two bounding boxes ## mergeBoxes - Merge two boxes, by computing their greatest extent ## randomPointInBox - Generate random point within a box ## drawBox - Draw a box defined by coordinate extents ## ## Various drawing functions ## drawBezierCurve - Draw a cubic bezier curve defined by 4 control points ## drawParabola - Draw a parabola on the current axis ## drawOrientedBox - Draw centered oriented rectangle ## drawRect - Draw rectangle on the current axis ## drawArrow - Draw an arrow on the current axis ## drawLabels - Draw labels at specified positions ## drawShape - Draw various types of shapes (circles, polygons...) ## ## Other shapes ## squareGrid - Generate equally spaces points in plane. ## hexagonalGrid - Generate hexagonal grid of points in the plane. ## triangleGrid - Generate triangular grid of points in the plane. ## crackPattern - Create a (bounded) crack pattern tessellation ## crackPattern2 - Create a (bounded) crack pattern tessellation ## ## ## Credits: ## * function 'enclosingCircle' rewritten from a file from Yazan Ahed ## , available on Matlab File Exchange ## ## @end deftypefn function geom2d_Contents () help('geom2d_Contents'); ## Deprecated functions # createMedian - create a median line # minDistance - compute minimum distance between a point and a set of points # homothecy - create a homothecy as an affine transform # rotation - return 3*3 matrix of a rotation # translation - return 3*3 matrix of a translation # scaling - return 3*3 matrix of a scaling in 2 dimensions # lineSymmetry - create line symmetry as 2D affine transform # vecnorm - compute norm of vector or of set of vectors # normalize - normalize a vector # onCircle - test if a point is located on a given circle. # inCircle - test if a point is located inside a given circle. # onEdge - test if a point belongs to an edge # onLine - test if a point belongs to a line # onRay - test if a point belongs to a ray # invertLine - return same line but with opposite orientation # clipLineRect - clip a line with a polygon # formatAngle - Ensure an angle value is comprised between 0 and 2*PI ## Others... # drawRect2 - Draw centered rectangle on the current axis endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/edgeAngle.m0000644000000000000000000000013212676233417017223 xustar0030 mtime=1459173135.365187495 30 atime=1459173135.365187495 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/edgeAngle.m0000644000175000017500000000434612676233417020411 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{theta} =} edgeAngle(@var{edge}) ## Return angle of edge ## ## A = edgeAngle(EDGE) ## Returns the angle between horizontal, right-axis and the edge EDGE. ## Angle is given in radians, between 0 and 2*pi, in counter-clockwise ## direction. ## Notation for edge is [x1 y1 x2 y2] (coordinates of starting and ending ## points). ## ## Example ## p1 = [10 20]; ## p2 = [30 40]; ## rad2deg(edgeAngle([p1 p2])) ## ans = ## 45 ## ## @seealso{edges2d, angles2d, edgeAngle, lineAngle, edgeLength} ## @end deftypefn function theta = edgeAngle(edge) line = createLine(edge(:,1:2), edge(:,3:4)); theta = lineAngle(line); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/transformEdge.m0000644000000000000000000000013212676233417020150 xustar0030 mtime=1459173135.477134124 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/transformEdge.m0000644000175000017500000000541212676233417021331 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{edge2} = } transformEdge (@var{edge1}, @var{T}) ## Transform an edge with an affine transform. ## ## Where @var{edge1} has the form [x1 y1 x2 y1], and @var{T} is a transformation ## matrix, return the edge transformed with affine transform @var{T}. ## ## Format of TRANS can be one of : ## [a b] , [a b c] , or [a b c] ## [d e] [d e f] [d e f] ## [0 0 1] ## ## Also works when @var{edge1} is a [Nx4] array of double. In this case, @var{edge2} ## has the same size as @var{edge1}. ## ## @seealso{edges2d, transforms2d, transformPoint, translation, rotation} ## @end deftypefn function dest = transformEdge(edge, trans) dest = zeros(size(edge)); # compute position dest(:,1) = edge(:,1)*trans(1,1) + edge(:,2)*trans(1,2); dest(:,2) = edge(:,1)*trans(2,1) + edge(:,2)*trans(2,2); dest(:,3) = edge(:,3)*trans(1,1) + edge(:,3)*trans(1,2); dest(:,4) = edge(:,4)*trans(2,1) + edge(:,4)*trans(2,2); # add translation vector, if exist if size(trans, 2)>2 dest(:,1) = dest(:,1)+trans(1,3); dest(:,2) = dest(:,2)+trans(2,3); dest(:,3) = dest(:,3)+trans(1,3); dest(:,4) = dest(:,4)+trans(2,3); end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/fitAffineTransform2d.m0000644000000000000000000000013212676233417021365 xustar0030 mtime=1459173135.437153185 30 atime=1459173135.437153185 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/fitAffineTransform2d.m0000644000175000017500000000464312676233417022553 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } fitAffineTransform2d (@var{pts1}, @var{pts2}) ## Fit an affine transform using two point sets. ## ## Example ## ## @example ## N = 10; ## pts = rand(N, 2)*10; ## trans = createRotation(3, 4, pi/4); ## pts2 = transformPoint(pts, trans); ## pts3 = pts2 + randn(N, 2)*2; ## fitted = fitAffineTransform2d(pts, pts2) ##@end example ## ## @seealso{transforms2d} ## @end deftypefn function trans = fitAffineTransform2d(pts1, pts2) # number of points N = size(pts1, 1); # main matrix of the problem A = [... pts1(:,1) pts1(:,2) ones(N,1) zeros(N, 3) ; ... zeros(N, 3) pts1(:,1) pts1(:,2) ones(N,1) ]; # conditions initialisations B = [pts2(:,1) ; pts2(:,2)]; # compute coefficients using least square coefs = A\B; # format to a matrix trans = [coefs(1:3)' ; coefs(4:6)'; 0 0 1]; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawRect.m0000644000000000000000000000013212676233417017123 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawRect.m0000644000175000017500000000662112676233417020307 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{r} = } drawRect (@var{x}, @var{y}, @var{w}, @var{h}) ## @deftypefnx {Function File} {@var{r} = } drawRect (@var{x}, @var{y}, @var{w}, @var{h}, @var{theta}) ## @deftypefnx {Function File} {@var{r} = } drawRect (@var{coord}) ## Draw rectangle on the current axis. ## ## r = DRAWRECT(x, y, w, h) draw rectangle with width W and height H, at ## position (X, Y). ## the four corners of rectangle are then : ## (X, Y), (X+W, Y), (X, Y+H), (X+W, Y+H). ## ## r = DRAWRECT(x, y, w, h, theta) also specifies orientation for ## rectangle. Theta is given in degrees. ## ## r = DRAWRECT(coord) is the same as DRAWRECT(X,Y,W,H), but all ## parameters are packed into one array, whose dimensions is 4*1 or 5*1. ## ## ## @seealso{drawBox, drawOrientedBox} ## @end deftypefn function varargout = drawRect(varargin) # default values theta = 0; # get entered values if length(varargin) > 3 x = varargin{1}; y = varargin{2}; w = varargin{3}; h = varargin{4}; if length(varargin)> 4 theta = varargin{5} * pi / 180; end else coord = varargin{1}; x = coord(1); y = coord(2); w = coord(3); h = coord(4); if length(coord) > 4 theta = coord(5) * pi / 180; end end r = zeros(size(x)); for i = 1:length(x) tx = zeros(5, 1); ty = zeros(5, 1); tx(1) = x(i); ty(1) = y(i); tx(2) = x(i) + w(i) * cos(theta(i)); ty(2) = y(i) + w(i) * sin(theta(i)); tx(3) = x(i) + w(i) * cos(theta(i)) - h(i) * sin(theta(i)); ty(3) = y(i) + w(i) * sin(theta(i)) + h(i) * cos(theta(i)); tx(4) = x(i) - h(i) * sin(theta(i)); ty(4) = y(i) + h(i) * cos(theta(i)); tx(5) = x(i); ty(5) = y(i); r(i) = line(tx, ty); end if nargout > 0 varargout{1} = r; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/transformPoint.m0000644000000000000000000000013212676233417020375 xustar0030 mtime=1459173135.481132218 30 atime=1459173135.477134124 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/transformPoint.m0000644000175000017500000000641612676233417021563 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pt2} = } transformPoint (@var{pt1}, @var{Trans}) ## @deftypefnx {Function File} {[@var{px2} @var{py2}]= } transformPoint (@var{px1}, @var{py1}, @var{Trans}) ## Transform a point with an affine transform. ## ## where @var{pt1} has the form [xp yp], and @var{Trans} is a [2x2], [2x3] or [3x3] ## matrix, returns the point transformed with affine transform @var{Trans}. ## ## Format of @var{Trans} can be one of : ## [a b] , [a b c] , or [a b c] ## [d e] [d e f] [d e f] ## [0 0 1] ## ## Also works when @var{pt1} is a [Nx2] array of double. In this case, @var{pt2} has ## the same size as @var{pt1}. ## ## Also works when @var{px1} and @var{py1} are arrays the same size. The function ## transform each couple of (@var{px1}, @var{py1}), and return the result in ## (@var{px2}, @var{py2}), which is the same size as (@var{px1} @var{py1}). ## ## @seealso{points2d, transforms2d, createTranslation, createRotation} ## @end deftypefn function varargout = transformPoint(varargin) if length(varargin)==2 var = varargin{1}; px = var(:,1); py = var(:,2); trans = varargin{2}; elseif length(varargin)==3 px = varargin{1}; py = varargin{2}; trans = varargin{3}; else error('wrong number of arguments in "transformPoint"'); end # compute position px2 = px*trans(1,1) + py*trans(1,2); py2 = px*trans(2,1) + py*trans(2,2); # add translation vector, if exist if size(trans, 2)>2 px2 = px2 + trans(1,3); py2 = py2 + trans(2,3); end if nargout==0 || nargout==1 varargout{1} = [px2 py2]; elseif nargout==2 varargout{1} = px2; varargout{2} = py2; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isPointInEllipse.m0000644000000000000000000000013212676233417020602 xustar0030 mtime=1459173135.449147467 30 atime=1459173135.449147467 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isPointInEllipse.m0000644000175000017500000000540412676233417021764 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{b} = } isPointInellipse (@var{point}, @var{ellipse}) ## Check if a point is located inside a given ellipse ## ## B = isPointInEllipse(POINT, ELLIPSE) ## Returns true if point is located inside the given ellipse. ## ## B = isPointInEllipse(POINT, ELLIPSE, TOL) ## Specifies the tolerance value ## ## Example: ## isPointInEllipse([1 0], [0 0 2 1 0]) ## ans = ## 1 ## isPointInEllipse([0 0], [0 0 2 1 0]) ## ans = ## 1 ## isPointInEllipse([1 1], [0 0 2 1 0]) ## ans = ## 0 ## isPointInEllipse([1 1], [0 0 2 1 30]) ## ans = ## 1 ## ## @seealso{ellipses2d, isPointInCircle} ## @end deftypefn function b = isPointInEllipse(point, ellipse, varargin) # extract computation tolerance tol = 1e-14; if ~isempty(varargin) tol = varargin{1}; end # compute ellipse to unit circle transform rot = createRotation(-deg2rad(ellipse(5))); sca = createScaling(1./ellipse(3:4)); trans = sca * rot; # transform points to unit circle basis pTrans = bsxfun(@minus, point, ellipse(:,1:2)); pTrans = transformPoint(pTrans, trans); # test if distance to origin smaller than 1 b = sqrt(sum(power(pTrans, 2), 2)) - 1 <= tol; endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawParabola.m0000644000000000000000000000013212676233417017747 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawParabola.m0000644000175000017500000001066512676233417021136 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawParabola (@var{parabola}) ## @deftypefnx {Function File} {@var{h} = } drawParabola (@var{parabola}, @var{t}) ## @deftypefnx {Function File} {@var{h} = } drawParabola (@dots{}, @var{param}, @var{value}) ## Draw a parabola on the current axis. ## ## drawParabola(PARABOLA); ## Draws a vertical parabola, defined by its vertex and its parameter. ## Such a parabola admits a vertical axis of symetry. ## ## The algebraic equation of parabola is given by: ## (Y - YV) = A * (X - VX)^2 ## Where XV and YV are vertex coordinates and A is parabola parameter. ## ## A parametric equation of parabola is given by: ## x(t) = t + VX; ## y(t) = A * t^2 + VY; ## ## PARABOLA can also be defined by [XV YV A THETA], with theta being the ## angle of rotation of the parabola (in degrees and Counter-Clockwise). ## ## drawParabola(PARABOLA, T); ## Specifies which range of 't' are used for drawing parabola. If T is an ## array with only two values, the first and the last values are used as ## interval bounds, and several values are distributed within this ## interval. ## ## drawParabola(..., NAME, VALUE); ## Can specify one or several graphical options using parameter name-value ## pairs. ## ## H = drawParabola(...); ## Returns an handle to the created graphical object. ## ## ## Example: ## @example ## figure(1); clf; hold on; ## drawParabola([50 50 .2 30]); ## drawParabola([50 50 .2 30], [-1 1], 'color', 'r', 'linewidth', 2); ## axis equal; ## @end example ## ## @seealso{drawCircle, drawEllipse} ## @end deftypefn function varargout = drawParabola(varargin) # Extract parabola if nargin<1 error('geom2d:IllegalArgument', ... 'Please specify parabola representation'); end # input parabola is given as a packed array parabola = varargin{1}; varargin(1) = []; x0 = parabola(:,1); y0 = parabola(:,2); a = parabola(:,3); if size(parabola, 2)>3 theta = parabola(:, 4); else theta = zeros(length(a), 1); end # extract parametrisation bounds bounds = [-100 100]; if ~isempty(varargin) var = varargin{1}; if isnumeric(var) bounds = var; varargin(1) = []; end end # create parametrisation if length(bounds)>2 t = bounds; else t = linspace(bounds(1), bounds(end), 100); end # create handle array (in the case of several parabola) h = zeros(size(x0)); # draw each parabola for i=1:length(x0) # compute transformation trans = ... createTranslation(x0(i), y0(i)) * ... createRotation(deg2rad(theta(i))) * ... createScaling(1, a); # compute points on the parabola [xt yt] = transformPoint(t(:), t(:).^2, trans); # draw it h(i) = plot(xt, yt, varargin{:}); end # process output arguments if nargout>0 varargout{1}=h; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/angle2Points.m0000644000000000000000000000013212676233417017715 xustar0030 mtime=1459173135.305216087 30 atime=1459173135.305216087 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/angle2Points.m0000644000175000017500000000677712676233417021115 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{alpha} =} angle2Points (@var{p1}, @var{p2}) ## Compute horizontal angle between 2 points ## ## @var{p1} and @var{p2} are either [1x2] arrays, or [Nx2] arrays, in this case ## @var{alpha} is a [Nx1] array. The angle computed is the horizontal angle of ## the line (@var{p1},@var{p2}). ## ## Result is always given in radians, between 0 and 2*pi. ## ## @seealso{points2d, angles2d, angle3points, normalizeAngle, vectorAngle} ## @end deftypefn function theta = angle2Points(varargin) # process input arguments if length(varargin)==2 p1 = varargin{1}; p2 = varargin{2}; elseif length(varargin)==1 var = varargin{1}; p1 = var(1,:); p2 = var(2,:); end # ensure data have correct size n1 = size(p1, 1); n2 = size(p2, 1); if n1~=n2 && min(n1, n2)>1 error('angle2Points: wrong size for inputs'); end # angle of line (P2 P1), between 0 and 2*pi. dp = bsxfun(@minus, p2, p1); theta = mod(atan2(dp(:,2), dp(:,1)) + 2*pi, 2*pi); endfunction %!test %! # all points inside window, possibly touching edges %! p1 = [0 0]; %! p2 = [10 0]; %! angle_ = angle2Points (p1, p2); %! assert (angle_,0,1e-6); %! angle_ = angle2Points (p2, p1); %! assert (angle_,pi,1e-6); %!test %! # all points inside window, possibly touching edges %! p1 = [0 0]; %! p2 = [0 10]; %! angle_ = angle2Points (p1, p2); %! assert (pi/2, angle_,1e-6); %! angle_ = angle2Points (p2, p1); %! assert (3*pi/2, angle_,1e-6); %!test %! # all points inside window, possibly touching edges %! p1 = [0 0;0 0;0 0;0 0]; %! p2 = [10 0;10 10;0 10;-10 10]; %! angle_ = angle2Points (p1, p2); %! assert (size (p1, 1), size (angle_, 1)); %! res = [0;pi/4;pi/2;3*pi/4]; %! assert (res, angle_, 1e-6); %!test %! # all points inside window, possibly touching edges %! p1 = [0 0]; %! p2 = [10 0;10 10;0 10;-10 10]; %! angle_ = angle2Points (p1, p2); %! assert(size (p2, 1), size (angle_, 1)); %! res = [0;pi/4;pi/2;3*pi/4]; %! assert(res, angle_,1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/circles2d.m0000644000000000000000000000013212676233417017222 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/circles2d.m0000644000175000017500000000504712676233417020407 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} circles2d () ## Description of functions operating on circles ## ## Circles are represented by their center and their radius: ## C = [xc yc r]; ## One sometimes considers orientation of circle, by adding an extra ## boolean value in 4-th position, with value TRUE for direct (i.e. ## turning Counter-clockwise) circles. ## ## Circle arcs are represented by their center, their radius, the starting ## angle and the angle extent, both in degrees: ## CA = [xc yc r theta0 dtheta]; ## ## Ellipses are represented by their center, their 2 semi-axis length, and ## their angle (in degrees) with Ox direction. ## E = [xc yc A B theta]; ## ## @seealso{ellipses2d, createCircle, createDirectedCircle, enclosingCircle ## isPointInCircle, isPointOnCircle ## intersectLineCircle, intersectCircles, radicalAxis ## circleAsPolygon, circleArcAsCurve ## drawCircle, drawCircleArc} ## @end deftypefn function circles2d(varargin) help('circles2d'); endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/isCounterClockwise.m0000644000000000000000000000013212676233417021167 xustar0030 mtime=1459173135.445149373 30 atime=1459173135.445149373 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/isCounterClockwise.m0000644000175000017500000001257612676233417022361 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{ccw} = } isCounterClockwise (@var{p1}, @var{p2}, @var{p3}) ## @deftypefnx {Function File} {@var{ccw} = } isCounterClockwise (@var{p1}, @var{p2}, @var{p3},@var{tol}) ## Compute relative orientation of 3 points ## ## Computes the orientation of the 3 points. The returns is: ## +1 if the path @var{p1}-> @var{p2}-> @var{p3} turns Counter-Clockwise (i.e., the point @var{p3} ## is located "on the left" of the line @var{p1}- @var{p2}) ## -1 if the path turns Clockwise (i.e., the point @var{p3} lies "on the right" ## of the line @var{p1}- @var{p2}) ## 0 if the point @var{p3} is located on the line segment [ @var{p1} @var{p2}]. ## ## This function can be used in more complicated algorithms: detection of ## line segment intersections, convex hulls, point in triangle... ## ## @var{ccw} = isCounterClockwise( @var{p1}, @var{p2}, @var{p3}, EPS); ## Specifies the threshold used for detecting colinearity of the 3 points. ## Default value is 1e-12 (absolute). ## ## Example ## ## @example ## isCounterClockwise([0 0], [10 0], [10 10]) ## ans = ## 1 ## isCounterClockwise([0 0], [0 10], [10 10]) ## ans = ## -1 ## isCounterClockwise([0 0], [10 0], [5 0]) ## ans = ## 0 ## @end example ## ## @seealso{points2d, isPointOnLine, isPointInTriangle} ## @end deftypefn function res = isCounterClockwise(p1, p2, p3, varargin) # get threshold value eps = 1e-12; if ~isempty(varargin) eps = varargin{1}; end # ensure all data have same size np = max([size(p1, 1) size(p2, 1) size(p3,1)]); if np > 1 if size(p1,1) == 1 p1 = repmat(p1, np, 1); end if size(p2,1) == 1 p2 = repmat(p2, np, 1); end if size(p3,1) == 1 p3 = repmat(p3, np, 1); end end # init with 0 res = zeros(np, 1); # extract vector coordinates x0 = p1(:, 1); y0 = p1(:, 2); dx1 = p2(:, 1) - x0; dy1 = p2(:, 2) - y0; dx2 = p3(:, 1) - x0; dy2 = p3(:, 2) - y0; # check non colinear cases res(dx1 .* dy2 > dy1 .* dx2) = 1; res(dx1 .* dy2 < dy1 .* dx2) = -1; # case of colinear points ind = abs(dx1 .* dy2 - dy1 .* dx2) < eps; res(ind( (dx1(ind) .* dx2(ind) < 0) | (dy1(ind) .* dy2(ind) < 0) )) = -1; res(ind( hypot(dx1(ind), dy1(ind)) < hypot(dx2(ind), dy2(ind)) )) = 1; endfunction %!shared p0,pu,pd,pl,pr %! p0 = [2, 3]; # center point %! pu = [2, 4]; # up point %! pd = [2, 2]; # down point %! pl = [1, 3]; # left point %! pr = [3, 3]; # right point %!assert (+1, isCounterClockwise(pl, p0, pu)); %!assert (+1, isCounterClockwise(pd, p0, pl)); %!assert (+1, isCounterClockwise(pr, p0, pd)); %!assert (+1, isCounterClockwise(pu, p0, pr)); # turn 90° right => return -1 %!assert (-1, isCounterClockwise(pl, p0, pd)); %!assert (-1, isCounterClockwise(pd, p0, pr)); %!assert (-1, isCounterClockwise(pr, p0, pu)); %!assert (-1, isCounterClockwise(pu, p0, pl)); %!test # turn 90° left => return +1 %! pts1 = [pl;pd;pr;pu;pl;pd;pr;pu]; %! pts2 = [p0;p0;p0;p0;p0;p0;p0;p0]; %! pts3 = [pu;pl;pd;pr;pd;pr;pu;pl]; %! expected = [1;1;1;1;-1;-1;-1;-1]; %! result = isCounterClockwise(pts1, pts2, pts3); %! assert (result, expected, 1e-6); # aligned with p0-p1-p2 => return +1 %!assert (+1, isCounterClockwise(pl, p0, pr)); %!assert (+1, isCounterClockwise(pu, p0, pd)); %!assert (+1, isCounterClockwise(pr, p0, pl)); %!assert (+1, isCounterClockwise(pd, p0, pu)); # aligned ]ith p0-p2-p1 => return 0 %!assert (0, isCounterClockwise(pl, pr, p0)); %!assert (0, isCounterClockwise(pu, pd, p0)); %!assert (0, isCounterClockwise(pr, pl, p0)); %!assert (0, isCounterClockwise(pd, pu, p0)); # aligned with p1-p0-p2 => return -1 %!assert (-1, isCounterClockwise(p0, pl, pr)); %!assert (-1, isCounterClockwise(p0, pu, pd)); %!assert (-1, isCounterClockwise(p0, pr, pl)); %!assert (-1, isCounterClockwise(p0, pr, pl)); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/minDistancePoints.m0000644000000000000000000000013212676233417021003 xustar0030 mtime=1459173135.461141748 30 atime=1459173135.461141748 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/minDistancePoints.m0000644000175000017500000002326012676233417022165 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } minDistancePoints (@var{pts}) ## @deftypefnx {Function File} {@var{dist} = } minDistancePoints (@var{pts1},@var{pts2}) ## @deftypefnx {Function File} {@var{dist} = } minDistancePoints (@dots{},@var{norm}) ## @deftypefnx {Function File} {[@var{dist} @var{i} @var{j}] = } minDistancePoints (@var{pts1}, @var{pts2}, @dots{}) ## @deftypefnx {Function File} {[@var{dist} @var{j}] = } minDistancePoints (@var{pts1}, @var{pts2}, @dots{}) ## Minimal distance between several points. ## ## Returns the minimum distance between all couple of points in @var{pts}. @var{pts} is ## an array of [NxND] values, N being the number of points and ND the ## dimension of the points. ## ## Computes for each point in @var{pts1} the minimal distance to every point of ## @var{pts2}. @var{pts1} and @var{pts2} are [NxD] arrays, where N is the number of points, ## and D is the dimension. Dimension must be the same for both arrays, but ## number of points can be different. ## The result is an array the same length as @var{pts1}. ## ## When @var{norm} is provided, it uses a user-specified norm. @var{norm}=2 means euclidean norm (the default), ## @var{norm}=1 is the Manhattan (or "taxi-driver") distance. ## Increasing @var{norm} growing up reduces the minimal distance, with a limit ## to the biggest coordinate difference among dimensions. ## ## ## Returns indices @var{i} and @var{j} of the 2 points which are the closest. @var{dist} ## verifies relation: ## @var{dist} = distancePoints(@var{pts}(@var{i},:), @var{pts}(@var{j},:)); ## ## If only 2 output arguments are given, it returns the indices of points which are the closest. @var{j} has the ## same size as @var{dist}. for each I It verifies the relation : ## @var{dist}(I) = distancePoints(@var{pts1}(I,:), @var{pts2}(@var{J},:)); ## ## ## Examples: ## ## @example ## # minimal distance between random planar points ## points = rand(20,2)*100; ## minDist = minDistancePoints(points); ## ## # minimal distance between random space points ## points = rand(30,3)*100; ## [minDist ind1 ind2] = minDistancePoints(points); ## minDist ## distancePoints(points(ind1, :), points(ind2, :)) ## # results should be the same ## ## # minimal distance between 2 sets of points ## points1 = rand(30,2)*100; ## points2 = rand(30,2)*100; ## [minDists inds] = minDistancePoints(points1, points2); ## minDists(10) ## distancePoints(points1(10, :), points2(inds(10), :)) ## # results should be the same ## @end example ## ## @seealso{points2d, distancePoints} ## @end deftypefn function varargout = minDistancePoints(p1, varargin) ## Initialisations # default norm (euclidean) n = 2; # flag for processing of all points allPoints = false; # process input variables if isempty(varargin) # specify only one array of points, not the norm p2 = p1; elseif length(varargin)==1 var = varargin{1}; if length(var)>1 # specify two arrays of points p2 = var; allPoints = true; else # specify array of points and the norm n = var; p2 = p1; end else # specify two array of points and the norm p2 = varargin{1}; n = varargin{2}; allPoints = true; end # number of points in each array n1 = size(p1, 1); n2 = size(p2, 1); # dimension of points d = size(p1, 2); ## Computation of distances # allocate memory dist = zeros(n1, n2); # different behaviour depending on the norm used if n==2 # Compute euclidian distance. this is the default case # Compute difference of coordinate for each pair of point ([n1*n2] array) # and for each dimension. -> dist is a [n1*n2] array. # in 2D: dist = dx.*dx + dy.*dy; for i=1:d dist = dist + (repmat(p1(:,i), [1 n2])-repmat(p2(:,i)', [n1 1])).^2; end # compute minimal distance: if ~allPoints # either on all couple of points mat = repmat((1:n1)', [1 n1]); ind = mat < mat'; [minSqDist ind] = min(dist(ind)); else # or for each point of P1 [minSqDist ind] = min(dist, [], 2); end # convert squared distance to distance minDist = sqrt(minSqDist); elseif n==inf # infinite norm corresponds to maximum absolute value of differences # in 2D: dist = max(abs(dx) + max(abs(dy)); for i=1:d dist = max(dist, abs(p1(:,i)-p2(:,i))); end else # compute distance using the specified norm. # in 2D: dist = power(abs(dx), n) + power(abs(dy), n); for i=1:d dist = dist + power((abs(repmat(p1(:,i), [1 n2])-repmat(p2(:,i)', [n1 1]))), n); end # compute minimal distance if ~allPoints # either on all couple of points mat = repmat((1:n1)', [1 n1]); ind = mat < mat'; [minSqDist ind] = min(dist(ind)); else # or for each point of P1 [minSqDist ind] = min(dist, [], 2); end # convert squared distance to distance minDist = power(minSqDist, 1/n); end if ~allPoints # convert index in array to row ad column subindices. # This uses the fact that index are sorted in a triangular matrix, # with the last index of each column being a so-called triangular # number ind2 = ceil((-1+sqrt(8*ind+1))/2); ind1 = ind - ind2*(ind2-1)/2; ind2 = ind2 + 1; end ## format output parameters # format output depending on number of asked parameters if nargout<=1 varargout{1} = minDist; elseif nargout==2 # If two arrays are asked, 'ind' is an array of indices, one for each # point in var{pts}1, corresponding to the result in minDist varargout{1} = minDist; varargout{2} = ind; elseif nargout==3 # If only one array is asked, minDist is a scalar, ind1 and ind2 are 2 # indices corresponding to the closest points. varargout{1} = minDist; varargout{2} = ind1; varargout{3} = ind2; end endfunction %!test %! pts = [50 10;40 60;30 30;20 0;10 60;10 30;0 10]; %! assert (minDistancePoints(pts), 20); %!test %! pts = [10 10;25 5;20 20;30 20;10 30]; %! [dist ind1 ind2] = minDistancePoints(pts); %! assert (10, dist, 1e-6); %! assert (3, ind1, 1e-6); %! assert (4, ind2, 1e-6); %!test %! pts = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20]; %! assert (minDistancePoints([40 50], pts), 10*sqrt(5), 1e-6); %! assert (minDistancePoints([25 30], pts), 5*sqrt(5), 1e-6); %! assert (minDistancePoints([30 40], pts), 10, 1e-6); %! assert (minDistancePoints([20 40], pts), 0, 1e-6); %!test %! pts1 = [40 50;25 30;40 20]; %! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20]; %! res = [10*sqrt(5);5*sqrt(5);10]; %! assert (minDistancePoints(pts1, pts2), res, 1e-6); %!test %! pts = [50 10;40 60;40 30;20 0;10 60;10 30;0 10]; %! assert (minDistancePoints(pts, 1), 30, 1e-6); %! assert (minDistancePoints(pts, 100), 20, 1e-6); %!test %! pts = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20]; %! assert (minDistancePoints([40 50], pts, 2), 10*sqrt(5), 1e-6); %! assert (minDistancePoints([25 30], pts, 2), 5*sqrt(5), 1e-6); %! assert (minDistancePoints([30 40], pts, 2), 10, 1e-6); %! assert (minDistancePoints([20 40], pts, 2), 0, 1e-6); %! assert (minDistancePoints([40 50], pts, 1), 30, 1e-6); %! assert (minDistancePoints([25 30], pts, 1), 15, 1e-6); %! assert (minDistancePoints([30 40], pts, 1), 10, 1e-6); %! assert (minDistancePoints([20 40], pts, 1), 0, 1e-6); %!test %! pts1 = [40 50;25 30;40 20]; %! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20]; %! res1 = [10*sqrt(5);5*sqrt(5);10]; %! assert (minDistancePoints(pts1, pts2, 2), res1, 1e-6); %! res2 = [30;15;10]; %! assert (minDistancePoints(pts1, pts2, 1), res2); %!test %! pts1 = [40 50;20 30;40 20]; %! pts2 = [0 80;10 60;20 40;30 20;40 0;0 0;100 0;0 100;0 -10;-10 -20]; %! dists0 = [10*sqrt(5);10;10]; %! inds1 = [3;3;4]; %! [minDists inds] = minDistancePoints(pts1, pts2); %! assert (dists0, minDists); %! assert (inds1, inds); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createBasisTransform.m0000644000000000000000000000013212676233417021471 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createBasisTransform.m0000644000175000017500000001001112676233417022641 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{T} = } createBasisTransfrom (@var{@var{target}}) ## @deftypefnx {Function File} {@var{T} = } createBasisTransfrom (@var{@var{source}}, @var{@var{target}}) ## Compute matrix for transforming a basis into another basis ## ## With only one input arguemnt, assumes the @var{source} is the standard (Oij) basis, with origin at (0,0), ## first direction vector equal to (1,0) and second direction vector ## equal to (0,1). Otherwise @var{@var{source}} specifies the @var{source} basis. ## ## Both @var{source} and @var{target} represent basis, in the following form: ## [x0 y0 ex1 ey1 ex2 ey2] ## [y0 y0] is the origin of the basis, [ex1 ey1] is the first direction ## vector, and [ex2 ey2] is the second direction vector. ## ## The result @var{T} is a 3-by-3 matrix such that a point expressed with ## coordinates of the first basis will be represented by new coordinates ## @code{P2 = transformPoint(P1, @var{T})} in the @var{target} basis. ## ## Example ## @example ## # standard basis transform ## src = [0 0 1 0 0 1]; ## # @var{target} transform, just a rotation by atan(2/3) followed by a scaling ## tgt = [0 0 .75 .5 -.5 .75]; ## # compute transform ## trans = createBasisTransform(src, tgt); ## # transform the point (.25,1.25) into the point (1,1) ## p1 = [.25 1.25]; ## p2 = transformPoint(p1, trans) ## ans = ## 1 1 ## @end example ## ## @seealso{transforms2d} ## @end deftypefn function transfo = createBasisTransform(source, target) # init basis transform to identity t1 = eye(3); t2 = eye(3); if nargin==2 # from source to reference basis t1(1:2, 1) = source(3:4); t1(1:2, 2) = source(5:6); t1(1:2, 3) = source(1:2); else # if only one input, use first input as target basis, and leave the # first matrix to identity target = source; end # from reference to target basis t2(1:2, 1) = target(3:4); t2(1:2, 2) = target(5:6); t2(1:2, 3) = target(1:2); # compute transfo # same as: transfo = inv(t2)*t1; transfo = t2\t1; endfunction %!demo %! # standard basis transform %! src = [0 0 1 0 0 1]; %! # target transform, just a rotation by atan(2/3) followed by a scaling %! tgt = [0 0 .75 .5 -.5 .75]; %! # compute transform %! trans = createBasisTransform(src, tgt); %! # transform the point (.25,1.25) into the point (1,1) %! p1 = [.25 1.25]; %! p2 = transformPoint(p1, trans) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/vectorNorm.m0000644000000000000000000000013212676233417017506 xustar0030 mtime=1459173135.485130312 30 atime=1459173135.485130312 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/vectorNorm.m0000644000175000017500000000661112676233417020671 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{nm} = } vectorNorm (@var{v}) ## @deftypefnx {Function File} {@var{nm} = } vectorNorm (@var{v},@var{n}) ## Compute norm of a vector, or of a set of vectors ## ## Without extra arguments, returns the euclidean norm of vector V. ## Optional argument @var{n} specifies the norm to use. N can be any value ## greater than 0. ## @table @samp ## @item N=1 ## City lock norm. ## @item N=2 ## Euclidean norm. ## @item N=inf ## Compute max coord. ## @end table ## ## When @var{v} is a MxN array, compute norm for each vector of the array. ## Vector are given as rows. Result is then a Mx1 array. ## ## Example ## ## @example ## n1 = vectorNorm([3 4]) ## n1 = ## 5 ## ## n2 = vectorNorm([1, 10], inf) ## n2 = ## 10 ## @end example ## ## @seealso{vectors2d, vectorAngle} ## @end deftypefn function n = vectorNorm(v, varargin) # size of vector dim = size(v); # extract the type of norm to compute d = 2; if ~isempty(varargin) d = varargin{1}; end if d==2 # euclidean norm: sum of squared coordinates, and take square root if dim(1)==1 || dim(2)==1 n = sqrt(sum(v.*v)); else n = sqrt(sum(v.*v, 2)); end elseif d==1 # absolute norm: sum of absolute coordinates if dim(1)==1 || dim(2)==1 n = sum(abs(v)); else n = sum(abs(v), 2); end elseif d==inf # infinite norm: uses the maximal corodinate if dim(1)==1 || dim(2)==1 n = max(v); else n = max(v, [], 2); end else # Other norms, use explicit but slower expression if dim(1)==1 || dim(2)==1 n = power(sum(power(v, d)), 1/d); else n = power(sum(power(v, d), 2), 1/d); end end endfunction %!assert (5, vectorNorm ([3 4])) %!assert(10, vectorNorm ([1, 10], inf)) geometry-2.1.1/inst/geom2d/PaxHeaders.5293/circleAsPolygon.m0000644000000000000000000000013212676233417020445 xustar0030 mtime=1459173135.337200838 30 atime=1459173135.337200838 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/circleAsPolygon.m0000644000175000017500000000507312676233417021631 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{P} = } circleAsPolygon (@var{circle}, @var{N}) ## Convert a circle into a series of points ## ## P = circleAsPolygon(CIRCLE, N); ## convert circle given as [x0 y0 r], where x0 and y0 are coordinate of ## center, and r is the radius, into an array of [(N+1)x2] double, ## containing x and y values of points. ## The polygon is closed ## ## P = circleAsPolygon(CIRCLE); ## uses a default value of N=64 points ## ## Example ## circle = circleAsPolygon([10 0 5], 16); ## figure; ## drawPolygon(circle); ## ## @seealso{circles2d, polygons2d, createCircle} ## @end deftypefn function varargout = circleAsPolygon(circle, varargin) # determines number of points N = 64; if ~isempty(varargin) N = varargin{1}; end # create circle t = linspace(0, 2*pi, N+1)'; x = circle(1) + circle(3)*cos(t); y = circle(2) + circle(3)*sin(t); if nargout==1 varargout{1}=[x y]; elseif nargout==2 varargout{1}=x; varargout{2}=y; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawOrientedBox.m0000644000000000000000000000013212676233417020450 xustar0030 mtime=1459173135.361189401 30 atime=1459173135.361189401 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawOrientedBox.m0000644000175000017500000000706212676233417021634 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{hb} = } drawOrientedBox (@var{box}) ## @deftypefnx {Function File} {@var{hb} = } drawOrientedBox (@dots{}, @var{param}, @var{value}) ## Draw centered oriented rectangle. ## ## Syntax ## drawOrientedBox(BOX) ## drawOrientedBox(BOX, 'PropertyName', propertyvalue, ...) ## ## Description ## drawOrientedBox(OBOX) ## Draws an oriented rectangle (or bounding box) on the current axis. ## OBOX is a 1-by-5 row vector containing box center, dimension (length ## and width) and orientation (in degrees): ## OBOX = [CX CY LENGTH WIDTH THETA]. ## ## When OBOX is a N-by-5 array, the N boxes are drawn. ## ## HB = drawOrientedBox(...) ## Returns a handle to the created graphic object(s). Object style can be ## modified using syntaw like: ## set(HB, 'color', 'g', 'linewidth', 2); ## ## @seealso{drawPolygon, drawRect, drawBox} ## @end deftypefn function varargout = drawOrientedBox(box, varargin) ## Parses input arguments if nargin > 4 && sum(cellfun(@isnumeric, varargin(1:4))) == 4 cx = box; cy = varargin{1}; hl = varargin{2} / 2; hw = varargin{3} / 2; theta = varargin{4}; varargin = varargin(5:end); else cx = box(:,1); cy = box(:,2); hl = box(:,3) / 2; hw = box(:,4) / 2; theta = box(:,5); end ## Draw each box # allocate memory for graphical handle hr = zeros(length(cx), 1); # iterate on oriented boxes for i = 1:length(cx) # pre-compute angle data cot = cosd(theta(i)); sit = sind(theta(i)); # x and y shifts lc = hl(i) * cot; ls = hl(i) * sit; wc = hw(i) * cot; ws = hw(i) * sit; # coordinates of box vertices vx = cx(i) + [-lc + ws; lc + ws ; lc - ws ; -lc - ws ; -lc + ws]; vy = cy(i) + [-ls - wc; ls - wc ; ls + wc ; -ls + wc ; -ls - wc]; # draw polygons hr(i) = line(vx, vy, varargin{:}); end ## Format output if nargout > 0 varargout = {hr}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawBox.m0000644000000000000000000000013212676233417016756 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawBox.m0000644000175000017500000000525712676233417020146 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawBox (@var{box}) ## @deftypefnx {Function File} {@var{h} =} drawBox (@var{box}, @var{param}, @var{value}, @dots{}) ## Draw a box defined by coordinate extents ## ## Draws a box defined by its extent: @var{box} = [@var{xmin} @var{xmax} ## @var{ymin} @var{ymax}]. Addtional ## arguments are passed to function @code{plot}. If requested, it returns the ## handle to the graphics object created. ## ## @seealso{drawOrientedBox, drawRect, plot} ## @end deftypefn function varargout = drawBox(box, varargin) # default values xmin = box(:,1); xmax = box(:,2); ymin = box(:,3); ymax = box(:,4); nBoxes = size(box, 1); r = zeros(nBoxes, 1); # iterate on boxes for i = 1:nBoxes # exract min and max values tx(1) = xmin(i); ty(1) = ymin(i); tx(2) = xmax(i); ty(2) = ymin(i); tx(3) = xmax(i); ty(3) = ymax(i); tx(4) = xmin(i); ty(4) = ymax(i); tx(5) = xmin(i); ty(5) = ymin(i); # display polygon r(i) = plot(tx, ty, varargin{:}); end # format output if nargout > 0 varargout = {r}; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/mergeBoxes.m0000644000000000000000000000013212676233417017450 xustar0030 mtime=1459173135.457143654 30 atime=1459173135.457143654 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/mergeBoxes.m0000644000175000017500000000506112676233417020631 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{box} =} mergeBoxes (@var{box1}, @var{box2}) ## Merge two boxes, by computing their greatest extent. ## # Example ## ## @example ## box1 = [5 20 5 30]; ## box2 = [0 15 0 15]; ## mergeBoxes(box1, box2) ## ans = ## 0 20 0 30 ## @end example ## ## @seealso{boxes2d, drawBox, intersectBoxes} ## @end deftypefn function bb = mergeBoxes(box1, box2) # unify sizes of data if size(box1,1) == 1 box1 = repmat(box1, size(box2,1), 1); elseif size(box2, 1) == 1 box2 = repmat(box2, size(box1,1), 1); elseif size(box1,1) != size(box2,1) error('geom2d:Error', 'Bad size for inputs'); end # compute extreme coords mini = min(box1(:,[1 3]), box2(:,[1 3])); maxi = max(box1(:,[2 4]), box2(:,[2 4])); # concatenate result into a new box structure bb = [mini(:,1) maxi(:,1) mini(:,2) maxi(:,2)]; endfunction %!test %! box1 = [5 20 10 25]; %! box2 = [0 15 15 20]; %! res = [0 20 10 25]; %! bb = mergeBoxes(box1, box2); %! assert (res, bb, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/drawLabels.m0000644000000000000000000000013212676233417017430 xustar0030 mtime=1459173135.357191307 30 atime=1459173135.357191307 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/drawLabels.m0000644000175000017500000000673112676233417020616 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawLabels (@var{x}, @var{y}, @var{lbl}) ## @deftypefnx {Function File} drawLabels (@var{pos}, @var{lbl}) ## @deftypefnx {Function File} drawLabels (@dots{}, @var{numbers}, @var{format}) ## Draw labels at specified positions. ## ## DRAWLABELS(X, Y, LBL) draw labels LBL at position X and Y. ## LBL can be either a string array, or a number array. In this case, ## string are created by using sprintf function, with '#.2f' mask. ## ## DRAWLABELS(POS, LBL) draw labels LBL at position specified by POS, ## where POS is a N*2 int array. ## ## DRAWLABELS(..., NUMBERS, FORMAT) create labels using sprintf function, ## with the mask given by FORMAT (e. g. '#03d' or '5.3f'), and the ## corresponding values. ## @end deftypefn function varargout = drawLabels(varargin) # check if enough inputs are given if isempty(varargin) error('wrong number of arguments in drawLabels'); end # process input parameters var = varargin{1}; if size(var, 2)==1 if length(varargin)<3 error('wrong number of arguments in drawLabels'); end px = var; py = varargin{2}; lbl = varargin{3}; varargin(1:3) = []; else if length(varargin)<2 error('wrong number of arguments in drawLabels'); end px = var(:,1); py = var(:,2); lbl = varargin{2}; varargin(1:2) = []; end format = '%.2f'; if ~isempty(varargin) format = varargin{1}; end if size(format, 1)==1 && size(px, 1)>1 format = repmat(format, size(px, 1), 1); end labels = cell(length(px), 1); if isnumeric(lbl) for i=1:length(px) labels{i} = sprintf(format(i,:), lbl(i)); end elseif ischar(lbl) for i=1:length(px) labels{i} = lbl(i,:); end elseif iscell(lbl) labels = lbl; end labels = char(labels); h = text(px, py, labels); if nargout>0 varargout{1}=h; end endfunction geometry-2.1.1/inst/geom2d/PaxHeaders.5293/lineAngle.m0000644000000000000000000000013012676233417017244 xustar0029 mtime=1459173135.45314556 29 atime=1459173135.45314556 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/lineAngle.m0000644000175000017500000000712012676233417020425 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{theta} =} lineAngle(varargin) ## Computes angle between two straight lines ## ## A = lineAngle(LINE); ## Returns the angle between horizontal, right-axis and the given line. ## Angle is fiven in radians, between 0 and 2*pi, in counter-clockwise ## direction. ## ## A = lineAngle(LINE1, LINE2); ## Returns the directed angle between the two lines. Angle is given in ## radians between 0 and 2*pi, in counter-clockwise direction. ## ## @seealso{lines2d, angles2d, createLine, normalizeAngle} ## @end deftypefn function theta = lineAngle(varargin) nargs = length(varargin); if nargs == 1 # angle of one line with horizontal line = varargin{1}; theta = mod(atan2(line(:,4), line(:,3)) + 2*pi, 2*pi); elseif nargs==2 # angle between two lines theta1 = lineAngle(varargin{1}); theta2 = lineAngle(varargin{2}); theta = mod(bsxfun(@minus, theta2, theta1)+2*pi, 2*pi); end endfunction # horizontal %!test %! line1 = createLine([2 3 1 0]); %! assert (lineAngle(line1), 0, 1e-6); %!test %! line1 = createLine([2 3 0 1]); %! assert (lineAngle(line1), pi/2, 1e-6); %!test %! line1 = createLine([2 3 1 1]); %! assert (lineAngle(line1), pi/4, 1e-6); %!test %! line1 = createLine([2 3 5 -1]); %! assert (lineAngle(line1), mod(atan2(-1, 5)+2*pi, 2*pi), 1e-6); %!test %! line1 = createLine([2 3 5000 -1000]); %! assert (lineAngle(line1), mod(atan2(-1, 5)+2*pi, 2*pi), 1e-6); %!test %! line1 = createLine([2 3 -1 0]); %! assert (lineAngle(line1), pi, 1e-6); # test lineAngle with two parameters : angle between 2 lines # check for 2 orthogonal lines %!test %! line1 = createLine([1 3 1 0]); %! line2 = createLine([-2 -1 0 1]); %! assert (lineAngle(line1, line2), pi/2, 1e-6); %! assert (lineAngle(line2, line1), 3*pi/2, 1e-6); # check for 2 orthogonal lines, with very different parametrizations %!test %! line1 = createLine([1 3 1 1]); %! line2 = createLine([-2 -1 -1000 1000]); %! assert (lineAngle(line1, line2), pi/2, 1e-6); %! assert (lineAngle(line2, line1), 3*pi/2, 1e-6); geometry-2.1.1/inst/geom2d/PaxHeaders.5293/createCircle.m0000644000000000000000000000013212676233417017735 xustar0030 mtime=1459173135.345197025 30 atime=1459173135.345197025 30 ctime=1459173135.645054067 geometry-2.1.1/inst/geom2d/createCircle.m0000644000175000017500000001016112676233417021113 0ustar00juanpijuanpi00000000000000## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{circle} = } createCircle (@var{p1}, @var{p2}, @var{p3}) ## @deftypefnx {Function File} {@var{circle} = } createCircle (@var{p1}, @var{p2}) ## Create a circle from 2 or 3 points. ## ## Creates the circle passing through the 3 given points. ## C is a 1x3 array of the form: [XC YX R]. ## ## When two points are given, creates the circle whith center @var{p1} and passing ## throuh the point @var{p2}. ## ## Works also when input are point arrays the same size, in this case the ## result has as many lines as the point arrays. ## ## Example ## ## @example ## # Draw a circle passing through 3 points. ## p1 = [10 15]; ## p2 = [15 20]; ## p3 = [10 25]; ## circle = createCircle(p1, p2, p3); ## figure; hold on; axis equal; axis([0 50 0 50]); ## drawPoint([p1 ; p2; p3]); ## drawCircle(circle); ## @end example ## ## @seealso{circles2d, createDirectedCircle} ## @end deftypefn function circle = createCircle(varargin) if nargin == 2 # inputs are the center and a point on the circle p1 = varargin{1}; p2 = varargin{2}; x0 = p1(:,1); y0 = p1(:,2); r = hypot((p2(:,1)-x0), (p2(:,2)-y0)); elseif nargin == 3 # inputs are three points on the circle p1 = varargin{1}; p2 = varargin{2}; p3 = varargin{3}; # compute circle center line1 = medianLine(p1, p2); line2 = medianLine(p1, p3); point = intersectLines(line1, line2); x0 = point(:, 1); y0 = point(:, 2); # circle radius r = hypot((p1(:,1)-x0), (p1(:,2)-y0)); end # create array for returning result circle = [x0 y0 r]; endfunction %!shared privpath %! privpath = [fileparts(which('geom2d_Contents')) filesep() 'private']; %!test %! addpath (privpath,'-end') %! p1 = [10 15]; %! p2 = [15 20]; %! p3 = [10 25]; %! exp = [10 20 5]; %! circle = createCircle(p1, p2, p3); %! assertEqual(exp, circle); %! circle = createCircle(p3, p1, p2); %! assertEqual(exp, circle); %! circle = createCircle(p2, p3, p1); %! assertEqual(exp, circle); %! rmpath (privpath); %!test %! addpath (privpath,'-end') %! p1 = [10 15]; %! p2 = [15 20]; %! p3 = [10 25]; %! exp = [10 20 5]; %! p1 = [p1; p1+10; p1+20; p1-5]; %! p2 = [p2; p2+10; p2+20; p2-5]; %! p3 = [p3; p3+10; p3+20; p3-5]; %! exp = repmat(exp, 4, 1) + [0 0 0;10 10 0;20 20 0;-5 -5 0]; %! circle = createCircle(p1, p2, p3); %! assertEqual(exp, circle); %! circle = createCircle(p3, p1, p2); %! assertEqual(exp, circle); %! circle = createCircle(p2, p3, p1); %! assertEqual(exp, circle); %! rmpath (privpath); geometry-2.1.1/inst/PaxHeaders.5293/io0000644000000000000000000000013212676233417014347 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/0000755000175000017500000000000012676233417015603 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/io/PaxHeaders.5293/drawing3.svg0000644000000000000000000000013212676233417016663 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing3.svg0000644000175000017500000000205212676233417020041 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/drawing4.svg0000644000000000000000000000013212676233417016664 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.561094095 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing4.svg0000644000175000017500000000407012676233417020044 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/drawing5.svg0000644000000000000000000000013212676233417016665 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.561094095 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing5.svg0000644000175000017500000000374612676233417020056 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/drawing.svg0000644000000000000000000000013212676233417016600 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing.svg0000644000175000017500000000340112676233417017755 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/private0000644000000000000000000000013212676233417016021 xustar0030 mtime=1459173135.565092189 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/0000755000175000017500000000000012676233417017255 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/io/private/PaxHeaders.5293/ruledSurfGeo.m0000644000000000000000000000013212676233417020662 xustar0030 mtime=1459173135.565092189 30 atime=1459173135.565092189 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/ruledSurfGeo.m0000644000175000017500000000333112676233417022041 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{str} = ruledSurfGeo (@var{id}, @var{nloop}, @var{loops}, @var{centerid}) ## Generates a string for Gmsh Ruled Surface format. ## ## Creates a ruled surface with identifier @var{id}, i.e., a surface that can be ## interpolated using transfinite interpolation. @var{nloop} indicates the number ## of loops that define the surface. @var{loops} should contain the identification ## number of a line loop composed of either three or four elementary lines. ## @var{centerid} is the identification number of the center of the sphere, this ## forces the surface to be a spherical patch. ## ## @end deftypefn function str = ruledSurfGeo(id,nloop,loops,centerid) substr = repmat(',%d',1,nloop-1); if ~isempty(centerid) str = sprintf(['Ruled Surface(%d) = {%d' substr '} In Sphere {%d};\n'], ... id,loops,centerid); else error('data2geo:Error',"The id of the centers shouldn't be empty"); end end geometry-2.1.1/inst/io/private/PaxHeaders.5293/lineLoopGeo.m0000644000000000000000000000013212676233417020470 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.561094095 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/lineLoopGeo.m0000644000175000017500000000264412676233417021655 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{str} = lineLoopGeo (@var{id}, @var{nl}, @var{lns}) ## Generates a string for Gmsh Line Loop format. ## ## The third elementary entity is the surface. In order to define a ## simple rectangular surface from defined lines, a ## line loop has first to be defined. A line loop is a list of ## connected lines, a sign being associated with each line (depending ## on the orientation of the line). @var{id} is an indentifier for the loop. ## @var{nl} is the number of lines in the loop. @var{lns} is the list of lines. ## ## @end deftypefn function str = lineLoopGeo(id,nl,lns) substr = repmat(',%d',1,nl-1); str = sprintf(['Line Loop(%d) = {%d' substr '};\n'],id,lns); end geometry-2.1.1/inst/io/private/PaxHeaders.5293/pointGeo.m0000644000000000000000000000013212676233417020040 xustar0030 mtime=1459173135.565092189 30 atime=1459173135.565092189 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/pointGeo.m0000644000175000017500000000256212676233417021224 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{str} = poointGeo (@var{n}, @var{xyz}, @var{l}) ## Generates a string for Gmsh Point format. ## ## Gmsh's simplest `elementary entity', a `Point'. A Point is defined by a list ## of five numbers: @var{n} the identificator, @var{xyz} three coordinates (X, Y ## and Z), and a characteristic length @var{l} that sets the target element size ## at the point: ## The distribution of the mesh element sizes is then obtained by ## interpolation of these characteristic lengths throughout the ## geometry. ## ## @end deftypefn function str = pointGeo(n,xyz,l) str = sprintf('Point(%d) = {%.16g,%.16g,%.16g,%.16g};\n',n,xyz,l); end geometry-2.1.1/inst/io/private/PaxHeaders.5293/planeSurfGeo.m0000644000000000000000000000013212676233417020646 xustar0030 mtime=1459173135.565092189 30 atime=1459173135.565092189 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/planeSurfGeo.m0000644000175000017500000000335412676233417022032 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{str} = planeSurfGeo (@var{id}, @var{nloop},@var{loops}) ## Generates a string for Gmsh Plane Surface format. ## ## @var{id} is the plane surface's identification number. ## @var{nloop} is the number of loops defining the surface. ## @var{loops} contain the identification numbers of all the line loops defining ## the surface. The first line loop defines the exterior boundary of the surface; ## all other line loops define holes in the surface. A line loop defining a hole ## should not have any lines in common with the exterior line loop (in which case ## it is not a hole, and the two surfaces should be defined separately). ## Likewise, a line loop defining a hole should not have any lines in common with ## another line loop defining a hole in the same surface (in which case the two ## line loops should be combined). ## ## @end deftypefn function str = planeSurfGeo(id,nloop,loops) substr = repmat(',%d',1,nloop-1); str = sprintf(['Plane Surface(%d) = {%d' substr '};\n'],id,loops); end geometry-2.1.1/inst/io/private/PaxHeaders.5293/lineGeo.m0000644000000000000000000000013212676233417017636 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.561094095 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/private/lineGeo.m0000644000175000017500000000232012676233417021012 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{str} = lineGeo (@var{n}, @var{pi}, @var{pj}) ## Generates a string for Gmsh Line format. ## ## Curves are Gmsh's second type of elementery entities, and, ## amongst curves, straight lines are the simplest. A straight line is ## defined by a list of point numbers. The initial point @var{pi}, the final ## point @var{pj}. @var{n} is an indetifier for the line. ## ## @end deftypefn function str = lineGeo(n,i,j) str = sprintf('Line(%d) = {%d,%d};\n',n,i,j); end geometry-2.1.1/inst/io/PaxHeaders.5293/data2geo.m0000644000000000000000000000013212676233417016270 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/data2geo.m0000644000175000017500000000704312676233417017453 0ustar00juanpijuanpi00000000000000## Copyright (C) 2016 - Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or ## (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . ## Author: Juan Pablo Carbajal ## -*- texinfo -*- ## @deftypefn {Function File} {@var{fileStr} =} data2geo (@var{data}, @var{lc}) ## @deftypefnx {Function File} {@var{fileStr} =} data2geo (@dots{}, @var{param}, @var{value}) ## Uses data to build a file compatible with Gmsh. ## ## @var{data} is assumed to describe a polygon in @code{polygon2d} format. ## The argument @var{lc} specifies the edge size. ## ## The optional parameters can be 'output' followed with a string specifying a file ## to write, and 'spherical' followed by a real number @var{r} indicating that the ## polygon describes a spherical surface of radious @var{r}. ## ## @seealso{polygon2d, @@svg/path2polygon} ## @end deftypefn function strFile = data2geo(data,lc,varargin) nl = @()sprintf('\n'); ## Parse options filegiven = []; spherical = []; if nargin > 2 filegiven = find(cellfun(@(x)strcmpi(x,'output'),varargin)); spherical = find(cellfun(@(x)strcmpi(x,'spherical'),varargin)); end [n dim] = size(data); if dim == 2 data(:,3) = zeros(n,1); end header = ' // File created with Octave'; strFile = [header nl()]; # Points strFile = [strFile '// Points' nl()]; for i=1:n strFile = [strFile pointGeo(i,data(i,:),lc)]; end # Lines strFile = [strFile '// Lines' nl()]; for i=1:n-1 strFile = [strFile lineGeo(i,i,i+1)]; end strFile = [strFile lineGeo(n,n,1)]; # Loop strFile = [strFile lineLoopGeo(n+1,n,1:n)]; # Surface if spherical sphr = varargin{spherical+1}; if dim ==2 sphr(1,3) = 0; end strFile = [strFile pointGeo(n+1,sphr,lc)]; strFile = [strFile ruledSurfGeo(n+3,1,n+1,n+1)]; else strFile = [strFile planeSurfGeo(n+2,1,n+1)]; end if filegiven outfile = varargin{filegiven+1}; fid = fopen(outfile,'w'); fprintf(fid,'%s',strFile); fclose(fid); disp(['DATA2GEO: Geometry file saved to ' outfile]) end endfunction %!demo %! points = [0 0 0; 0.1 0 0; 0.1 .3 0; 0 0.3 0]; %! strFile = data2geo(points,0.009); %! disp(strFile) %!demo %! dc = svg('drawing6.svg'); %! ids = dc.pathid(); %! P = dc.path2polygon(ids{1},12)(1:end-1,:); %! P = bsxfun(@minus, P, centroid(P)); %! P = simplifypolygon(P,'tol',5e-1); %! filename = tmpnam (); %! meshsize = sqrt(mean(sumsq(diff(P,1,1),2)))/2; %! data2geo (P, meshsize, 'output', [filename '.geo']); %! %! pkg load msh fpl %! T = msh2m_gmsh(filename); %! pdemesh(T.p,T.e,T.t) %! view(2) %! axis tight %! # -------------------------------------------------------------------------- %! # We load the drawing6.svg file into Octave and transform it into a polygon. %! # Then we create a temporary file where the .geo mesh will be written. %! # If the packages msh and fpl are available, a mesh is created from the .geo %! # file. geometry-2.1.1/inst/io/PaxHeaders.5293/drawing2.svg0000644000000000000000000000013212676233417016662 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing2.svg0000644000175000017500000000371712676233417020051 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/drawing6.svg0000644000000000000000000000013212676233417016666 xustar0030 mtime=1459173135.561094095 30 atime=1459173135.561094095 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/drawing6.svg0000644000175000017500000000260412676233417020047 0ustar00juanpijuanpi00000000000000 image/svg+xml geometry-2.1.1/inst/io/PaxHeaders.5293/@svg0000644000000000000000000000013212676233417015246 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/@svg/0000755000175000017500000000000012676233417016502 5ustar00juanpijuanpi00000000000000geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/pathid.m0000644000000000000000000000013212676233417016752 xustar0030 mtime=1459173135.553097908 30 atime=1459173135.553097908 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/@svg/pathid.m0000644000175000017500000000156212676233417020135 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} function_name () ## @end deftypefn function ids = pathid(obj,varargin) ids = fieldnames (obj.Path); endfunction geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/svg.m0000644000000000000000000000013212676233417016300 xustar0030 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 geometry-2.1.1/inst/io/@svg/svg.m0000644000175000017500000000477412676233417017473 0ustar00juanpijuanpi00000000000000## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{obj} =} svg () ## @deftypefnx {Function File} {@var{obj} =} svg (@var{str}) ## Create object of the svg class. ## ## If no input argument is provided the object is empty. @var{str} can be a filename ## or a string defining an inline SVG. ## ## @end deftypefn function svg = svg(name='') svg = struct; ## SVG data. All the attributes of the node. ## The field unparsed contains all the attributes that are not being parsed. svg.Data = struct('height',[],'width',[],'id','null','normalized',false); ## SVG metadata. All the attributes of the node. ## The field unparsed contains all the attributes that are not being parsed. svg.Metadata = struct('unparsed',' '); ## SVG paths. It is a vector of path structs. Maybe path can be a object too? ## Order of Path.Data is important so we store in a cell (could be a matrix padded with zeros). ## All the paths stored in polyval compatible format. Straigth segments are also stored as a polynomial. svg.Path = struct(); svg = class (svg, 'svg'); if !isempty (name) if exist(name,"file") == 2 name = file_in_path(path(), name); else error("svg:BadArguemnt", "File #s doesn't exist",name); end paths = loadpaths(svg, name); svg.Path = paths; data = loadsvgdata(svg, name); svg.Data = data; svg.Data.normalized = false; elseif !ischar(name) print_usage ; endif endfunction %!test %! dc = svg('drawing5.svg'); %! dc.getpath(); %! dc.pathid(); %! dc.getpath('path3756'); %! %! dc = svg('drawing.svg'); %! ids = dc.pathid(); %! dc.getpath({ids{[1 3]}}); %!test %! dc = svg('drawing6.svg'); %! ids = dc.pathid(); %! P = dc.path2polygon(ids{1}); %!test %! dc = svg('drawing6.svg'); %! dc.plot(); %! dc.plot('color','r','linewidth',2); ����geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/normalize.m���������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017501� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.549099814 30 atime=1459173135.549099814 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/normalize.m�������������������������������������������������������������0000644�0001750�0001750�00000005674�12676233417�020674� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{SVGn} = normalize (@var{SVG}) ## normalizes and SVG. ## @end deftypefn function [SVGn bb] = normalize (obj) SVGn = obj; bb = []; if ! obj.Data.normalized ids = fieldnames (obj.Path); npath = numel(ids); v = zeros(npath,2); bb = zeros(1,4); for ip = 1:npath v(ip,:) = shapecentroid(obj.Path.(ids{ip}).data); p = shape2polygon(obj.Path.(ids{ip}).data); bb = mergeBoxes(bb, [min(p) max(p)]([1 3 2 4])); end if npath > 1 v = mean(v)(:); else v = v.'; end ## check whether document and bounding box agree. bbHeight = bb(2)-bb(1); bbWidth = bb(4)-bb(2); if obj.Data.height != bbHeight warning("svg:normalize:Sanitycheck",... ["Height of SVG #g and height boundingbox #g don't match.\n" ... "Using bounding box.\n"],obj.Data.height,bbHeight) end if obj.Data.width != bbWidth warning("svg:normalize:Sanitycheck",... ["Width of SVG #g and width boundingbox #g don't match.\n" ... "Using bounding box.\n"],obj.Data.width,bbWidth) end ## Move paths such that center of SVG is at 0,0 ## Put coordinates in the usual frame ## Scale such that diagonal of bounding box is 1 Dnorm = sqrt (bbWidth ^ 2 + bbHeight ^ 2); S = (1 / Dnorm) * eye (2); bb = zeros(1,4); for ip = 1:npath SVGn.Path.(ids{ip}).data = shapetransform(obj.Path.(ids{ip}).data,-v); # Put to middle SVGn.Path.(ids{ip}).data = ... shapetransform(SVGn.Path.(ids{ip}).data,[0; -bbHeight/2]); # Reflect y SVGn.Path.(ids{ip}).data = ... shapetransform(SVGn.Path.(ids{ip}).data,[1 0;0 -1]); # Put to bottom SVGn.Path.(ids{ip}).data = ... shapetransform(SVGn.Path.(ids{ip}).data,[0; bbHeight/2]); # Scale SVGn.Path.(ids{ip}).data = ... shapetransform(SVGn.Path.(ids{ip}).data,S); p = shape2polygon(SVGn.Path.(ids{ip}).data); bb = mergeBoxes(bb, [min(p) max(p)]([1 3 2 4])); end bbHeight = bb(2)-bb(1); bbWidth = bb(4)-bb(2); SVGn.Data.height = bbHeight; SVGn.Data.width = bbWidth; SVGn.Data.normalized = true; end end ��������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/width.m�������������������������������������������������0000644�0000000�0000000�00000000132�12676233417�016620� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.557096002 30 atime=1459173135.557096002 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/width.m�����������������������������������������������������������������0000644�0001750�0001750�00000001546�12676233417�020005� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} function_name () ## @end deftypefn function o = width(obj,varargin) o = obj.Data.width; endfunction ����������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/inkex.py������������������������������������������������0000644�0000000�0000000�00000000130�12676233417�017011� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 29 atime=1459173135.54510172 30 ctime=1459173135.645054067 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/inkex.py����������������������������������������������������������������0000644�0001750�0001750�00000020200�12676233417�020164� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������#!/usr/bin/env python """ inkex.py A helper module for creating Inkscape extensions Copyright (C) 2005,2007 Aaron Spike, aaron@ekips.org This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA """ import sys, copy, optparse, random, re import gettext from math import * _ = gettext.gettext #a dictionary of all of the xmlns prefixes in a standard inkscape doc NSS = { u'sodipodi' :u'http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd', u'cc' :u'http://creativecommons.org/ns#', u'ccOLD' :u'http://web.resource.org/cc/', u'svg' :u'http://www.w3.org/2000/svg', u'dc' :u'http://purl.org/dc/elements/1.1/', u'rdf' :u'http://www.w3.org/1999/02/22-rdf-syntax-ns#', u'inkscape' :u'http://www.inkscape.org/namespaces/inkscape', u'xlink' :u'http://www.w3.org/1999/xlink', u'xml' :u'http://www.w3.org/XML/1998/namespace' } #a dictionary of unit to user unit conversion factors uuconv = {'in':90.0, 'pt':1.25, 'px':1, 'mm':3.5433070866, 'cm':35.433070866, 'm':3543.3070866, 'km':3543307.0866, 'pc':15.0, 'yd':3240 , 'ft':1080} def unittouu(string): '''Returns userunits given a string representation of units in another system''' unit = re.compile('(%s)$' % '|'.join(uuconv.keys())) param = re.compile(r'(([-+]?[0-9]+(\.[0-9]*)?|[-+]?\.[0-9]+)([eE][-+]?[0-9]+)?)') p = param.match(string) u = unit.search(string) if p: retval = float(p.string[p.start():p.end()]) else: retval = 0.0 if u: try: return retval * uuconv[u.string[u.start():u.end()]] except KeyError: pass return retval def uutounit(val, unit): return val/uuconv[unit] try: from lxml import etree except: sys.exit(_('The fantastic lxml wrapper for libxml2 is required by inkex.py and therefore this extension. Please download and install the latest version from http://cheeseshop.python.org/pypi/lxml/, or install it through your package manager by a command like: sudo apt-get install python-lxml')) def debug(what): sys.stderr.write(str(what) + "\n") return what def errormsg(msg): """Intended for end-user-visible error messages. (Currently just writes to stderr with an appended newline, but could do something better in future: e.g. could add markup to distinguish error messages from status messages or debugging output.) Note that this should always be combined with translation: import gettext _ = gettext.gettext ... inkex.errormsg(_("This extension requires two selected paths.")) """ sys.stderr.write((unicode(msg) + "\n").encode("UTF-8")) def check_inkbool(option, opt, value): if str(value).capitalize() == 'True': return True elif str(value).capitalize() == 'False': return False else: raise optparse.OptionValueError("option %s: invalid inkbool value: %s" % (opt, value)) def addNS(tag, ns=None): val = tag if ns!=None and len(ns)>0 and NSS.has_key(ns) and len(tag)>0 and tag[0]!='{': val = "{%s}%s" % (NSS[ns], tag) return val class InkOption(optparse.Option): TYPES = optparse.Option.TYPES + ("inkbool",) TYPE_CHECKER = copy.copy(optparse.Option.TYPE_CHECKER) TYPE_CHECKER["inkbool"] = check_inkbool class Effect: """A class for creating Inkscape SVG Effects""" def __init__(self, *args, **kwargs): self.document=None self.ctx=None self.selected={} self.doc_ids={} self.options=None self.args=None self.OptionParser = optparse.OptionParser(usage="usage: %prog [options] SVGfile",option_class=InkOption) self.OptionParser.add_option("--id", action="append", type="string", dest="ids", default=[], help="id attribute of object to manipulate") def effect(self): pass def getoptions(self,args=sys.argv[1:]): """Collect command line arguments""" self.options, self.args = self.OptionParser.parse_args(args) def parse(self,file=None): """Parse document in specified file or on stdin""" try: try: stream = open(file,'r') except: stream = open(self.svg_file,'r') except: stream = sys.stdin self.document = etree.parse(stream) stream.close() def getposinlayer(self): #defaults self.current_layer = self.document.getroot() self.view_center = (0.0,0.0) layerattr = self.document.xpath('//sodipodi:namedview/@inkscape:current-layer', namespaces=NSS) if layerattr: layername = layerattr[0] layer = self.document.xpath('//svg:g[@id="%s"]' % layername, namespaces=NSS) if layer: self.current_layer = layer[0] xattr = self.document.xpath('//sodipodi:namedview/@inkscape:cx', namespaces=NSS) yattr = self.document.xpath('//sodipodi:namedview/@inkscape:cy', namespaces=NSS) doc_height = unittouu(self.document.getroot().get('height')) if xattr and yattr: x = xattr[0] y = yattr[0] if x and y: self.view_center = (float(x), doc_height - float(y)) # FIXME: y-coordinate flip, eliminate it when it's gone in Inkscape def getselected(self): """Collect selected nodes""" for i in self.options.ids: path = '//*[@id="%s"]' % i for node in self.document.xpath(path, namespaces=NSS): self.selected[i] = node def getElementById(self, id): path = '//*[@id="%s"]' % id el_list = self.document.xpath(path, namespaces=NSS) if el_list: return el_list[0] else: return None def getParentNode(self, node): for parent in self.document.getiterator(): if node in parent.getchildren(): return parent break def getdocids(self): docIdNodes = self.document.xpath('//@id', namespaces=NSS) for m in docIdNodes: self.doc_ids[m] = 1 def getNamedView(self): return self.document.xpath('//sodipodi:namedview', namespaces=NSS)[0] def createGuide(self, posX, posY, angle): atts = { 'position': str(posX)+','+str(posY), 'orientation': str(sin(radians(angle)))+','+str(-cos(radians(angle))) } guide = etree.SubElement( self.getNamedView(), addNS('guide','sodipodi'), atts ) return guide def output(self): """Serialize document into XML on stdout""" self.document.write(sys.stdout) def affect(self, args=sys.argv[1:], output=True): """Affect an SVG document with a callback effect""" self.svg_file = args[-1] self.getoptions(args) self.parse() self.getposinlayer() self.getselected() self.getdocids() self.effect() if output: self.output() def uniqueId(self, old_id, make_new_id = True): new_id = old_id if make_new_id: while new_id in self.doc_ids: new_id += random.choice('0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ') self.doc_ids[new_id] = 1 return new_id def xpathSingle(self, path): try: retval = self.document.xpath(path, namespaces=NSS)[0] except: errormsg(_("No matching node for expression: %s") % path) retval = None return retval # vim: expandtab shiftwidth=4 tabstop=8 softtabstop=4 encoding=utf-8 textwidth=99 ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/simplepath.py�������������������������������������������0000644�0000000�0000000�00000000132�12676233417�020043� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.553097908 30 atime=1459173135.553097908 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/simplepath.py�����������������������������������������������������������0000644�0001750�0001750�00000015642�12676233417�021232� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������#!/usr/bin/env python """ simplepath.py functions for digesting paths into a simple list structure Copyright (C) 2005 Aaron Spike, aaron@ekips.org This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA """ import re, math def lexPath(d): """ returns and iterator that breaks path data identifies command and parameter tokens """ offset = 0 length = len(d) delim = re.compile(r'[ \t\r\n,]+') command = re.compile(r'[MLHVCSQTAZmlhvcsqtaz]') parameter = re.compile(r'(([-+]?[0-9]+(\.[0-9]*)?|[-+]?\.[0-9]+)([eE][-+]?[0-9]+)?)') while 1: m = delim.match(d, offset) if m: offset = m.end() if offset >= length: break m = command.match(d, offset) if m: yield [d[offset:m.end()], True] offset = m.end() continue m = parameter.match(d, offset) if m: yield [d[offset:m.end()], False] offset = m.end() continue #TODO: create new exception raise Exception, 'Invalid path data!' ''' pathdefs = {commandfamily: [ implicitnext, #params, [casts,cast,cast], [coord type,x,y,0] ]} ''' pathdefs = { 'M':['L', 2, [float, float], ['x','y']], 'L':['L', 2, [float, float], ['x','y']], 'H':['H', 1, [float], ['x']], 'V':['V', 1, [float], ['y']], 'C':['C', 6, [float, float, float, float, float, float], ['x','y','x','y','x','y']], 'S':['S', 4, [float, float, float, float], ['x','y','x','y']], 'Q':['Q', 4, [float, float, float, float], ['x','y','x','y']], 'T':['T', 2, [float, float], ['x','y']], 'A':['A', 7, [float, float, float, int, int, float, float], ['r','r','a',0,'s','x','y']], 'Z':['L', 0, [], []] } def parsePath(d): """ Parse SVG path and return an array of segments. Removes all shorthand notation. Converts coordinates to absolute. """ retval = [] lexer = lexPath(d) pen = (0.0,0.0) subPathStart = pen lastControl = pen lastCommand = '' while 1: try: token, isCommand = lexer.next() except StopIteration: break params = [] needParam = True if isCommand: if not lastCommand and token.upper() != 'M': raise Exception, 'Invalid path, must begin with moveto.' else: command = token else: #command was omited #use last command's implicit next command needParam = False if lastCommand: if lastCommand.isupper(): command = pathdefs[lastCommand][0] else: command = pathdefs[lastCommand.upper()][0].lower() else: raise Exception, 'Invalid path, no initial command.' numParams = pathdefs[command.upper()][1] while numParams > 0: if needParam: try: token, isCommand = lexer.next() if isCommand: raise Exception, 'Invalid number of parameters' except StopIteration: raise Exception, 'Unexpected end of path' cast = pathdefs[command.upper()][2][-numParams] param = cast(token) if command.islower(): if pathdefs[command.upper()][3][-numParams]=='x': param += pen[0] elif pathdefs[command.upper()][3][-numParams]=='y': param += pen[1] params.append(param) needParam = True numParams -= 1 #segment is now absolute so outputCommand = command.upper() #Flesh out shortcut notation if outputCommand in ('H','V'): if outputCommand == 'H': params.append(pen[1]) if outputCommand == 'V': params.insert(0,pen[0]) outputCommand = 'L' if outputCommand in ('S','T'): params.insert(0,pen[1]+(pen[1]-lastControl[1])) params.insert(0,pen[0]+(pen[0]-lastControl[0])) if outputCommand == 'S': outputCommand = 'C' if outputCommand == 'T': outputCommand = 'Q' #current values become "last" values if outputCommand == 'M': subPathStart = tuple(params[0:2]) pen = subPathStart if outputCommand == 'Z': pen = subPathStart else: pen = tuple(params[-2:]) if outputCommand in ('Q','C'): lastControl = tuple(params[-4:-2]) else: lastControl = pen lastCommand = command retval.append([outputCommand,params]) return retval def formatPath(a): """Format SVG path data from an array""" return "".join([cmd + " ".join([str(p) for p in params]) for cmd, params in a]) def translatePath(p, x, y): for cmd,params in p: defs = pathdefs[cmd] for i in range(defs[1]): if defs[3][i] == 'x': params[i] += x elif defs[3][i] == 'y': params[i] += y def scalePath(p, x, y): for cmd,params in p: defs = pathdefs[cmd] for i in range(defs[1]): if defs[3][i] == 'x': params[i] *= x elif defs[3][i] == 'y': params[i] *= y elif defs[3][i] == 'r': # radius parameter params[i] *= x elif defs[3][i] == 's': # sweep-flag parameter if x*y < 0: params[i] = 1 - params[i] elif defs[3][i] == 'a': # x-axis-rotation angle if y < 0: params[i] = - params[i] def rotatePath(p, a, cx = 0, cy = 0): if a == 0: return p for cmd,params in p: defs = pathdefs[cmd] for i in range(defs[1]): if defs[3][i] == 'x': x = params[i] - cx y = params[i + 1] - cy r = math.sqrt((x**2) + (y**2)) if r != 0: theta = math.atan2(y, x) + a params[i] = (r * math.cos(theta)) + cx params[i + 1] = (r * math.sin(theta)) + cy # vim: expandtab shiftwidth=4 tabstop=8 softtabstop=4 encoding=utf-8 textwidth=99 ����������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/plot.m��������������������������������������������������0000644�0000000�0000000�00000000132�12676233417�016457� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.553097908 30 atime=1459173135.553097908 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/plot.m������������������������������������������������������������������0000644�0001750�0001750�00000002601�12676233417�017635� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } plot () ## Plots and SVG object. ## ## @end deftypefn function h = plot(obj, varargin) # Get path ids ids = fieldnames(obj.Path); npath = numel(ids); t = linspace (0, 1, 64); args={}; if !isempty (varargin) args = varargin; end holded = false; if ~ishold(gca) hold on; holded = true; end for i = 1:npath x = []; y = []; data = obj.Path.(ids{i}).data; for j = 1:numel(data) x = cat (2, x, polyval (data{j}(1,:),t)); y = cat (2, y, polyval (data{j}(2,:),t)); end h = plot(x,y,args{:}); end if holded hold off end axis tight axis equal endfunction �������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/loadpaths.m���������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017460� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.549099814 30 atime=1459173135.549099814 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/loadpaths.m�������������������������������������������������������������0000644�0001750�0001750�00000005327�12676233417�020646� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . function Paths = loadpaths (obj, svg, varargin) here = which ("@svg/loadpaths"); here = fileparts (here); script = fullfile (here, 'parsePath.py'); ## Call python script if exist (svg,'file') # read from file [st str]=system (sprintf ('python %s %s', script, svg)); else # inline SVG [st str]=system (sprintf ('python %s < %s', script, svg)); end ## Parse ouput strpath = strsplit (str(1:end-1), '$', true); npaths = numel (strpath); ## Convert path data to polynoms for ip = 1:npaths eval (strpath{ip}); ## FIXME: intialize struct with cell field svgpath2.cmd = svgpath(1).cmd; svgpath2.data = {svgpath.data}; nD = length(svgpath2.cmd); pathdata = cell (nD-1,1); point_end=[]; ## If the path is closed, last command is Z and we set initial point == final if svgpath2.cmd(end) == 'Z' nD -= 1; point_end = svgpath2.data{1}; svgpath2.data(end) = []; end ## Initial point points(1,:) = svgpath2.data{1}; for jp = 2:nD switch svgpath2.cmd(jp) case 'L' ## Straigth segment to polygon points(2,:) = svgpath2.data{jp}; pp = [(points(2,:)-points(1,:))' points(1,:)']; clear points points(1,:) = [polyval(pp(1,:),1) polyval(pp(2,:),1)]; case 'C' ## Cubic bezier to polygon points(2:4,:) = reshape (svgpath2.data{jp}, 2, 3).'; pp = cbezier2poly (points); clear points points(1,:) = [polyval(pp(1,:),1) polyval(pp(2,:),1)]; end pathdata{jp-1} = pp; end if ~isempty(point_end) ## Straight segment to close the path points(2,:) = point_end; pp = [(points(2,:)-points(1,:))' points(1,:)']; if all ( abs(pp(:,1)) < sqrt(eps) ) # Final point of last segment is already initial point pathdata(end) = []; else pathdata{end} = pp; end end ## TODO # pathdata = shapetransform(pathdata); Paths.(svgpathid).data = pathdata; end endfunction ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/parsePath.py��������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017624� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.549099814 30 atime=1459173135.549099814 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/parsePath.py������������������������������������������������������������0000644�0001750�0001750�00000004212�12676233417�021002� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������#!/usr/bin/env python ## Copyright (c) 2012 Juan Pablo Carbajal ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . import inkex, simplepath import sys #import getopt def parsePaths (filen=None): svg = inkex.Effect () svg.parse (filen) paths = svg.document.xpath ('//svg:path', namespaces=inkex.NSS) for path in paths: D = simplepath.parsePath (path.attrib['d']) cmdlst = []; parlst = []; for cmd,params in D: cmdlst.append(cmd) parlst.append(params) print 'svgpath = struct("cmd","{0}","data",{{{1}}});' \ .format(''.join(cmdlst),str(parlst).replace('[[','[').replace(']]',']')) print 'svgpathid = "{0}"; $'.format(path.attrib['id']) # ---------------------------- if __name__=="__main__": ''' try: optlist,args = getopt.getopt(sys.argv[1:],"thdp") except getopt.GetoptError: usage() sys.exit(2) doHelp = 0 c = Context() c.doPrint = 1 for opt in optlist: if opt[0] == "-d": c.debug = 1 if opt[0] == "-p": c.plot = 1 if opt[0] == "-t": c.triangulate = 1 if opt[0] == "-h": doHelp = 1 if not doHelp: pts = [] fp = sys.stdin if len(args) > 0: fp = open(args[0],'r') for line in fp: fld = line.split() x = float(fld[0]) y = float(fld[1]) pts.append(Site(x,y)) if len(args) > 0: fp.close() if doHelp or len(pts) == 0: usage() sys.exit(2) ''' svg = sys.argv[1] parsePaths(svg) ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/parseSVGData.py�����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020161� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.549099814 30 atime=1459173135.549099814 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/parseSVGData.py���������������������������������������������������������0000644�0001750�0001750�00000002324�12676233417�021341� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������#!/usr/bin/env python ## Copyright (c) 2012 Juan Pablo Carbajal ## ## This program is free software: you can redistribute it and/or modify ## it under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## any later version. ## ## This program is distributed in the hope that it will be useful, ## but WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program. If not, see . import inkex import sys #import getopt def parseSVGData (filen=None): svg = inkex.Effect () svg.parse (filen) root = svg.document.xpath ('//svg:svg', namespaces=inkex.NSS) print 'data = struct("height",{0},"width",{1},"id","{2}");' \ .format(root[0].attrib['height'],root[0].attrib['width'], root[0].attrib['id']) # ---------------------------- if __name__=="__main__": svg = sys.argv[1] parseSVGData(svg) ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/display.m�����������������������������������������������0000644�0000000�0000000�00000000130�12676233417�017144� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 29 atime=1459173135.54510172 30 ctime=1459173135.645054067 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/display.m���������������������������������������������������������������0000644�0001750�0001750�00000001543�12676233417�020330� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . function display (obj) fields = fieldnames (obj); for i = 1 : numel(fields) printf ("#s\n", fields{i}); obj.(fields{i}) end endfunction �������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/subsref.m�����������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017152� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.553097908 30 atime=1459173135.553097908 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/subsref.m���������������������������������������������������������������0000644�0001750�0001750�00000004717�12676233417�020342� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} function_name () ## @end deftypefn function varargout = subsref (obj, idx) persistent __method__ method4field typeNotImplemented if isempty(__method__) __method__ = struct(); __method__.plot = @(o,varargin) plot (o, varargin{:}); __method__.getpath = @(o,varargin) getpath (o, varargin{:}); __method__.pathid = @(o,varargin) pathid(o,varargin{:}); __method__.path2polygon = @(o,varargin) path2polygon (o, varargin{:}); __method__.normalize = @(o,varargin) normalize (o, varargin{:}); __method__.height = @(o,varargin) height(o, varargin{:}); __method__.width = @(o,varargin) width(o,varargin{:}); # Error strings method4field = "Class #s has no field #s. Use #s() for the method."; typeNotImplemented = "#s no implemented for class #s."; end if ( !strcmp (class (obj), 'svg') ) error ("Object must be of the svg class but '#s' was used", class (obj) ); elseif ( idx(1).type != '.' ) error ("Invalid index for class #s", class (obj) ); endif method = idx(1).subs; if ~isfield(__method__, method) error('Unknown method #s.',method); else fhandle = __method__.(method); end if strcmp(method,'normalize') warning("svg:Devel",["Not returning second output argument of #s" ... " use method(obj) API to get it"],method); end if numel (idx) == 1 # can't access properties, only methods error (method4field, class (obj), method, method); end if strcmp (idx(2).type, '()') args = idx(2).subs; if isempty(args) out = fhandle (obj); else out = fhandle (obj, args{:}); end varargout{1} = out; else error (typeNotImplemented,[method idx(2).type], class (obj)); end endfunction �������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/loadsvgdata.m�������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017772� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.549099814 30 atime=1459173135.549099814 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/loadsvgdata.m�����������������������������������������������������������0000644�0001750�0001750�00000002253�12676233417�021153� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . function data = loadsvgdata (obj, svg, varargin) here = which ("@svg/loadsvgdata"); here = fileparts (here); script = fullfile (here, 'parseSVGData.py'); ## Call python script if exist (svg,'file') # read from file [st str]=system (sprintf ('python %s %s', script, svg)); else # inline SVG [st str]=system (sprintf ('python %s < %s', script, svg)); end ## Parse ouput strdata = strsplit (str(1:end-1), '$', true); eval (strdata); endfunction �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/getpath.m�����������������������������������������������0000644�0000000�0000000�00000000130�12676233417�017133� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 29 atime=1459173135.54510172 30 ctime=1459173135.645054067 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/getpath.m���������������������������������������������������������������0000644�0001750�0001750�00000003762�12676233417�020324� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {@var{paths} = } getpath (@var{ids}) ## Returns paths in @var{ids}. ## ## @end deftypefn function paths = getpath(obj, varargin) if !isempty(varargin) ids = varargin; if iscell (ids) && numel(ids) == 1 && iscell(ids{1}) # dealing with ids given as cell ids = ids{1}; if !all ( cellfun (@ischar, ids) ) print_usage end elseif !all ( cellfun (@ischar, ids) ) print_usage end else paths = obj.Path; return end tf = ismember (ids, fieldnames (obj.Path)); cellfun (@(s) printf("'#s' is not a valid path id.\n", s) , {ids{!tf}}); paths = []; if any (tf) stuff = {ids{tf}}; for i = 1: numel(stuff) paths{i} = obj.Path.(ids{i}).data; endfor # Variation # paths = cellfun(@(s) obj.Path.(s).data, stuff,'UniformOutput',false); # Another variation # paths = cellfun(@(s) getfield(obj,'Path').(s).data, stuff,'UniformOutput',false); # Yet another # paths = cellfun(@(s) getfield(obj.Path,s).data, stuff,'UniformOutput',false); # Yet yet another # dummy = @(s) obj.Path.(s).data; # paths = cellfun(dummy, stuff,'UniformOutput',false); if numel(paths) == 1 paths = paths{1}; end end endfunction ��������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/path2polygon.m������������������������������������������0000644�0000000�0000000�00000000132�12676233417�020127� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.553097908 30 atime=1459173135.553097908 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/path2polygon.m����������������������������������������������������������0000644�0001750�0001750�00000003255�12676233417�021313� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} @var{P} = path2polygon (@var{id}) ## Converts the SVG path to an array of polygons. ## ## @end deftypefn function P = path2polygon (obj,varargin) narg = numel(varargin); if narg == 1 id = varargin{1}; n = 32; elseif narg == 2 id = varargin{1}; n = varargin{2}; else error("svg:path2polygon:InvalidArgument", "Wrong number of arguments."); end P = shape2polygon(getpath(obj, id)); endfunction #{ pd = obj.Path.(id).data; P = cellfun(@(x)convertpath(x,n),pd,'UniformOutput',false); P = cell2mat(P); end function p = convertpath(x,np) n = size(x,2); switch n case 2 p = zeros(2,2); # Straight segment p(:,1) = polyval (x(1,:), [0; 1]); p(:,2) = polyval (x(2,:), [0; 1]); case 4 p = zeros(np,2); # Cubic bezier t = linspace (0, 1, np).'; p(:,1) = polyval (x(1,:),t); p(:,2) = polyval (x(2,:),t); end end #} ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/PaxHeaders.5293/height.m������������������������������������������������0000644�0000000�0000000�00000000130�12676233417�016747� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 29 atime=1459173135.54510172 30 ctime=1459173135.645054067 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/io/@svg/height.m����������������������������������������������������������������0000644�0001750�0001750�00000001550�12676233417�020131� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2012 Juan Pablo Carbajal ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} function_name () ## @end deftypefn function o = height(obj,varargin) o = obj.Data.height; endfunction ��������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/PaxHeaders.5293/polygons2d������������������������������������������������������0000644�0000000�0000000�00000000132�12676233417�016040� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/���������������������������������������������������������������������0000755�0001750�0001750�00000000000�12676233417�017274� 5����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonCentroid.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021452� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonCentroid.m����������������������������������������������������0000644�0001750�0001750�00000006010�12676233417�022626� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[ @var{pt}, @var{area} ] = } polygonCentroid (@var{points}) ## @deftypefnx {Function File} {[ @dots{} ]= } polygonCentroid (@var{ptx},@var{pty}) ## Compute the centroid (center of mass) of a polygon. ## ## Computes the center of mass of a polygon defined by @var{points}. @var{points} is a ## N-by-2 matrix. The two columns can be given separately using @var{ptx} and @var{pty} ## for the x and y component respectively. ## ## The area of the polygon is returned in the second output argument. ## ## Adapted from @url{http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/} ## ## @seealso{polygons2d, polygonArea, drawPolygon} ## @end deftypefn function [pt A] = polygonCentroid(varargin) if nargin==1 var = varargin{1}; px = var(:,1); py = var(:,2); elseif nargin==2 px = varargin{1}; py = varargin{2}; end # Algorithme P. Bourke (vectorized) inext = [2:N 1]; cros = (px.*py(inext) - px(inext).*py); sx_ = sum ( (px + px(inext)) .* cros); sy_ = sum ( (py + py(inext)) .* cros); A = sum(cros) / 2; pt_ = [sx_ sy_]/A/6; # sx = 0; # sy = 0; # N = length(px); # for i=1:N-1 # sx = sx + (px(i)+px(i+1))*(px(i)*py(i+1) - px(i+1)*py(i)); # sy = sy + (py(i)+py(i+1))*(px(i)*py(i+1) - px(i+1)*py(i)); # end # sx = sx + (px(N)+px(1))*(px(N)*py(1) - px(1)*py(N)); # sy = sy + (py(N)+py(1))*(px(N)*py(1) - px(1)*py(N)); # pt = [sx sy]/6/polygonArea(px, py) endfunction ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygon2shape.m��������������������������������������0000644�0000000�0000000�00000000132�12676233417�021065� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygon2shape.m������������������������������������������������������0000644�0001750�0001750�00000005256�12676233417�022254� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{shape} = } polygon2shape (@var{polygon}) ## Converts a polygon to a shape with edges defined by smooth polynomials. ## ## @var{polygon} is a N-by-2 matrix, each row representing a vertex. ## @var{shape} is a N-by-1 cell, where each element is a pair of polynomials ## compatible with polyval. ## ## In its current state, the shape is formed by polynomials of degree 1. Therefore ## the shape representation costs more memory except for colinear points in the ## polygon. ## ## @seealso{shape2polygon, simplifypolygon, polyval} ## @end deftypefn function shape = polygon2shape (polygon) # Filter colinear points polygon = simplifypolygon (polygon); np = size(polygon,1); # polygonal shapes are memory inefficient!! # TODO filter the regions where edge angles are canging slowly and fit # polynomial of degree 3; pp = nan (2*np,2); # Transform edges into polynomials of degree 1; # pp = [(p1-p0) p0]; pp(:,1) = diff(polygon([1:end 1],:)).'(:); pp(:,2) = polygon.'(:); shape = mat2cell(pp, 2*ones (1,np), 2); endfunction %!test %! pp = [0 0; 1 0; 1 1; 0 1]; %! s = polygon2shape (pp); ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/reversePolygon.m�������������������������������������0000644�0000000�0000000�00000000132�12676233417�021316� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/reversePolygon.m�����������������������������������������������������0000644�0001750�0001750�00000003723�12676233417�022502� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{poly2} = } reversePolygon (@var{poly}) ## Reverse a polygon, by iterating vertices from the end ## ## POLY2 = reversePolygon(POLY) ## POLY2 has same vertices as POLY, but in different order. The first ## vertex of the polygon is still the same. ## ## @seealso{reversePolyline} ## @end deftypefn function rev = reversePolygon(poly) rev = poly([1 end:-1:2], :); endfunction ���������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/curvature.m������������������������������������������0000644�0000000�0000000�00000000132�12676233417�020313� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/curvature.m����������������������������������������������������������0000644�0001750�0001750�00000014215�12676233417�021475� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{kappa} = } curvature (@var{t}, @var{px}, @var{py},@var{method},@var{degree}) ## @deftypefnx {Function File} {@var{kappa} = } curvature (@var{t}, @var{poly},@var{method},@var{degree}) ## @deftypefnx {Function File} {@var{kappa} = } curvature (@var{px}, @var{py},@var{method},@var{degree}) ## @deftypefnx {Function File} {@var{kappa} = } curvature (@var{points},@var{method},@var{degree}) ## @deftypefnx {Function File} {[@var{kappa} @var{poly} @var{t}] = } curvature (@dots{}) ## Estimate curvature of a polyline defined by points. ## ## First compute an approximation of the curve given by PX and PY, with ## the parametrization @var{t}. Then compute the curvature of approximated curve ## for each point. ## @var{method} used for approximation can be only: 'polynom', with specified degree. ## Further methods will be provided in a future version. ## @var{t}, @var{px}, and @var{py} are N-by-1 array of the same length. The points ## can be specified as a single N-by-2 array. ## ## If the argument @var{t} is not given, the parametrization is estimated using ## function @code{parametrize}. ## ## If requested, @var{poly} contains the approximating polygon evlauted at the ## parametrization @var{t}. ## ## @seealso{parametrize, polygons2d} ## @end deftypefn function [kappa, varargout] = curvature(varargin) # default values degree = 5; t=0; # parametrization of curve tc=0; # indices of points wished for curvature # ================================================================= # Extract method and degree ------------------------------ nargin = length(varargin); varN = varargin{nargin}; varN2 = varargin{nargin-1}; if ischar(varN2) # method and degree are specified method = varN2; degree = varN; varargin = varargin(1:nargin-2); elseif ischar(varN) # only method is specified, use degree 6 as default method = varN; varargin = varargin{1:nargin-1}; else # method and degree are implicit : use 'polynom' and 6 method = 'polynom'; end # extract input parametrization and curve. ----------------------- nargin = length(varargin); if nargin==1 # parameters are just the points -> compute caracterization. var = varargin{1}; px = var(:,1); py = var(:,2); elseif nargin==2 var = varargin{2}; if size(var, 2)==2 # parameters are t and POINTS px = var(:,1); py = var(:,2); t = varargin{1}; else # parameters are px and py px = varargin{1}; py = var; end elseif nargin==3 var = varargin{2}; if size(var, 2)==2 # parameters are t, POINTS, and tc px = var(:,1); py = var(:,2); t = varargin{1}; else # parameters are t, px and py t = varargin{1}; px = var; py = varargin{3}; end elseif nargin==4 # parameters are t, px, py and tc t = varargin{1}; px = varargin{2}; py = varargin{3}; tc = varargin{4}; end # compute implicit parameters -------------------------- # if t and/or tc are not computed, use implicit definition if t==0 t = parametrize(px, py, 'norm'); end # if tc not defined, compute curvature for all points if tc==0 tc = t; else # else convert from indices to parametrization values tc = t(tc); end # ================================================================= # compute curvature for each point of the curve if strcmp(method, 'polynom') # compute coefficients of interpolation functions x0 = polyfit(t, px, degree); y0 = polyfit(t, py, degree); # compute coefficients of first and second derivatives. In the case of a # polynom, it is possible to compute coefficient of derivative by # multiplying with a matrix. derive = diag(degree:-1:0); xp = circshift(x0*derive, [0 1]); yp = circshift(y0*derive, [0 1]); xs = circshift(xp*derive, [0 1]); ys = circshift(yp*derive, [0 1]); # compute values of first and second derivatives for needed points xprime = polyval(xp, tc); yprime = polyval(yp, tc); xsec = polyval(xs, tc); ysec = polyval(ys, tc); # compute value of curvature kappa = (xprime.*ysec - xsec.*yprime)./ ... power(xprime.*xprime + yprime.*yprime, 3/2); if nargout > 1 varargout{1} = [polyval(x0,tc(:)) polyval(y0,tc(:))]; if nargout > 2 varargout{2} = tc; end end else error('unknown method'); end endfunction �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonSubcurve.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021501� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonSubcurve.m����������������������������������������������������0000644�0001750�0001750�00000006354�12676233417�022670� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2003-2011 David Legland ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## ## The views and conclusions contained in the software and documentation are ## those of the authors and should not be interpreted as representing official ## policies, either expressed or implied, of the copyright holders. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{poly2} =} polygonSubcurve (@var{polygon}, @var{pos0},@var{pos1}) ## Extract a portion of a polygon ## ## Create a new polyline, by keeping vertices located between positions ## @var{pos0} and @var{pos1}, and adding points corresponding to positions @var{pos0} and ## @var{pos1} if they are not already vertices. ## ## Example: ## @example ## Nv = 100; ## poly = circleAsPolygon ([10 20 30], Nv); ## poly2 = polygonSubcurve (poly, 15, 65); ## drawPolyline (poly2); ## @end example ## ## @seealso{polygons2d, polylineSubcurve} ## @end deftypefn function res = polygonSubcurve(poly, t0, t1) # number of vertices Nv = size(poly, 1); if t0 ## Adapted: JuanPi Carbajal ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{P}, @var{D}] =} projPointOnPolyline (@var{point}, @var{poly}) ## @deftypefnx {Function File} {[@dots{}] =} projPointOnPolyline (@dots{}, @var{closed}) ## ## Compute the position of the orthogonal projection of a point on a ## polyline. ## ## @var{point} is a 1x2 row vector containing point coordinates ## @var{poly} is a Nx2 array containing coordinates of polyline vertices ## @var{pos} is the position of the point on the polyline, between 0 and the ## number of vertices of the polyline. @var{pos} can be a non-integer value, in ## this case, the integer part correspond to the polyline edge index ## (between 0 and N-1), and the floating-point part correspond to the ## relative position on i-th edge (between 0 and 1, 0: edge start, 1: edge ## end). ## ## When @var{point} is an array of points, returns a column vector with as many ## rows as the number of points. ## ## If third input argument @var{closed} is given, it specifies if the polyline ## is closed or not. @var{closed} can be one of: ## @table @asis ## @item 'closed' ## The polyline is closed ## ## @item 'open' ## The polyline is open ## ## @item a logical column vector ## It should have the same number of elements as the number of points and it ## specifies individually if each polyline is closed (true=closed). ## ## @end table ## ## @seealso{points2d, polygons2d, polylinePoint, distancePointPolyline} ## @end deftypefn function [pos minDist] = projPointOnPolyline (point, poly, closed=false) warning ('Octave:deprecated-keyword', ... "This function is deprecated use distancePointPolyline instead.\n"); [minDist pos] = distancePointPolyline (point, poly, closed); # # check if input polyline is closed or not # if strcmp ('closed', closed) # closed = true; # elseif strcmp ('open', closed) # closed = false; # endif # # closes the polyline if necessary # if closed # poly = [poly; poly(1,:)]; # endif # # number of points # Np = size (point, 1); # # number of vertices in polyline # Nv = size (poly, 1); # # allocate memory results # pos = zeros (Np, 1); # minDist = inf (Np, 1); # # iterate on points # for p=1:Np # # compute smallest distance to each edge # for i=1:Nv-1 # # build current edge # edge = [poly(i,:) poly(i+1,:)]; # # compute distance between current point and edge # [dist edgePos] = distancePointEdge (point(p, :), edge); # # update distance and position if necessary # if dist < minDist(p) # minDist(p) = dist; # pos(p) = i - 1 + edgePos; # endif # endfor # endfor endfunction %!demo %! warning ("off", "Octave:deprecated-keyword", "local"); %! point = [2 1] .* rand (10,2) - [1 0]; %! t = linspace (0,pi,25).'; %! poly = [cos(t) sin(t)]; %! [pos d] = arrayfun (@(i)projPointOnPolyline (point(i,:),poly), (1:10).'); %! %! # Calculate the projection on the polyline to plot %! p_ = zeros (10, 2); %! %! # projection on vertices of the polyline %! isvertex = abs (pos - fix (pos)) < eps; %! p_(isvertex,:) = poly (pos(isvertex)+1,:); %! %! # the rest %! pos = pos (!isvertex); %! i = fix (pos) + 1; %! x = pos - fix (pos); %! p_(!isvertex,:) = poly(i,:) + x.*(poly(i+1,:)-poly(i,:)); %! %! # Plot %! plot (poly(:,1), poly(:,2),'.-', ... %! point(:,1), point(:,2), 'o', ... %! p_(:,1), p_(:,2),'.'); %! legend ('Polyline', 'Points', 'Projections'); %! line ([point(:,1) p_(:,1)].',[point(:,2) p_(:,2)].'); %! arrayfun (@(i)text ((p_(i,1)+point(i,1))/2, (p_(i,2)+point(i,2))/2, ... %! sprintf("%.2f", d(i))), 1:10); %! axis tight %! axis equal �����������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/supportFunction.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021515� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/supportFunction.m����������������������������������������������������0000644�0001750�0001750�00000005145�12676233417�022701� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } suppportFunction (@var{polygon}) ## @deftypefnx {Function File} {@var{h} = } suppportFunction (@var{polygon}, @var{n}) ## @deftypefnx {Function File} {@var{h} = } suppportFunction (@var{polygon}, @var{v}) ## Compute support function of a polygon ## ## H = supportFunction(POLYGON, N) ## uses N points for suport function approximation ## ## H = supportFunction(POLYGON) ## assume 24 points for approximation ## ## H = supportFunction(POLYGON, V) ## where V is a vector, uses vector V of angles to compute support ## function. ## ## @seealso{convexification} ## @end deftypefn function h = supportFunction(polygon, varargin) N = 24; u = (0:2*pi/N:2*pi*(1-1/N)).'; if length(varargin)==1 var = varargin{1}; if length(var)==1 N = var; u = (0:2*pi/N:2*pi*(1-1/N)).'; else u = var(:); end end h = zeros(size(u)); for i=1:length(u) v = repmat([cos(u(i)) sin(u(i))], [size(polygon, 1), 1]); h(i) = max(dot(polygon, v, 2)); end endfunction ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonSelfIntersections.m���������������������������0000644�0000000�0000000�00000000132�12676233417�023346� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonSelfIntersections.m�������������������������������������������0000644�0001750�0001750�00000006251�12676233417�024531� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts} = } polygonSelfIntersections (@var{poly}) ## @deftypefnx {Function File} {[@var{pts} @var{pos1} @var{pos2}] = } polygonSelfIntersections (@var{poly}) ## Find-self intersection points of a polygon ## ## Return the position of self intersection points ## ## Also return the 2 positions of each intersection point (the position ## when meeting point for first time, then position when meeting point ## for the second time). ## ## Example ## @example ## # use a '8'-shaped polygon ## poly = [10 0;0 0;0 10;20 10;20 20;10 20]; ## polygonSelfIntersections(poly) ## ans = ## 10 10 ## @end example ## ## @seealso{polygons2d, polylineSelfIntersections} ## @end deftypefn function varargout = polygonSelfIntersections(poly, varargin) tol = 1e-14; # ensure the last point equals the first one if sum(abs(poly(end, :)-poly(1,:)) < tol) ~= 2 poly = [poly; poly(1,:)]; end # compute intersections by calling algo for polylines [points pos1 pos2] = polylineSelfIntersections(poly); # It may append that first vertex of polygon is detected as intersection, # the following tries to detect this n = size(poly, 1) - 1; inds = (pos1 == 0 & pos2 == n) | (pos1 == n & pos2 == 0); points(inds, :) = []; pos1(inds) = []; pos2(inds) = []; # remove multiple intersections [points I J] = unique(points, 'rows', 'first'); ##ok pos1 = pos1(I); pos2 = pos2(I); ## Post-processing # process output arguments if nargout <= 1 varargout = {points}; elseif nargout == 3 varargout = {points, pos1, pos2}; end endfunction �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/fillPolygon.m����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020571� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/fillPolygon.m��������������������������������������������������������0000644�0001750�0001750�00000007270�12676233417�021756� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2003-2011 David Legland ## Copyright (C) 2016 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## ## The views and conclusions contained in the software and documentation are ## those of the authors and should not be interpreted as representing official ## policies, either expressed or implied, of the copyright holders. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} fillPolygon (@var{p}) ## @deftypefnx {Function File} {@var{h} =} fillPolygon (@var{px},@var{py}) ## Fill a polygon specified by a list of points ## ## @var{p} is a single [N*2] array. ## With one input argument, it fills the interior of the polygon specified ## by @var{p}. The boundary of the polygon is not drawn, use 'drawPolygon' ## to do it. ## ## If @var{p} contains NaN-couples, each portion between the [NaN;NaN] will ## be filled separately. ## ## Two input arguments specify coordinates of the polygon in separate arrays. ## ## Also returns a handle to the created patch. ## ## @seealso{polygons2d, drawCurve, drawPolygon} ## @end deftypefn function h = fillPolygon (varargin) # check input if isempty (varargin) error ('need to specify a polygon'); end # case of a set of polygons stored in a cell array var = varargin{1}; if iscell (var) N = length (var); h = zeros (N, 1); for i = 1:N # check for empty polygons if ~isempty (var{i}) h(i) = fillPolygon (var{i}, varargin{2:end}); end end return; end # Extract coordinates of polygon vertices if size (var, 2) > 1 # first argument is a polygon array px = var(:, 1); py = var(:, 2); varargin(1) = []; else # arguments 1 and 2 correspond to x and y coordinate respectively if length (varargin) < 2 error ('should specify either a N*2 array, or 2 N*1 vectors'); end px = varargin{1}; py = varargin{2}; varargin(1:2) = []; end # Find position of breaks, and copies first point of each loop at the # end inds = find (isnan (px(:))); i1 = [inds ; length(px)+1]; i0 = [1 ; inds+1]; px(i1, :) = px(i0, :); py(i1, :) = py(i0, :); # set default line format if isempty (varargin) varargin = {'b'}; end # fill the polygon with desired style h = fill (px, py, varargin{:}, 'lineStyle', 'none'); endfunction ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonArea.m����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020553� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonArea.m��������������������������������������������������������0000644�0001750�0001750�00000006467�12676233417�021747� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{area} = } polygonArea (@var{points}) ## @deftypefnx {Function File} {@var{area} = } polygonArea (@var{px},@var{py}) ## Compute the signed area of a polygon. ## ## Compute area of a polygon defined by @var{points}. @var{points} is a N-by-2 ## matrix containing coordinates of vertices. ## ## Vertices of the polygon are supposed to be oriented Counter-Clockwise ## (CCW). In this case, the signed area is positive. ## If vertices are oriented Clockwise (CW), the signed area is negative. ## ## If polygon is self-crossing, the result is undefined. ## ## If @var{points} is a cell, each element is considered a polygon and the area ## of each one is returned in the matrix @var{area}. The matrix has the same shape ## as the cell. ## ## References: ## Algorithm adapted from P. Bourke web page ## http://local.wasp.uwa.edu.au/~pbourke/geometry/polyarea/ ## ## @seealso{polygons2d, polygonCentroid, drawPolygon} ## @end deftypefn function area = polygonArea(varargin) var = varargin{1}; # in case of polygon sets, computes several areas if iscell (var) area = cellfun (@func, var); # area = zeros(length(var), 1); # for i = 1:length(var) # area(i) = polygonArea(var{i}, varargin{2:end}); # end # return; # end else # extract coordinates if nargin == 1 area = func(var) elseif nargin == 2 px = varargin{1}; py = varargin{2}; # indices of next vertices N = length(px); iNext = [2:N 1]; # compute area (vectorized version) area = sum(px .* py(iNext) - px(iNext) .* py) / 2; end end endfunction function a = func (c) N = length (c); iNext = [2:N 1]; a = sum (c(:,1) .* c(iNext,2) - c(iNext,1) .* c(:,2)) / 2; endfunction ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/simplifypolygon.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021537� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/simplifypolygon.m����������������������������������������������������0000644�0001750�0001750�00000005455�12676233417�022727� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{spoly} = } simplifypolygon (@var{poly}) ## Simplify a polygon using the Ramer-Douglas-Peucker algorithm. ## ## @var{poly} is a N-by-2 matrix, each row representing a vertex. ## ## @seealso{simplifypolyline, shape2polygon} ## @end deftypefn function polygonsimp = simplifypolygon (polygon, varargin) polygonsimp = simplifypolyline (polygon,varargin{:}); # Remove parrallel consecutive edges PL = polygonsimp(1:end-1,:); PC = polygonsimp(2:end,:); PR = polygonsimp([3:end 1],:); a = PL - PC; b = PR - PC; tf = find (isParallel(a,b))+1; polygonsimp (tf,:) = []; endfunction %!test %! P = [0 0; 1 0; 0 1]; %! P2 = [0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1; 0 0.7; 0 0.6; 0 0.3; 0 0.1]; %! assert(simplifypolygon (P2),P,min(P2(:))*eps) %!demo %! %! P = [0 0; 1 0; 0 1]; %! P2 = [0 0; 0.1 0; 0.2 0; 0.25 0; 1 0; 0 1; 0 0.7; 0 0.6; 0 0.3; 0 0.1]; %! Pr = simplifypolygon (P2); %! %! cla %! drawPolygon(P,'or;Reference;'); %! hold on %! drawPolygon(P2,'x-b;Redundant;'); %! drawPolygon(Pr,'*g;Simplified;'); %! hold off %! %! # -------------------------------------------------------------------------- %! # The two polygons describe the same figure, a triangle. Extra points are %! # removed form the redundant one. �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/drawPolyline.m���������������������������������������0000644�0000000�0000000�00000000132�12676233417�020744� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/drawPolyline.m�������������������������������������������������������0000644�0001750�0001750�00000011154�12676233417�022125� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2003-2011 David Legland ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## ## The views and conclusions contained in the software and documentation are ## those of the authors and should not be interpreted as representing official ## policies, either expressed or implied, of the copyright holders. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{} =} drawPolyline (@var{}, @var{}) ##DRAWPOLYLINE Draw a polyline specified by a list of points ## ## drawPolyline(COORD); ## packs coordinates in a single [N*2] array. ## ## drawPolyline(PX, PY); ## specifies coordinates in separate arrays. PX and PY must be column ## vectors with the same length. ## ## drawPolyline(..., TYPE); ## where TYPE is either 'closed' or 'open', specifies if last point must ## be connected to the first one ('closed') or not ('open'). ## Default is 'open'. ## ## drawPolyline(..., PARAM, VALUE); ## specify plot options as described for plot command. ## ## H = drawPolyline(...) also return a handle to the list of line objects. ## ## Example: ## @example ## # Draw a curve representing an ellipse ## t = linspace(0, 2*pi, 100)'; ## px = 10*cos(t); py = 5*sin(t); ## drawPolyline([px py], 'closed'); ## axis equal; ## ## # The same, with different drawing options ## drawPolyline([px py], 'closed', 'lineWidth', 2, 'lineStyle', '--'); ## @end example ## ## @seealso{polygons2d, drawPolygon} ## @end deftypefn function varargout = drawPolyline(varargin) # default values closed = false; # If first argument is a cell array, draw each curve individually, # and eventually returns handle of each plot. var = varargin{1}; if iscell(var) h = []; for i=1:length(var(:)) h = [h ; drawPolyline(var{i}, varargin{2:end})]; end if nargout>0 varargout{1}=h; end return; end # extract curve coordinate if size(var, 2)==1 # first argument contains x coord, second argument contains y coord px = var; if length(varargin)==1 error('Wrong number of arguments in drawPolyline'); end py = varargin{2}; varargin = varargin(3:end); else # first argument contains both coordinate px = var(:, 1); py = var(:, 2); varargin = varargin(2:end); end # check if curve is closed or open if ~isempty(varargin) var = varargin{1}; if strncmpi(var, 'close', 5) closed = true; varargin = varargin(2:end); elseif strncmpi(var, 'open', 4) closed = false; varargin = varargin(2:end); end end # if curve is closed, add first point at the end of the list if closed px = [px; px(1)]; py = [py; py(1)]; end # plot the curve, with eventually optional parameters h = plot(px, py, varargin{:}); # format output arguments if nargout>0 varargout{1}=h; end endfunction %!demo %! t = linspace (0, 2*pi, 100)'; %! px = 10*cos (t); py = 5*sin (t); %! %! subplot (1,2,1) %! drawPolyline ([px py], 'closed'); %! axis equal; %! %! subplot (1,2,2) %! drawPolyline([px py], 'closed', 'lineWidth', 2, 'lineStyle', '--'); %! axis equal; %! # ------------------------------------------------- %! # Draw a curve representing an ellipse with two drawing options ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonLoops.m���������������������������������������0000644�0000000�0000000�00000000132�12676233417�020777� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonLoops.m�������������������������������������������������������0000644�0001750�0001750�00000010427�12676233417�022162� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{loops} = } polygonLoops (@var{poly}) ## Divide a possibly self-intersecting polygon into a set of simple loops ## ## @var{poly} is a polygone defined by a series of vertices, ## @var{loops} is a cell array of polygons, containing the same vertices of the ## original polygon, but no loop self-intersect, and no couple of loops ## intersect each other. ## ## Example: ## @example ## poly = [0 0;0 10;20 10;20 20;10 20;10 0]; ## loops = polygonLoops(poly); ## figure(1); hold on; ## drawPolygon(loops); ## polygonArea(loops) ## @end example ## ## @seealso{polygons2d, polygonSelfIntersections} ## @end deftypefn function loops = polygonLoops(poly) ## Initialisations # compute intersections [inters pos1 pos2] = polygonSelfIntersections(poly); # case of a polygon without self-intersection if isempty(inters) loops = {poly}; return; end # array for storing loops loops = cell(0, 1); positions = sortrows([pos1 pos2;pos2 pos1]); ## First loop pos0 = 0; loop = polygonSubcurve(poly, pos0, positions(1, 1)); pos = positions(1, 2); positions(1, :) = []; while true # index of next intersection point ind = find(positions(:,1)>pos, 1, 'first'); # if not found, break if isempty(ind) break; end # add portion of curve loop = [loop; polygonSubcurve(poly, pos, positions(ind, 1))]; ##ok # look for next intersection point pos = positions(ind, 2); positions(ind, :) = []; end # add the last portion of curve loop = [loop;polygonSubcurve(poly, pos, pos0)]; # remove redundant vertices loop(sum(loop(1:end-1,:) == loop(2:end,:) ,2)==2, :) = []; if sum(diff(loop([1 end], :))==0)==2 loop(end, :) = []; end # add current loop to the list of loops loops{1} = loop; ## Other loops Nl = 1; while ~isempty(positions) loop = []; pos0 = positions(1, 2); pos = positions(1, 2); while true # index of next intersection point ind = find(positions(:,1)>pos, 1, 'first'); # add portion of curve loop = [loop;polygonSubcurve(poly, pos, positions(ind, 1))]; ##ok # look for next intersection point pos = positions(ind, 2); positions(ind, :) = []; # if not found, break if pos==pos0 break; end end # remove redundant vertices loop(sum(loop(1:end-1,:) == loop(2:end,:) ,2)==2, :) = []; ##ok if sum(diff(loop([1 end], :))==0)==2 loop(end, :) = []; ##ok end # add current loop to the list of loops Nl = Nl + 1; loops{Nl} = loop; end endfunction �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/parametrize.m����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020616� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/parametrize.m��������������������������������������������������������0000644�0001750�0001750�00000007253�12676233417�022004� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{par} = } parametrize (@var{poly}) ## @deftypefnx {Function File} {@var{par} = } parametrize (@var{px},@var{py}) ## @deftypefnx {Function File} {@var{par} = } parametrize (@dots{},@var{normalize}) ## ## Parametrization of a curve, based on edges length ## ## Returns a parametrization of the curve defined by the serie of points, ## based on euclidean distance between two consecutive points. ## POLY is a N-by-2 array, representing coordinates of vertices. The ## result PAR is N-by-1, and contains the cumulative length of edges until ## corresponding vertex. The function also accepts the polygon as two inputs ## @var{px} and @var{py} representinx coordinates x and y respectively. ## When optional argument @var{normalize} is non-empty @var{par} is rescaled ## such that the last element equals 1, i.e. @code{@var{par}(end)==1}. ## ## Example ## @example ## # Parametrize a circle approximation ## poly = circleToPolygon([0 0 1], 200); ## p = parametrize(poly); ## p(end) ## ans = ## 6.2829 ## p = parametrize(poly,'norm'); ## p(end) ## ans = ## 1 ## p = parametrize(poly,true); ## p(end) ## ans = ## 1 ## @end example ## ## @seealso{polygons2d, polylineLength} ## @end deftypefn function par = parametrize(varargin) ## Process inputs # extract vertex coordinates if size(varargin{1}, 2) > 1 # vertices in a single array pts = varargin{1}; normalize = numel(varargin) > 1; elseif size(varargin{1}, 2) == 1 && numel(varargin) >= 2 # points as separate arrays pts = [varargin{1} varargin{2}]; normalize = numel(varargin) > 2; end ## Parametrize polyline # compute cumulative sum of euclidean distances between consecutive # vertices, setting distance of first vertex to 0. if size(pts, 2) == 2 # process points in 2D par = [0 ; cumsum(hypot(diff(pts(:,1)), diff(pts(:,2))))]; else # process points in arbitrary dimension par = [0 ; cumsum(sqrt(sum(diff(pts).^2, 2)))]; end # eventually rescale between 0 and 1 if normalize par = par / par(end); end endfunction �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/drawPolygon.m����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020600� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/drawPolygon.m��������������������������������������������������������0000644�0001750�0001750�00000007767�12676233417�022000� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2016 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} = } drawPolygon (@var{coord}) ## @deftypefnx {Function File} {@var{h} = } drawPolygon (@var{px}, @var{py}) ## @deftypefnx {Function File} {@var{h} = } drawPolygon (@var{polys}) ## Draw a polygon specified by a list of points. ## ## drawPolygon(COORD); ## Packs coordinates in a single [N*2] array. ## ## drawPolygon(PX, PY); ## Specifies coordinates in separate arrays. ## ## drawPolygon(POLYS) ## Packs coordinate of several polygons in a cell array. Each element of ## the array is a Ni*2 double array. ## ## H = drawPolygon(...); ## Also return a handle to the list of line objects. ## ## ## @seealso{polygons2d, drawCurve} ## @end deftypefn function varargout = drawPolygon (varargin) # check input if isempty(varargin) error('need to specify a polygon'); end var = varargin{1}; state = ishold(gca); hold on; ## Manage cell arrays of polygons # case of a set of polygons stored in a cell array if iscell(var) N = length(var); h = zeros(N, 1); for i = 1:N # check for empty polygons if ~isempty(var{i}) h(i) = drawPolygon(var{i}, varargin{2:end}); end end if nargout > 0 varargout = {h}; end if ~state hold off end return; end ## Parse coordinates and options # Extract coordinates of polygon vertices if size(var, 2) > 1 # first argument is a polygon array px = var(:, 1); py = var(:, 2); varargin(1) = []; else # arguments 1 and 2 correspond to x and y coordinate respectively if length(varargin) < 2 error('Should specify either a N-by-2 array, or 2 N-by-1 vectors'); end px = varargin{1}; py = varargin{2}; varargin(1:2) = []; end # set default line format if isempty(varargin) varargin = {'b-'}; end # check case of polygons with holes if sum(isnan(px(:))) > 0 polygons = splitPolygons([px py]); h = drawPolygon(polygons); if nargout > 0 varargout = {h}; end if ~state hold off end return; end ## Draw the polygon # ensure last point is the same as the first one px(size(px, 1)+1, :) = px(1,:); py(size(py, 1)+1, :) = py(1,:); # draw the polygon outline h = plot(px, py, varargin{:}); if ~state hold off end # format output arg if nargout > 0 varargout = {h}; end endfunction ���������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/splitPolygons.m��������������������������������������0000644�0000000�0000000�00000000132�12676233417�021161� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/splitPolygons.m������������������������������������������������������0000644�0001750�0001750�00000005051�12676233417�022341� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{polygons} = } splitPolygons (@var{polygon}) ## Convert a NaN separated polygon list to a cell array of polygons. ## ## @var{polygon} is a N-by-2 array of points, with possibly couples of NaN values. ## The functions separates each component separated by NaN values, and ## returns a cell array of polygons. ## ## @seealso{polygons2d} ## @end deftypefn function polygons = splitPolygons(polygon) if iscell(polygon) # case of a cell array polygons = polygon; elseif sum(isnan(polygon(:)))==0 # single polygon -> no break polygons = {polygon}; else # find indices of NaN couples inds = find(sum(isnan(polygon), 2)>0); # number of polygons N = length(inds)+1; polygons = cell(N, 1); # iterate over NaN-separated regions to create new polygon inds = [0;inds;size(polygon, 1)+1]; for i=1:N polygons{i} = polygon((inds(i)+1):(inds(i+1)-1), :); end end endfunction ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygonPoint.m���������������������������������������0000644�0000000�0000000�00000000132�12676233417�020774� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.585082659 30 atime=1459173135.585082659 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygonPoint.m�������������������������������������������������������0000644�0001750�0001750�00000005601�12676233417�022155� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2003-2011 David Legland ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## ## The views and conclusions contained in the software and documentation are ## those of the authors and should not be interpreted as representing official ## policies, either expressed or implied, of the copyright holders. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{point} =} polygonPoint (@var{poly}, @var{pos}) ## Extract a point from a polygon ## @seealso{polygons2d, polylinePoint} ## @end deftypefn function point = polygonPoint(poly, pos) # eventually copy first point at the end to ensure closed polygon if sum(poly(end, :)==poly(1,:))~=2 poly = [poly; poly(1,:)]; end # number of points to compute Np = length(pos(:)); # number of vertices in polygon Nv = size(poly, 1)-1; # allocate memory results point = zeros(Np, 2); # iterate on points for i=1:Np # compute index of edge (between 0 and Nv) ind = floor(pos(i)); # special case of last point of polyline if ind==Nv point(i,:) = poly(end,:); continue; end # format index to ensure being on polygon ind = min(max(ind, 0), Nv-1); # position on current edge t = min(max(pos(i)-ind, 0), 1); # parameters of current edge x0 = poly(ind+1, 1); y0 = poly(ind+1, 2); dx = poly(ind+2,1)-x0; dy = poly(ind+2,2)-y0; # compute position of current point point(i, :) = [x0+t*dx, y0+t*dy]; end endfunction �������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/medialAxisConvex.m�����������������������������������0000644�0000000�0000000�00000000132�12676233417�021536� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/medialAxisConvex.m���������������������������������������������������0000644�0001750�0001750�00000013235�12676233417�022721� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{n} @var{e}] = } medialAxisConvex (@var{polygon}) ## Compute medial axis of a convex polygon ## ## @var{polygon} is given as a set of points [x1 y1;x2 y2 ...], returns ## the medial axis of the polygon as a graph. ## @var{n} is a set of nodes. The first elements of @var{n} are the vertices of the ## original polygon. ## @var{e} is a set of edges, containing indices of source and target nodes. ## Edges are sorted according to order of creation. Index of first vertex ## is lower than index of last vertex, i.e. edges always point to newly ## created nodes. ## ## Notes: ## - Is not fully implemented, need more development (usually crashes for ## polygons with more than 6-7 points...) ## - Works only for convex polygons. ## - Complexity is not optimal: this algorithm is O(n*log n), but linear ## algorithms exist. ## ## @seealso{polygons2d, bisector} ## @end deftypefn function [nodes, edges] = medialAxisConvex(points) # eventually remove the last point if it is the same as the first one if points(1,:) == points(end, :) nodes = points(1:end-1, :); else nodes = points; end # special case of triangles: # compute directly the gravity center, and simplify computation. if size(nodes, 1)==3 nodes = [nodes; mean(nodes, 1)]; edges = [1 4;2 4;3 4]; return end # number of nodes, and also of initial rays N = size(nodes, 1); # create ray of each vertex rays = zeros(N, 4); rays(1, 1:4) = bisector(nodes([2 1 N], :)); rays(N, 1:4) = bisector(nodes([1 N N-1], :)); for i=2:N-1 rays(i, 1:4) = bisector(nodes([i+1, i, i-1], :)); end # add indices of edges producing rays (indices of first vertex, second # vertex is obtained by adding one modulo N). rayEdges = [[N (1:N-1)]' (1:N)']; pint = intersectLines(rays, rays([2:N 1], :)); #ti = linePosition(pint, rays); #ti = min(linePosition(pint, rays), linePosition(pint, rays([2:N 1], :))); ti = distancePointLine(pint, ... createLine(points([N (1:N-1)]', :), points((1:N)', :))); # create list of events. # terms are : R1 R2 X Y t0 # R1 and R2 are indices of involved rays # X and Y is coordinate of intersection point # t0 is position of point on rays events = sortrows([ (1:N)' [2:N 1]' pint ti], 5); # initialize edges edges = zeros(0, 2); # ------------------- # process each event until there is no more # start after index of last vertex, and process N-3 intermediate rays for i=N+1:2*N-3 # add new node at the rays intersection nodes(i,:) = events(1, 3:4); # add new couple of edges edges = [edges; events(1,1) i; events(1,2) i]; # find the two edges creating the new emanating ray n1 = rayEdges(events(1, 1), 1); n2 = rayEdges(events(1, 2), 2); # create the new ray line1 = createLine(nodes(n1, :), nodes(mod(n1,N)+1, :)); line2 = createLine(nodes(mod(n2,N)+1, :), nodes(n2, :)); ray0 = bisector(line1, line2); # set its origin to emanating point ray0(1:2) = nodes(i, :); # add the new ray to the list rays = [rays; ray0]; rayEdges(size(rayEdges, 1)+1, 1:2) = [n1 n2]; # find the two neighbour rays ind = sum(ismember(events(:,1:2), events(1, 1:2)), 2)==0; ir = unique(events(ind, 1:2)); ir = ir(~ismember(ir, events(1,1:2))); # create new intersections pint = intersectLines(ray0, rays(ir, :)); #ti = min(linePosition(pint, ray0), linePosition(pint, rays(ir, :))) + events(1,5); ti = distancePointLine(pint, line1); # remove all events involving old intersected rays ind = sum(ismember(events(:,1:2), events(1, 1:2)), 2)==0; events = events(ind, :); # add the newly formed events events = [events; ir(1) i pint(1,:) ti(1); ir(2) i pint(2,:) ti(2)]; # and sort them according to 'position' parameter events = sortrows(events, 5); end # centroid computation for last 3 rays nodes = [nodes; mean(events(:, 3:4))]; edges = [edges; [unique(events(:,1:2)) ones(3, 1)*(2*N-2)]]; endfunction �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polylineSelfIntersections.m��������������������������0000644�0000000�0000000�00000000132�12676233417�023512� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.589080753 30 atime=1459173135.589080753 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polylineSelfIntersections.m������������������������������������������0000644�0001750�0001750�00000011347�12676233417�024677� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{pts} = } polylineSelfIntersections (@var{poly}) ## Find self-intersections points of a polyline ## ## Return the position of self intersection points ## ## Also return the 2 positions of each intersection point (the position ## when meeting point for first time, then position when meeting point ## for the second time). ## ## Example ## @example ## # use a gamma-shaped polyline ## poly = [0 0;0 10;20 10;20 20;10 20;10 0]; ## polylineSelfIntersections(poly) ## ans = ## 10 10 ## ## # use a 'S'-shaped polyline ## poly = [10 0;0 0;0 10;20 10;20 20;10 20]; ## polylineSelfIntersections(poly) ## ans = ## 10 10 ## @end example ## ## @seealso{polygons2d, intersectPolylines, polygonSelfIntersections} ## @end deftypefn function varargout = polylineSelfIntersections(poly, varargin) ## Initialisations # determine whether the polyline is closed closed = false; if ~isempty(varargin) closed = varargin{1}; if ischar(closed) if strcmp(closed, 'closed') closed = true; elseif strcmp(closed, 'open') closed = false; end end end # if polyline is closed, ensure the last point equals the first one if closed if sum(abs(poly(end, :)-poly(1,:))<1e-14)~=2 poly = [poly; poly(1,:)]; end end # arrays for storing results points = zeros(0, 2); pos1 = zeros(0, 1); pos2 = zeros(0, 1); # number of vertices Nv = size(poly, 1); ## Main processing # index of current intersection ip = 0; # iterate over each couple of edge ( (N-1)*(N-2)/2 iterations) for i=1:Nv-2 # create first edge edge1 = [poly(i, :) poly(i+1, :)]; for j=i+2:Nv-1 # create second edge edge2 = [poly(j, :) poly(j+1, :)]; # check conditions on bounding boxes if min(edge1([1 3]))>max(edge2([1 3])) continue; end if max(edge1([1 3]))max(edge2([2 4])) continue; end if max(edge1([2 4])) points(ind,:) = []; pos1(ind) = []; pos2(ind) = []; end ## Post-processing # process output arguments if nargout<=1 varargout{1} = points; elseif nargout==3 varargout{1} = points; varargout{2} = pos1; varargout{3} = pos2; end endfunction �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/simplifypolyline.m�����������������������������������0000644�0000000�0000000�00000000132�12676233417�021703� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/simplifypolyline.m���������������������������������������������������0000644�0001750�0001750�00000013253�12676233417�023066� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{pline2} @var{idx}] = } simplifypolyline (@var{pline}) ## @deftypefnx {Function File} {@dots{} = } simplifypolyline (@dots{},@var{property},@var{value},@dots{}) ## Simplify or subsample a polyline using the Ramer-Douglas-Peucker algorithm, ## a.k.a. the iterative end-point fit algorithm or the split-and-merge algorithm. ## ## The @var{pline} as a N-by-2 matrix. Rows correspond to the ## verices (compatible with @code{polygons2d}). The vector @var{idx} constains ## the indexes on vetices in @var{pline} that generates @var{pline2}, i.e. ## @code{pline2 = pline(idx,:)}. ## ## @strong{Parameters} ## @table @samp ## @item 'Nmax' ## Maximum number of vertices. Default value @code{1e3}. ## @item 'Tol' ## Tolerance for the error criteria. Default value @code{1e-4}. ## @item 'MaxIter' ## Maximum number of iterations. Default value @code{10}. ## @item 'Method' ## Not implemented. ## @end table ## ## Run @code{demo simplifypolyline} to see an example. ## ## @seealso{curve2polyline, curveval} ## @end deftypefn function [pline idx] = simplifypolyline (pline_o, varargin) ## TODO do not print warnings if user provided Nmax or MaxIter. # --- Parse arguments --- # parser = inputParser (); parser.FunctionName = "simplifypolyline"; parser.addParamValue ('Nmax', 1e3, @(x)x>0); toldef = 1e-4;#max(sumsq(diff(pline_o),2))*2; parser.addParamValue ('Tol', toldef, @(x)x>0); parser.addParamValue ('MaxIter', 100, @(x)x>0); parser.parse(varargin{:}); Nmax = parser.Results.Nmax; tol = parser.Results.Tol; MaxIter = parser.Results.MaxIter; clear parser toldef msg = ["simplifypolyline: Maximum number of points reached with maximum error %g." ... " Increase %s if the result is not satisfactory."]; # ------ # [N dim] = size(pline_o); idx = [1 N]; for iter = 1:MaxIter # Find the point with the maximum distance. [dist ii] = maxdistance (pline_o, idx); tf = dist > tol; n = sum(tf); if all(!tf); break; end idx(end+1:end+n) = ii(tf); idx = sort(idx); if length(idx) >= Nmax ## TODO remove extra points warning('geometry:MayBeWrongOutput', sprintf(msg,max(dist),'Nmax')); break; end end if iter == MaxIter warning('geometry:MayBeWrongOutput', sprintf(msg,max(dist),'MaxIter')); end pline = pline_o(idx,:); endfunction function [dist ii] = maxdistance (p, idx) ## Separate the groups of points according to the edge they can divide. func = @(x,y) x:y; idxc = arrayfun (func, idx(1:end-1), idx(2:end), "UniformOutput",false); points = cellfun (@(x)p(x,:), idxc, "UniformOutput",false); ## Build the edges edges = [p(idx(1:end-1),:) p(idx(2:end),:)]; edges = mat2cell (edges, ones(1,size(edges,1)), 4)'; ## Calculate distance between the points and the corresponding edge [dist ii] = cellfun(@dd, points,edges,idxc); endfunction function [dist ii] = dd (p,e,idx) [d pos] = distancePointEdge(p,e); [dist ii] = max(d); ii = idx(ii); endfunction %!demo %! t = linspace(0,1,100).'; %! y = polyval([1 -1.5 0.5 0],t); %! pline = [t y]; %! %! figure(1) %! clf %! plot (t,y,'-r;Original;','linewidth',2); %! hold on %! %! tol = [8 2 1 0.5]*1e-2; %! colors = jet(4); %! %! for i=1:4 %! pline_ = simplifypolyline(pline,'tol',tol(i)); %! msg = sprintf('-;%g;',tol(i)); %! h = plot (pline_(:,1),pline_(:,2),msg); %! set(h,'color',colors(i,:),'linewidth',2,'markersize',4); %! end %! hold off %! %! # --------------------------------------------------------- %! # Four approximations of the initial polyline with decreasing tolerances. %!demo %! P = [0 0; 3 1; 3 4; 1 3; 2 2; 1 1]; %! func = @(x,y) linspace(x,y,5); %! P2(:,1) = cell2mat( ... %! arrayfun (func, P(1:end-1,1),P(2:end,1), ... %! 'uniformoutput',false))'(:); %! P2(:,2) = cell2mat( ... %! arrayfun (func, P(1:end-1,2),P(2:end,2), ... %! 'uniformoutput',false))'(:); %! %! P2s = simplifypolyline (P2); %! %! plot(P(:,1),P(:,2),'s',P2(:,1),P2(:,2),'o',P2s(:,1),P2s(:,2),'-ok'); %! %! # --------------------------------------------------------- %! # Simplification of a polyline in the plane. �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/rectAsPolygon.m��������������������������������������0000644�0000000�0000000�00000000132�12676233417�021064� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/rectAsPolygon.m������������������������������������������������������0000644�0001750�0001750�00000005676�12676233417�022261� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2003-2011 David Legland ## Copyright (C) 2016 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## ## The views and conclusions contained in the software and documentation are ## those of the authors and should not be interpreted as representing official ## policies, either expressed or implied, of the copyright holders. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{p} =} rectAsPolygon (@var{rect}) ## @deftypefnx {Function File} {[@var{x}, @var{y}] =} rectAsPolygon (@var{rect}) ## Convert a (centered) rectangle into a series of points ## ## Converts rectangle given as [x0 y0 w h] or [x0 y0 w h theta] into a ## 4*2 array double, containing coordinate of rectangle vertices. ## with two output arguments the coordinates are splitted in @var{x} and @var{y}. ## ## @seealso{polygons2d, drawRect, drawRect2, drawPolygon, drawShape} ## @end deftypefn function [tx ty] = rectAsPolygon (rect) theta = 0; x = rect(1); y = rect(2); w = rect(3) / 2; # easier to compute with w and h divided by 2 h = rect(4) / 2; if length (rect) > 4 theta = rect(5); endif v = [cos(theta); sin(theta)]; M = [-1 1; 1 1; 1 -1; -1 -1] .* [w h]; %M = bsxfun (@times, [-1 1; 1 1; 1 -1; -1 -1], [w h]); tx = x + M * v; ty = y + M(4:-1:1,[2 1]) * v; # tx(1) = x - w*cot + h*sit; # tx(2) = x + w*cot + h*sit; # tx(3) = x + w*cot - h*sit; # tx(4) = x - w*cot - h*sit; # ty(1) = y - h*cot - w*sit ; # ty(2) = y - h*cot + w*sit; # ty(3) = y + h*cot + w*sit; # ty(4) = y + h*cot - w*sit; if nargout == 1 tx = [tx ty]; endif endfunction ������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/reversePolyline.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021462� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.625063598 30 atime=1459173135.625063598 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/reversePolyline.m����������������������������������������������������0000644�0001750�0001750�00000003665�12676233417�022653� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{poly2} = } reversePolyline (@var{poly}) ## Reverse a polyline, by iterating vertices from the end ## ## POLY2 = reversePolyline(POLY) ## POLY2 has same vertices as POLY, but POLY2(i,:) is the same as ## POLY(END-i+1,:). ## ## @seealso{reversePolygon} ## @end deftypefn function rev = reversePolyline(poly) rev = poly(end:-1:1, :); endfunction ���������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/distancePointPolygon.m�������������������������������0000644�0000000�0000000�00000000132�12676233417�022447� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/distancePointPolygon.m�����������������������������������������������0000644�0001750�0001750�00000004271�12676233417�023632� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } distancePointPolygon (@var{point},@var{poly}) ## Compute shortest distance between a point and a polygon ## ## @seealso{polygons2d, points2d, distancePointPolyline, distancePointEdge, projPointOnPolyline} ## @end deftypefn function varargout = distancePointPolygon(point, poly) # eventually copy first point at the end to ensure closed polygon if sum(poly(end, :)==poly(1,:))~=2 poly = [poly; poly(1,:)]; end # call to distancePointPolyline minDist = distancePointPolyline(point, poly); # process output arguments if nargout<=1 varargout{1} = minDist; end endfunction ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/expandPolygon.m��������������������������������������0000644�0000000�0000000�00000000132�12676233417�021122� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/expandPolygon.m������������������������������������������������������0000644�0001750�0001750�00000006736�12676233417�022315� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{loops} = } expandPolygon (@var{poly}, @var{dist}) ## Expand a polygon by a given (signed) distance ## ## Associates to each edge of the polygon @var{poly} the parallel line located ## at distance @var{dist} from the current edge, and compute intersections with ## neighbor parallel lines. The resulting polygon is simplified to remove ## inner "loops", and can be disconnected. ## The result is a cell array, each cell containing a simple linear ring. ## ## This is a kind of dilation, but behaviour on corners is different. ## This function keeps angles of polygons, but there is no direct relation ## between length of 2 polygons. ## ## It is also possible to specify negative distance, and get all points ## inside the polygon. If the polygon is convex, the result equals ## morphological erosion of polygon by a ball with radius equal to the ## given distance. ## ## @seealso{polygons2d} ## @end deftypefn function loops = expandPolygon(poly, dist) # eventually copy first point at the end to ensure closed polygon if sum(poly(end, :)==poly(1,:))~=2 poly = [poly; poly(1,:)]; end # number of vertices of the polygon N = size(poly, 1)-1; # find lines parallel to polygon edges located at distance DIST lines = zeros(N, 4); for i=1:N side = createLine(poly(i,:), poly(i+1,:)); lines(i, 1:4) = parallelLine(side, dist); end # compute intersection points of consecutive lines lines = [lines;lines(1,:)]; poly2 = zeros(N, 2); for i=1:N poly2(i,1:2) = intersectLines(lines(i,:), lines(i+1,:)); end # split result polygon into set of loops (simple polygons) loops = polygonLoops(poly2); # keep only loops whose distance to original polygon is correct distLoop = zeros(length(loops), 1); for i=1:length(loops) distLoop(i) = distancePolygons(loops{i}, poly); end loops = loops(abs(distLoop-abs(dist)) ## Author: 2016 Juan Pablo Carbajal ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } distancePointPolyline (@var{point},@var{poly}) ## Compute shortest distance between a point and a polyline ## Example: ## @example ## pt1 = [30 20]; ## pt2 = [30 5]; ## poly = [10 10;50 10;50 50;10 50]; ## distancePointPolyline([pt1;pt2], poly) ## ans = ## 10 ## 5 ## @end example ## ## @seealso{polygons2d, points2d,distancePointEdge, projPointOnPolyline} ## @end deftypefn function [minDist pos] = distancePointPolyline (point, poly, closed = false) # check if input polyline is closed or not if strcmp ('closed', closed) closed = true; elseif strcmp ('open', closed) closed = false; endif # closes the polyline if necessary if closed poly = [poly; poly(1,:)]; endif # number of points Np = size (point, 1); # allocate memory for result minDist = inf (Np, 1); ## construct the set of edges edges = [poly(1:end-1, :) poly(2:end, :)]; ## compute distance between current each point and all edges [dist edgepos] = distancePointEdge (point, edges); ## get the minimum distance [minDist i] = min (dist, [], 2); # Contributed by Raghu Charan A 02.2016 pos = []; if nargout == 2 Ne = size (edgepos, 2); j = sub2ind ([Np,Ne], (1:Np).', i); pos = i - 1 + edgepos(j); endif endfunction %!demo %! point = [2 1] .* rand (10,2) - [1 0]; %! t = linspace (0,pi,25).'; %! poly = [cos(t) sin(t)]; %! [d pos] = distancePointPolyline (point,poly); %! %! # Calculate the projection on the polyline to plot %! p_ = zeros (10, 2); %! %! # projection on vertices of the polyline %! isvertex = abs (pos - fix (pos)) < eps; %! p_(isvertex,:) = poly (pos(isvertex)+1,:); %! %! # the rest %! pos = pos (!isvertex); %! i = fix (pos) + 1; %! x = pos - fix (pos); %! p_(!isvertex,:) = poly(i,:) + x.*(poly(i+1,:)-poly(i,:)); %! %! # Plot %! plot (poly(:,1), poly(:,2),'.-', ... %! point(:,1), point(:,2), 'o', ... %! p_(:,1), p_(:,2),'.'); %! legend ('Polyline', 'Points', 'Projections'); %! line ([point(:,1) p_(:,1)].',[point(:,2) p_(:,2)].'); %! arrayfun (@(i)text ((p_(i,1)+point(i,1))/2, (p_(i,2)+point(i,2))/2, ... %! sprintf("%.2f", d(i))), 1:10); %! axis tight %! axis equal ��������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/distancePolygons.m�����������������������������������0000644�0000000�0000000�00000000132�12676233417�021620� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.581084565 30 atime=1459173135.581084565 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/distancePolygons.m���������������������������������������������������0000644�0001750�0001750�00000004007�12676233417�023000� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{dist} = } distancePolygons (@var{poly1},@var{poly2}) ## Compute the shortest distance between 2 polygons ## ## @end deftypefn function dist = distancePolygons(poly1, poly2) # compute distance of each vertex of a polygon to the other polygon dist1 = min(distancePointPolygon(poly1, poly2)); dist2 = min(distancePointPolygon(poly2, poly1)); # keep the minimum of the two distances dist = min(dist1, dist2); endfunction �������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/PaxHeaders.5293/polygons2d.m�����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020373� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.589080753 30 atime=1459173135.589080753 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/polygons2d/polygons2d.m���������������������������������������������������������0000644�0001750�0001750�00000021775�12676233417�021566� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {} polygons2d () ## Description of functions operating on 2D polygons ## ## The 'polygons' module contains functions operating on shapes composed ## of a vertex list, like polygons or polylines. ## ## We call 'polyline' the curve defined by a series of vertices. ## A polyline can be either closed or open, depending on whether the last ## vertex is connected to the first one or not. This can be given as an ## option is some functions in the module. ## A 'polygon' is the planar domain delimited by a closed polyline. We ## sometimes want to consider 'complex polygons', whose boundary is ## composed of several disjoint domains. The domain defined by a single ## closed polyline is called 'simple polygon'. ## We call 'curve' a polyline with many vertices, such that the polyline ## can be considered as a discrete approximation of a "real" curve. ## ## A simple polygon or polyline is represented by a N-by-2 array, each row ## of the array representing the coordinates of a vertex. ## Simple polygons are assumed to be closed, so there is no need to repeat ## the first vertex at the end. ## As both polygons and polylines can be represented by a list of vertex ## coordinates, some functions also consider the vertex list itself. Such ## functions are prefixed by 'pointSet'. Also, many functions prefixed by ## 'polygon' or 'polyline' works also on the other type of shape. ## ## For multiple-connected polygons, the different connected boundaries are ## separated by a row [NaN NaN]. ## ## For some functions, the orientation of the polygon can be relevant: CCW ## stands for 'Conter-Clockwise' (positive orientation), CW stands for ## 'Clockwise'. ## ## Polylines are parametrized in the following way: ## * the i-th vertex is located at position i-1 ## * points of the i-th edge have positions ranging linearly from i-1 to i ## The parametrization domain for an open polyline is from 0 to Nv-1, and ## from 0 to Nv for a closed polyline (positions 0 and Nv correspond to ## the same point). ## ## Example: ## # Simple polygon: ## P1 = [1 1;2 1;2 2;1 2]; ## drawPolygon(P1); ## axis([0 5 0 5]); ## # Multiple polygon: ## P2 = [10 10;40 10;40 40;10 40;NaN NaN;20 20;20 30;30 30;30 20]; ## figure;drawPolygon(P2); axis([0 50 0 50]); ## ## ## Point Sets ## pointSetBounds - Bounding box of a set of points ## pointSetsAverage - Compute the average of several point sets ## minimumCaliperDiameter - Minimum caliper diameter of a set of points ## findPoint - Find index of a point in an set from its coordinates ## ## Polylines ## polylinePoint - Extract a point from a polyline ## polylineLength - Return length of a polyline given as a list of points ## polylineCentroid - Compute centroid of a curve defined by a series of points ## polylineSubcurve - Extract a portion of a polyline ## reversePolyline - Reverse a polyline, by iterating vertices from the end ## isPointOnPolyline - Test if a point belongs to a polyline ## projPointOnPolyline - Compute position of a point projected on a polyline ## distancePointPolyline - Compute shortest distance between a point and a polyline ## distancePolylines - Compute the shortest distance between 2 polylines ## intersectPolylines - Find the common points between 2 polylines ## polylineSelfIntersections - Find self-intersections points of a polyline ## ## Curves (polylines with lot of vertices) ## parametrize - Parametrization of a curve, based on edges length ## curvature - Estimate curvature of a polyline defined by points ## cart2geod - Convert cartesian coordinates to geodesic coord. ## geod2cart - Convert geodesic coordinates to cartesian coord. ## curveMoment - Compute inertia moment of a 2D curve ## curveCMoment - Compute centered inertia moment of a 2D curve ## curveCSMoment - Compute centered scaled moment of a 2D curve ## ## Polygons ## polygonPoint - Extract a point from a polygon ## polygonSubcurve - Extract a portion of a polygon ## reversePolygon - Reverse a polygon, by iterating vertices from the end ## projPointOnPolygon - Compute position of a point projected on a polygon ## splitPolygons - Convert a NaN separated polygon list to a cell array of polygons ## clipPolygon - Clip a polygon with a rectangular box ## clipPolygonHP - Clip a polygon with a Half-plane defined by a directed line ## intersectLinePolygon - Intersection points between a line and a polygon ## intersectRayPolygon - Intersection points between a ray and a polygon ## polygonSelfIntersections - Find-self intersection points of a polygon ## convexHull - Convex hull of a set of points ## polygonLoops - Divide a possibly self-intersecting polygon into a set of simple loops ## expandPolygon - Expand a polygon by a given (signed) distance ## medialAxisConvex - Compute medial axis of a convex polygon ## ## Measures on Polygons ## isPointInPolygon - Test if a point is located inside a polygon ## polygonContains - Test if a point is contained in a multiply connected polygon ## polygonCentroid - Compute the centroid (center of mass) of a polygon ## polygonArea - Compute the signed area of a polygon ## polygonLength - Perimeter of a polygon ## polygonNormalAngle - Compute the normal angle at a vertex of the polygon ## polygonBounds - Compute the bounding box of a polygon ## distancePointPolygon - Compute shortest distance between a point and a polygon ## distancePolygons - Compute the shortest distance between 2 polygons ## ## Triangles ## isPointInTriangle - Test if a point is located inside a triangle ## triangleArea - Area of a triangle ## ## Functions from stochastic geometry ## steinerPoint - Compute steiner point (weighted centroid) of a polygon ## steinerPolygon - Create a Steiner polygon from a set of vectors ## supportFunction - Compute support function of a polygon ## convexification - Compute the convexification of a polygon ## ## Input, Output and conversions ## readPolygon - Read a polygon stored in a file ## polygonToRow - Convert polygon coordinates to a row vector ## rowToPolygon - Create a polygon from a row vector ## rectAsPolygon - Convert a (centered) rectangle into a series of points ## ## Drawing functions ## drawPolyline - Draw a polyline specified by a list of points ## drawPolygon - Draw a polygon specified by a list of points ## fillPolygon - Fill a polygon specified by a list of points ## ## ## Credits: ## * function intersectPolylines uses the 'interX' contribution from "NS" ## (file exchange 22441, called 'curve-intersections') ## ## ----- ## Author: David Legland ## e-mail: david.legland@@grignon.inra.fr ## created the 07/11/2005. ## Homepage: @url{http://matgeom.sourceforge.net/} ## @url{http://www.pfl-cepia.inra.fr/index.php?page=geom2d} ## Copyright INRA - Cepia Software Platform. ## ## @end deftypefn function polygons2d () help('polygons2d'); endfunction ���geometry-2.1.1/inst/PaxHeaders.5293/__geometry_package_register__.m���������������������������������0000644�0000000�0000000�00000000132�12676233417�022201� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.301217993 30 atime=1459173135.301217993 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/__geometry_package_register__.m�������������������������������������������������0000644�0001750�0001750�00000002707�12676233417�023366� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2016 Carnë Draug ## ## This program is free software; you can redistribute it and/or ## modify it under the terms of the GNU General Public License as ## published by the Free Software Foundation; either version 3 of the ## License, or (at your option) any later version. ## ## This program is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with this program; if not, see ## . ## -*- texinfo -*- ## @deftypefn {} {} __geometry_package_register__ () ## Undocumented internal function of geometry package. ## @end deftypefn ## PKG_ADD: __geometry_package_register__ (1); ## PKG_DEL: __geometry_package_register__ (-1); function subdir_paths = __geometry_package_register__ (loading = 0) subdirlist = {"geom2d","io","polygons2d","shape2d", "graphs",... "geom3d","meshes3d","polynomialCurves2d"}; ## Get full path, with luck we can retreive the package name from here base_pkg_path = fileparts (make_absolute_filename (mfilename ("fullpath"))); subdir_paths = fullfile (base_pkg_path, subdirlist); if (loading > 0) addpath (subdir_paths{:}); elseif (loading < 0) rmpath (subdir_paths{:}); endif endfunction ���������������������������������������������������������geometry-2.1.1/inst/PaxHeaders.5293/meshes3d��������������������������������������������������������0000644�0000000�0000000�00000000132�12676233417�015453� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/�����������������������������������������������������������������������0000755�0001750�0001750�00000000000�12676233417�016707� 5����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/PaxHeaders.5293/drawMesh.m���������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017460� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.569090283 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/drawMesh.m�������������������������������������������������������������0000644�0001750�0001750�00000012436�12676233417�020645� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{h} =} drawMesh (@var{vertices}, @var{faces}) ## @deftypefnx {Function File} {@var{h} =} drawMesh (@var{mesh}) ## @deftypefnx {Function File} {@var{h} =} drawMesh (@dots{}, @var{color}) ## @deftypefnx {Function File} {@var{h} =} drawMesh (@dots{}, @var{name},@var{value}) ## Draw a 3D mesh defined by vertices and faces ## ## drawMesh(VERTICES, FACES) ## Draws the 3D mesh defined by vertices VERTICES and the faces FACES. ## vertices is a [NVx3] array containing coordinates of vertices, and FACES ## is either a [NFx3] or [NFx4] array containing indices of vertices of ## the triangular or rectangular faces. ## FACES can also be a cell array, in the content of each cell is an array ## of indices to the vertices of the current face. Faces can have different ## number of vertices. ## ## drawMesh(MESH) ## Where mesh is a structure with fields 'vertices' and 'faces', draws the ## given mesh. ## ## drawMesh(..., COLOR) ## Use the specified color to render the mesh faces. ## ## drawMesh(..., NAME, VALUE) ## Use one or several pairs of parameter name/value to specify drawing ## options. Options are the same as the 'patch' function. ## ## ## H = drawMesh(...); ## Also returns a handle to the created patch. ## ## WARNING: This function doesn't work with gnuplot (as of version 4.2) ## ## Example: ## @example ## [v f] = createSoccerBall; ## drawMesh(v, f); ## @end example ## ## @seealso{polyhedra, meshes3d, patch} ## @end deftypefn function varargout = drawMesh(vertices, faces, varargin) ## Initialisations # Check if the input is a mesh structure if isstruct(vertices) # refresh options if nargin > 1 varargin = [{faces} varargin]; end # extract data to display faces = vertices.faces; vertices = vertices.vertices; end # process input arguments switch length(varargin) case 0 # default color is red varargin = {'facecolor', [1 0 0]}; case 1 # use argument as color for faces varargin = {'facecolor', varargin{1}}; otherwise # otherwise keep varargin unchanged end # overwrites on current figure state = ishold(gca); hold on; # if vertices are 2D points, add a z=0 coordinate if size(vertices, 2)==2 vertices(1,3)=0; end ## Use different processing depending on the type of faces if isnumeric(faces) # array FACES is a NC*NV indices array, with NV : number of vertices of # each face, and NC number of faces h = patch('vertices', vertices, 'faces', faces, varargin{:}); elseif iscell(faces) # array FACES is a cell array h = zeros(length(faces(:)), 1); for f=1:length(faces(:)) # get vertices of the cell face = faces{f}; # Special processing in case of multiple polygonal face: # each polygonal loop is separated by a NaN. if sum(isnan(face))~=0 # find indices of loops breaks inds = find(isnan(face)); # replace NaNs by index of first vertex of each polygon face(inds(2:end)) = face(inds(1:end-1)+1); face(inds(1)) = face(1); face(length(face)+1)= face(inds(end)+1); end # draw current face cnodes = vertices(face, :); h(f) = patch(cnodes(:, 1), cnodes(:, 2), cnodes(:, 3), [1 0 0]); end # set up drawing options set(h, varargin{:}); else error('second argument must be a face array'); end if ~state hold off end ## Process output arguments # format output parameters if nargout>0 varargout{1}=h; end endfunction %!demo %! [v f] = createCubeOctahedron; %! drawMesh(v, f); %! view (3) ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/PaxHeaders.5293/createCube.m�������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017750� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.565092189 30 atime=1459173135.565092189 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/createCube.m�����������������������������������������������������������0000644�0001750�0001750�00000006206�12676233417�021133� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{v},@var{e},@var{f}] =} createCube () ## @deftypefnx {Function File} {[@var{v},@var{f}] =} createCube () ## @deftypefnx {Function File} {@var{mesh} =} createCube () ## Create a 3D mesh representing the unit cube ## ## [V E F] = createCube ## Create a unit cube, as a polyhedra representation. ## c has the form [V E F], where V is a 8-by-3 array with vertices ## coordinates, E is a 12-by-2 array containing indices of neighbour ## vertices, and F is a 6-by-4 array containing vertices array of each ## face. ## ## [V F] = createCube; ## Returns only the vertices and the face vertex indices. ## ## MESH = createCube; ## Returns the data as a mesh structure, with fields 'vertices', 'edges' ## and 'faces'. ## ## Example ## @example ## [n e f] = createCube; ## drawMesh(n, f); ## @end example ## ## @seealso{meshes3d, drawMesh, createOctahedron, createTetrahedron, ## createDodecahedron, createIcosahedron, createCubeOctahedron} ## @end deftypefn function varargout = createCube() x0 = 0; dx= 1; y0 = 0; dy= 1; z0 = 0; dz= 1; nodes = [... x0 y0 z0; ... x0+dx y0 z0; ... x0 y0+dy z0; ... x0+dx y0+dy z0; ... x0 y0 z0+dz; ... x0+dx y0 z0+dz; ... x0 y0+dy z0+dz; ... x0+dx y0+dy z0+dz]; edges = [1 2;1 3;1 5;2 4;2 6;3 4;3 7;4 8;5 6;5 7;6 8;7 8]; # faces are oriented such that normals point outwards faces = [1 3 4 2;5 6 8 7;2 4 8 6;1 5 7 3;1 2 6 5;3 7 8 4]; # format output varargout = formatMeshOutput(nargout, nodes, edges, faces); endfunction %!demo %! [n e f] = createCube; %! drawMesh (n, f); %! view (3); ������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/PaxHeaders.5293/meshes3d_Contents.m������������������������������������0000644�0000000�0000000�00000000132�12676233417�021276� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.569090283 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/meshes3d_Contents.m����������������������������������������������������0000644�0001750�0001750�00000013044�12676233417�022457� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} meshes3d_Contents () ## MESHES3D 3D Surface Meshes ## Version 1.0 21-Mar-2011 . ## ## Creation, vizualization, and manipulation of 3D surface meshes or ## polyhedra. ## ## Meshes and Polyhedra are represented by a couple of variables @{V, F@}: ## V: Nv-by-3 array of vertices: [x1 y1 z1; @dots{} ; xn yn zn]; ## F: is either a NF-by-3 or NF-by-4 array containing reference for ## vertices of each face, or a NF-by-1 cell array, where each cell is an ## array containing a variable number of node indices. ## For some functions, the array E of edges is needed. It consists in a ## NE-by-2 array containing indices of source and target vertices. ## ## The library provides function to create basic polyhedric meshes (the 5 ## platonic solids, plus few others), as well as functions to perform ## basic computations (surface area, normal angles, face centroids @dots{}). ## The 'MengerSponge' structure is an example of mesh that is not simply ## connected (multiple tunnels in the structure). ## ## The drawMesh function is mainly a wrapper to the Matlab 'patch' ## function, allowing passing arguments more quickly. ## ## Example ## @example ## # create a soccer ball mesh and display it ## [n e f] = createSoccerBall; ## drawMesh(n, f, 'faceColor', 'g', 'linewidth', 2); ## axis equal; ## @end example ## ## ## General functions ## meshFace - Return the vertex indices of a face in a mesh ## computeMeshEdges - Computes edges array from face array ## meshEdgeFaces - Compute index of faces adjacent to each edge of a mesh ## faceCentroids - Compute centroids of a mesh faces ## faceNormal - Compute normal vector of faces in a 3D mesh ## ## Measures on meshes ## meshSurfaceArea - Surface area of a polyhedral mesh ## trimeshSurfaceArea - Surface area of a triangular mesh ## meshEdgeLength - Lengths of edges of a polygonal or polyhedral mesh ## meshDihedralAngles - Dihedral at edges of a polyhedal mesh ## polyhedronNormalAngle - Compute normal angle at a vertex of a 3D polyhedron ## polyhedronMeanBreadth - Mean breadth of a convex polyhedron ## ## Basic processing ## triangulateFaces - Convert face array to an array of triangular faces ## meshReduce - Merge coplanar faces of a polyhedral mesh ## minConvexHull - Return the unique minimal convex hull of a set of 3D points ## polyhedronSlice - Intersect a convex polyhedron with a plane. ## checkMeshAdjacentFaces - Check if adjacent faces of a mesh have similar orientation ## clipMeshVertices - Clip vertices of a surfacic mesh and remove outer faces ## clipConvexPolyhedronHP - Clip a convex polyhedron by a plane ## ## Typical polyhedra ## polyhedra - Index of classical polyhedral meshes ## createCube - Create a 3D mesh representing the unit cube ## createOctahedron - Create a 3D mesh representing an octahedron ## createCubeOctahedron - Create a 3D mesh representing a cube-octahedron ## createIcosahedron - Create a 3D mesh representing an Icosahedron. ## createDodecahedron - Create a 3D mesh representing a dodecahedron ## createTetrahedron - Create a 3D mesh representing a tetrahedron ## createRhombododecahedron - Create a 3D mesh representing a rhombododecahedron ## createTetrakaidecahedron - Create a 3D mesh representing a tetrakaidecahedron ## ## Less typical polyhedra ## createSoccerBall - Create a 3D mesh representing a soccer ball ## createMengerSponge - Create a cube with an inside cross removed ## steinerPolytope - Create a steiner polytope from a set of vectors ## ## Drawing functions ## drawFaceNormals - Draw normal vector of each face in a mesh ## drawMesh - Draw a 3D mesh defined by vertices and faces ## @end deftypefn function meshes3d_Contents () help meshes3d_Contents endfunction ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/PaxHeaders.5293/private������������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017125� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/private/���������������������������������������������������������������0000755�0001750�0001750�00000000000�12676233417�020361� 5����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/private/PaxHeaders.5293/parseMeshData.m��������������������������������0000644�0000000�0000000�00000000132�12676233417�022101� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.569090283 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/private/parseMeshData.m������������������������������������������������0000644�0001750�0001750�00000005702�12676233417�023264� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{mesh} =} parseMeshData (@var{vertices},@var{edges},@var{faces}) ## @deftypefnx {Function File} {@var{mesh} =} parseMeshData (@var{vertices},@var{faces}) ## @deftypefnx {Function File} {[@var{vertices},@var{edges},@var{faces}] =} parseMeshData (@var{mesh}) ## @deftypefnx {Function File} {[@var{vertices},@var{faces}] =} parseMeshData (@var{mesh}) ## Conversion of data representation for meshes ## ## MESH = parseMeshData(VERTICES, EDGES, FACES) ## MESH = parseMeshData(VERTICES, FACES) ## [VERTICES EDGES FACES] = parseMeshData(MESH) ## [VERTICES FACES] = parseMeshData(MESH) ## ## ## @seealso{meshes3d, formatMeshOutput} ## @end deftypefn function varargout = parseMeshData(varargin) # initialize edges edges = []; # Process input arguments if nargin == 1 # input is a data structure mesh = varargin{1}; vertices = mesh.vertices; faces = mesh.faces; if isfield(mesh, 'edges') edges = mesh.edges; end elseif nargin == 2 # input are vertices and faces vertices = varargin{1}; faces = varargin{2}; elseif nargin == 3 # input are vertices, edges and faces vertices = varargin{1}; edges = varargin{2}; faces = varargin{3}; else error('Wrong number of arguments'); end varargout = formatMeshOutput(nargout, vertices, edges, faces); endfunction ��������������������������������������������������������������geometry-2.1.1/inst/meshes3d/private/PaxHeaders.5293/formatMeshOutput.m�����������������������������0000644�0000000�0000000�00000000132�12676233417�022706� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.569090283 30 atime=1459173135.569090283 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/private/formatMeshOutput.m���������������������������������������������0000644�0001750�0001750�00000006655�12676233417�024101� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{output} =} formatMeshOutput (@var{nbargs}, @var{vertices},@var{edges},@var{faces}) ## @deftypefnx {Function File} {@var{output} =} formatMeshOutput (@var{nbargs}, @var{vertices},@var{faces}) ## Format mesh output depending on nargout ## ## OUTPUT = formatMeshOutput(@var{nbargs}, VERTICES, EDGES, FACES) ## Utilitary function to convert mesh data . ## If @var{nbargs} is 0 or 1, return a matlab structure with fields vertices, ## edges and faces. ## If @var{nbargs} is 2, return a cell array with data VERTICES and FACES. ## If @var{nbargs} is 3, return a cell array with data VERTICES, EDGES and ## FACES. ## ## OUTPUT = formatMeshOutput(@var{nbargs}, VERTICES, FACES) ## Same as before, but do not intialize EDGES in output. NARGOUT can not ## be equal to 3. ## ## Example ## # Typical calling sequence (for a very basic mesh of only one face) ## v = [0 0; 0 1;1 0;1 1]; ## e = [1 2;1 3;2 4;3 4]; ## f = [1 2 3 4]; ## ## varargout = formatMeshOutput(nargout, v, e, f); ## ## @seealso{meshes3d, parseMeshData} ## @end deftypefn function res = formatMeshOutput(nbArgs, vertices, edges, faces) if nargin < 4 faces = edges; edges = []; end switch nbArgs case {0, 1} # output is a data structure with fields vertices, edges and faces mesh.vertices = vertices; mesh.edges = edges; mesh.faces = faces; res = {mesh}; case 2 # keep only vertices and faces res = cell(nbArgs, 1); res{1} = vertices; res{2} = faces; case 3 # return vertices, edges and faces as 3 separate outputs res = cell(nbArgs, 1); res{1} = vertices; res{2} = edges; res{3} = faces; otherwise error('Can not manage more than 3 outputs'); end endfunction �����������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/PaxHeaders.5293/createCubeOctahedron.m���������������������������������0000644�0000000�0000000�00000000132�12676233417�021757� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.565092189 30 atime=1459173135.565092189 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/meshes3d/createCubeOctahedron.m�������������������������������������������������0000644�0001750�0001750�00000006207�12676233417�023143� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{v}, @var{e}, @var{f}] =} createCubeOctahedron () ## @deftypefnx {Function File} {@var{mesh} =} createCubeOctahedron () ## Create a 3D mesh representing a cube-octahedron ## ## [V E F] = createCubeOctahedron; ## Cubeoctahedron can be seen either as a truncated cube, or as a ## truncated octahedron. ## V is the 12-by-3 array of vertex coordinates ## E is the 27-by-2 array of edge vertex indices ## F is the 1-by-14 cell array of face vertex indices ## ## [V F] = createCubeOctahedron; ## Returns only the vertices and the face vertex indices. ## ## MESH = createCubeOctahedron; ## Returns the data as a mesh structure, with fields 'vertices', 'edges' ## and 'faces'. ## ## @seealso{meshes3d, drawMesh, createCube, createOctahedron} ## @end deftypefn function varargout = createCubeOctahedron() nodes = [... 0 -1 1;1 0 1;0 1 1;-1 0 1; ... 1 -1 0;1 1 0;-1 1 0;-1 -1 0;... 0 -1 -1;1 0 -1;0 1 -1;-1 0 -1]; edges = [... 1 2; 1 4; 1 5; 1 8; ... 2 3; 2 5; 2 6; ... 3 4; 3 6; 3 7; ... 4 7; 4 8; ... 5 9; 5 10; ... 6 10; 6 11; ... 7 11; 7 12; ... 8 9; 8 12; ... 9 10; 9 12; ... 10 11; 11 12]; faces = {... [1 2 3 4], [1 5 2], [2 6 3], [3 7 4], [4 8 1], ... [5 10 6 2], [3 6 11 7], [4 7 12 8], [1 8 9 5], ... [5 9 10], [6 10 11], [7 11 12], [8 12 9], [9 12 11 10]}; # format output varargout = formatMeshOutput(nargout, nodes, edges, faces); endfunction %!demo %! [n e f] = createCubeOctahedron; %! drawMesh (n, f); %! view (3); �����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/PaxHeaders.5293/graphs����������������������������������������������������������0000644�0000000�0000000�00000000131�12676233417�015223� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 30 atime=1459173135.645054067 30 ctime=1459173135.645054067 ���������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/�������������������������������������������������������������������������0000755�0001750�0001750�00000000000�12676233417�016460� 5����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/PaxHeaders.5293/graphs_Contents.m����������������������������������������0000644�0000000�0000000�00000000132�12676233417�020620� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.541103626 30 atime=1459173135.541103626 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/graphs_Contents.m��������������������������������������������������������0000644�0001750�0001750�00000016422�12676233417�022004� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} graphs_Contents () ## GRAPHS Simple Toolbox for manipulating Geometric Graphs ## Version 0.5 11-Apr-2010 . ## ## The aim of this package is to provides functions to easily create, ## modify and display geometric graphs (geometric in a sense position ## of vertices is kept in memory). ## ## Graph structure is represented by at least two arrays: ## * NODES, which contains coordinates of each vertex ## * EDGES, which contains indices of start and end vertex. ## ## Others arrays may sometimes be used: ## * FACES, which contains indices of vertices of each face (either a ## double array, or a cell array) ## * CELLS, which contains indices of faces of each cell. ## ## An alternative representation is to use a structure, with fields: ## * edges ## * faces ## * cells ## corresponding to the data described above. ## ## Note that topological description of 2D graph is entirely contained in ## EDGES array, and that NODES array is used only to display graph ## ## Caution: this type of data structure is easy to create and to manage, ## but may be very inefficient for some algorithms. ## ## Graphs are usually considered as non-oriented in this package. ## ## ## Graph creation ## knnGraph - Create the k-nearest neighbors graph of a set of points ## delaunayGraph - Graph associated to Delaunay triangulation of input points ## euclideanMST - Build euclidean minimal spanning tree of a set of points ## prim_mst - Minimal spanning tree by Prim's algorithm ## ## Create graph from images ## imageGraph - Create equivalent graph of a binary image ## boundaryGraph - Get boundary of image as a graph ## gcontour2d - Creates contour graph of a 2D binary image. ## gcontour3d - Create contour graph of a 3D binary image. ## vectorize - Transform a binary skeleton into a graph (nodes and edges) ## ## Graph information ## grNodeDegree - Degree of a node in a (undirected) graph ## grNodeInnerDegree - Inner degree of a node in a graph ## grNodeOuterDegree - Outer degree of a node in a graph ## grNeighborNodes - Find adjacent nodes of a given node ## grNeighborEdges - Find adjacent edges of a given node ## grOppositeNode - Return opposite node in an edge ## grLabel - Associate a label to each connected component of the graph ## ## Graph management (low level operations) ## grRemoveNode - Remove a node in a graph ## grRemoveNodes - Remove several nodes in a graph ## grRemoveEdge - Remove an edge in a graph. ## grRemoveEdges - Remove several edges from a graph ## ## Graph processing (general applications) ## mergeGraphs - Merge two graphs, by adding nodes, edges and faces lists. ## grMergeNodes - Merge two (or more) nodes in a graph. ## grMergeMultipleNodes - Simplify a graph by merging multiple nodes ## grMergeMultipleEdges - Remove all edges sharing the same extremities ## grSimplifyBranches - Replace branches of a graph by single edges ## ## Filtering operations on Graph ## grMean - Compute mean from neihgbours ## grMedian - Compute median from neihgbours ## grDilate - Morphological dilation on graph ## grErode - Morphological erosion on graph ## grClose - Morphological closing on graph ## grOpen - Morphological opening on graph ## ## Geodesic operations ## grPropagateDistance - Propagates distances from a vertex to other vertices ## grVertexEccentricity - Eccentricity of vertices in the graph ## graphDiameter - Diameter of a graph ## graphPeripheralVertices - Peripheral vertices of a graph ## graphCenter - Center of a graph ## graphRadius - Radius of a graph ## grFindGeodesicPath - Find a geodesic path between two nodes in the graph ## grFindMaximalLengthPath - Find a path that maximizes sum of edge weights ## ## Operations for geometric graphs ## grMergeNodeClusters - Merge cluster of connected nodes in a graph ## grMergeNodesMedian - Replace several nodes by their median coordinate ## clipGraph - Clip a graph with a rectangular area ## addSquareFace - Add a (square) face defined from its vertices to a graph ## grFaceToPolygon - Compute the polygon corresponding to a graph face ## graph2Contours - Convert a graph to a set of contour curves ## ## Voronoi Graphs ## voronoi2d - Compute a voronoi diagram as a graph structure ## boundedVoronoi2d - Return a bounded voronoi diagram as a graph structure ## centroidalVoronoi2d - Create a 2D Centroidal Voronoi Tesselation ## cvtUpdate - Update germs of a CVT with given points ## cvtIterate - Update germs of a CVT using random points with given density ## ## Graph display ## drawGraph - Draw a graph, given as a set of vertices and edges ## drawGraphEdges - Draw edges of a graph ## drawGraphFaces - Draw faces of a graph ## drawDigraph - Draw a directed graph, given as a set of vertices and edges ## drawDirectedEdges - Draw edges with arrow indicating direction ## drawEdgeLabels - Draw values associated to graph edges ## drawNodeLabels - Draw values associated to graph nodes ## drawSquareMesh - Draw a 3D square mesh given as a graph ## patchGraph - Transform 3D graph (mesh) into a patch handle ## ## @end deftypefn function graphs_Contents() help graphs_Contents endfunction ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/PaxHeaders.5293/drawGraph.m����������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017376� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.541103626 30 atime=1459173135.541103626 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/drawGraph.m��������������������������������������������������������������0000644�0001750�0001750�00000021504�12676233417�020557� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} drawGraph (@var{nodes}, @var{edges}) ## @deftypefnx {Function File} drawGraph (@var{nodes}, @var{edges}, @var{faces}) ## @deftypefnx {Function File} drawGraph (@var{graph}) ## @deftypefnx {Function File} drawGraph (@dots{}, @var{snodes}) ## @deftypefnx {Function File} drawGraph (@dots{}, @var{snodes}, @var{sedges}) ## @deftypefnx {Function File} drawGraph (@dots{}, @var{snodes}, @var{sedges}, @var{sfaces}) ## @deftypefnx {Function File} {@var{h} = } drawGraph (@dots{}) ## @deftypefnx {Function File} {[@var{h} @var{he}] = } drawGraph (@dots{}) ## @deftypefnx {Function File} {[@var{h} @var{he} @var{hf}] = } drawGraph (@dots{}) ## Draw a graph, given as a set of vertices and edges ## ## DRAWGRAPH(NODES, EDGES) ## draw a graph specified by a set of nodes (array N*2 or N*3, ## corresponding to coordinate of each node), and a set of edges (an array ## Ne*2, containing for each edge the first and the second node). ## Default drawing is a red circle for nodes and a blue line for edges. ## ## DRAWGRAPH(NODES, EDGES, FACES) ## also draw faces of the graph as patches. ## ## DRAWGRAPH(GRAPH) ## passes argument in a srtucture with at least 2 fields named 'nodes' and ## 'edges', and possibly one field 'faces', corresponding to previously ## described parameters. ## GRAPH can also be a cell array, whose first element is node array, ## second element is edges array, and third element, if present, is faces ## array. ## ## ## DRAWGRAPH(..., SNODES) ## DRAWGRAPH(..., SNODES, SEDGES) ## DRAWGRAPH(..., SNODES, SEDGES, SFACES) ## specify the draw mode for each element, as in the classical 'plot' ## function. To not display some elements, uses 'none'. ## ## ## H = DRAWGRAPH(...) ## return handle to the set of edges. ## ## [HN, HE] = DRAWGRAPH(...) ## return handle to the set of nodes and to the set of edges. ## ## [HN, HE, HF] = DRAWGRAPH(...) ## Also return handle to the set of faces. ## ## @end deftypefn function varargout = drawGraph(varargin) ## initialisations # uses empty arrays by default for edges and faces e = []; f = []; # default styles for nodes, edges, and faces # nodes are drawn as red circles sn = {'linestyle', 'none', 'color', 'r', 'marker', 'o'}; # edges are drawn as blue lines se = {'linestyle', '-', 'color', 'b'}; # faces are cyan, their edges are not drawn sf = {'EdgeColor', 'none', 'Facecolor', 'c'}; ## Process input arguments # case of a call without arguments if nargin==0 help drawGraph; return; end # --------------------------------------------------------------- # First extract the graph structure var = varargin{1}; if iscell(var) # graph is stored as a cell array: first cell is nodes, second one is # edges, and third is faces n = var{1}; if length(var)>1 e = var{2}; end if length(var)>2 f = var{3}; end varargin(1) = []; elseif isstruct(var) # graph is stored as a structure, with fields 'nodes', 'edges', and # eventually 'faces'. n = var.nodes; e = var.edges; if isfield(var, 'faces') f = var.faces; end varargin(1) = []; else # graph is stored as set of variables: nodes, edges, and eventually # faces n = varargin{1}; e = varargin{2}; varargin(1:2) = []; if ~isempty(varargin) var = varargin{1}; if isnumeric(var) # faces are stored in a numeric array of indices f = var; varargin(1) = []; elseif iscell(var) if ~ischar(var{1}) # faces are stored in a cell array, each cell containing a # row vector of indices f = var; varargin(1) = []; end end end end # extract drawing style if ~isempty(varargin) sn = concatArguments(sn, varargin{1}); end if length(varargin)>1 se = concatArguments(se, varargin{2}); end if length(varargin)>2 sf = concatArguments(sf, varargin{3}); end ## main drawing processing # overwrites on current figure state = ishold(gca); hold on; if size(n, 2)==2 # Draw a 2 dimensional graph ---------------------- # Draw faces of the graph ------------ if ~strcmp(sf{1}, 'none') && ~isempty(f) if iscell(f) # each face is contained in a cell. hf = zeros(size(f)); for fi=1:length(f) hf(fi) = patch('Faces', f{fi}, 'Vertices', n, sf{:}); end else # process faces as an Nf*N array. Nf is the number of faces, # and all faces have the same number of vertices (nodes). hf = patch('Faces', f, 'Vertices', n, sf{:}); end end # Draw 2D Edges ---------------------- if ~strcmp(se{1}, 'none') && size(e, 1)>0 he = plot([n(e(:,1),1) n(e(:,2),1)]', [n(e(:,1),2) n(e(:,2),2)]', se{:}); end # Draw 2D nodes ---------------------- if ~strcmp(sn{1}, 'none') hn = plot(n(:,1), n(:,2), sn{:}); end elseif size(n, 2)==3 # Draw a 3 dimensional graph ---------------------- # use a zbuffer to avoid display pbms. set(gcf, 'renderer', 'zbuffer'); # Draw 3D Faces ---------------------- if ~strcmp(sf{1}, 'none') if iscell(f) # each face is contained in a cell. hf = zeros(size(f)); for fi=1:length(f) hf(fi) = patch('Faces', f{fi}, 'Vertices', n, sf{:}); end else # process faces as an Nf*N array. Nf i the number of faces, # and all faces have the same number of vertices (nodes). hf = patch('Faces', f, 'Vertices', n, sf{:}); end end # Draw 3D edges ---------------------- if ~strcmp(se{1}, 'none') && size(e, 1)>0 # he = plot3(... # [n(e(:,1),1) n(e(:,2),1)]', ... # [n(e(:,1),2) n(e(:,2),2)]', ... # [n(e(:,1),3) n(e(:,2),3)]', ... # se{:}); he = line(... [n(e(:,1),1) n(e(:,2),1)]', ... [n(e(:,1),2) n(e(:,2),2)]', ... [n(e(:,1),3) n(e(:,2),3)]', ... se{:}); end # Draw 3D nodes ---------------------- if ~strcmp(sn{1}, 'none'); hn = plot3(n(:,1), n(:,2), n(:,3), sn{:}); end end if ~state hold off end ## Format output arguments # return handle to edges if nargout==1 varargout{1} = he; end # return handle to nodes and edges if nargout==2 varargout{1} = hn; varargout{2} = he; end # return handle to nodes, edges and faces if nargout==3 varargout{1} = hn; varargout{2} = he; varargout{3} = hf; end endfunction function res = concatArguments(in1, in2) # in1 is a cell array already initialized # in2 is an argument that can be: # - empty # - the string 'none' # - another cell array if isempty(in2) res = in1; return; end if ischar(in2) if strcmp('none', in2) res = {'none'}; return; end end if iscell(in1) res = [in1(:)' in2(:)']; else res = [{in1} in2(:)]; end endfunction ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/PaxHeaders.5293/knnGraph.m�����������������������������������������������0000644�0000000�0000000�00000000132�12676233417�017227� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.541103626 30 atime=1459173135.541103626 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/knnGraph.m���������������������������������������������������������������0000644�0001750�0001750�00000004664�12676233417�020420� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{edges} = } knnGrpah (@var{nodes}) ## Create the k-nearest neighbors graph of a set of points ## ## EDGES = knnGraph(NODES) ## ## Example ## @example ## ## nodes = rand(10, 2); ## edges = knnGraph(nodes); ## drawGraph(nodes, edges); ## ## @end example ## ## @end deftypefn function edges = knnGraph(nodes, varargin) # get number of neighbors for each node k = 2; if ~isempty(varargin) k = varargin{1}; end # init size of arrays n = size(nodes, 1); edges = zeros(k*n, 2); # iterate on nodes for i = 1:n dists = distancePoints(nodes(i,:), nodes); [dists inds] = sort(dists); ##ok for j = 1:k edges(k*(i-1)+j, :) = [i inds(j+1)]; end end # remove double edges edges = unique(sort(edges, 2), 'rows'); endfunction %!demo %! nodes = rand(10, 2); %! edges = knnGraph(nodes); %! drawGraph(nodes, edges); %! axis tight ����������������������������������������������������������������������������geometry-2.1.1/inst/graphs/PaxHeaders.5293/voronoi2d.m����������������������������������������������0000644�0000000�0000000�00000000130�12676233417�017376� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������29 mtime=1459173135.54510172 29 atime=1459173135.54510172 30 ctime=1459173135.645054067 ����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/voronoi2d.m��������������������������������������������������������������0000644�0001750�0001750�00000004712�12676233417�020563� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{nodes} @var{edges} @var{faces}] = } voronoi2d (@var{germs}) ## Compute a voronoi diagram as a graph structure ## ## [NODES EDGES FACES] = voronoi2d(GERMS) ## GERMS an array of points with dimension 2 ## NODES, EDGES, FACES: usual graph representation, FACES as cell array ## ## Example ## @example ## ## [n e f] = voronoi2d(rand(100, 2)*100); ## drawGraph(n, e); ## ## @end example ## ## @end deftypefn function [nodes edges faces] = voronoi2d(germs) [V C] = voronoin(germs); nodes = V(2:end, :); edges = zeros(0, 2); faces = {}; for i=1:length(C) cell = C{i}; if ismember(1, cell) continue; end cell = cell-1; edges = [edges; sort([cell' cell([2:end 1])'], 2)]; ##ok faces{length(faces)+1} = cell; ##ok end edges = unique(edges, 'rows'); endfunction %!demo %! [n e f] = voronoi2d(rand(100, 2)*100); %! drawGraph(n, e); %! axis tight ������������������������������������������������������geometry-2.1.1/inst/graphs/PaxHeaders.5293/delaunayGraph.m������������������������������������������0000644�0000000�0000000�00000000132�12676233417�020243� x����������������������������������������������������������������������������������������������������ustar�00�������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������30 mtime=1459173135.541103626 30 atime=1459173135.541103626 30 ctime=1459173135.645054067 ��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������geometry-2.1.1/inst/graphs/delaunayGraph.m����������������������������������������������������������0000644�0001750�0001750�00000006571�12676233417�021433� 0����������������������������������������������������������������������������������������������������ustar�00juanpi��������������������������juanpi��������������������������0000000�0000000������������������������������������������������������������������������������������������������������������������������������������������������������������������������## Copyright (C) 2004-2011 David Legland ## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas) ## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal ## All rights reserved. ## ## Redistribution and use in source and binary forms, with or without ## modification, are permitted provided that the following conditions are met: ## ## 1 Redistributions of source code must retain the above copyright notice, ## this list of conditions and the following disclaimer. ## 2 Redistributions in binary form must reproduce the above copyright ## notice, this list of conditions and the following disclaimer in the ## documentation and/or other materials provided with the distribution. ## ## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS'' ## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE ## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR ## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL ## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR ## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER ## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, ## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE ## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ## -*- texinfo -*- ## @deftypefn {Function File} {[@var{points} @var{edges}]= } delaunayGraph (@var{points}) ## Graph associated to Delaunay triangulation of input points ## ## Compute the Delaunay triangulation of the set of input points, and ## convert to a set of edges. The output NODES is the same as the input ## POINTS. ## ## WARNING: 3d pltottig works correctly in Octave >= 3.6 ## ## Example ## @example ## ## # Draw a planar graph correpspionding to Delaunay triangulation ## points = rand(30, 2) * 100; ## [nodes edges] = delaunayGraph(points); ## figure; ## drawGraph(nodes, edges); ## ## # Draw a 3Dgraph corresponding to Delaunay tetrahedrisation ## points = rand(20, 3) * 100; ## [nodes edges] = delaunayGraph(points); ## figure; ## drawGraph(nodes, edges); ## view(3); ## ## @end example ## ## @seealso{delaunay, delaunayn} ## @end deftypefn function [points edges] = delaunayGraph(points, varargin) # compute triangulation tri = delaunayn(points, varargin{:}); # number of simplices (triangles), and of vertices by simplex (3 in 2D) nt = size(tri, 1); nv = size(tri, 2); # allocate memory edges = zeros(nt * nv, 2); # compute edges of each simplex for i = 1:nv-1 edges((1:nt) + (i-1)*nt, :) = sort([tri(:, i) tri(:, i+1)], 2); end edges((1:nt) + (nv-1)*nt, :) = sort([tri(:, end) tri(:, 1)], 2); # remove multiple edges edges = unique(edges, 'rows'); endfunction %!demo %! # Draw a planar graph correpspionding to Delaunay triangulation %! points = rand(30, 2) * 100; %! [nodes edges] = delaunayGraph(points); %! figure; %! drawGraph(nodes, edges); %! axis tight %!demo %! # WARNING 3d pltottig works correctly in Octave >= 3.6 %! # Draw a 3Dgraph corresponding to Delaunay tetrahedrisation %! points = rand(20, 3) * 100; %! [nodes edges] = delaunayGraph(points); %! figure; %! drawGraph(nodes, edges); %! view(3); %! axis tight 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