pax_global_header00006660000000000000000000000064127176670760014535gustar00rootroot0000000000000052 comment=ceb67f712a5e8dea0e19a167cce5dd77bfbf940d affine-2.0.0/000077500000000000000000000000001271766707600127645ustar00rootroot00000000000000affine-2.0.0/.coveragerc000066400000000000000000000000341271766707600151020ustar00rootroot00000000000000[run] omit = affine/tests/* affine-2.0.0/.gitignore000066400000000000000000000010401271766707600147470ustar00rootroot00000000000000# Byte-compiled / optimized / DLL files __pycache__/ *.py[cod] # C extensions *.so # Distribution / packaging .Python env/ bin/ build/ develop-eggs/ dist/ eggs/ lib/ lib64/ parts/ sdist/ var/ *.egg-info/ .installed.cfg *.egg # Installer logs pip-log.txt pip-delete-this-directory.txt # Unit test / coverage reports htmlcov/ .tox/ .coverage .cache nosetests.xml coverage.xml # Translations *.mo # Mr Developer .mr.developer.cfg .project .pydevproject # Rope .ropeproject # Django stuff: *.log *.pot # Sphinx documentation docs/_build/ affine-2.0.0/.travis.yml000066400000000000000000000011231271766707600150720ustar00rootroot00000000000000sudo: false language: python python: - "2.6" - "2.7" - "3.3" - "3.4" - "3.5" install: - "pip install pytest pytest-cov nose" - "pip install coveralls" - "pip install -e ." script: - python -m pytest affine/tests --cov affine --cov-report term-missing after_success: - coveralls deploy: on: tags: true provider: pypi distributions: "sdist bdist_wheel" user: seang password: secure: "FlfcoO8a26yNTtxJ9BmzLHCM18r0sDSJvXWNQ2LN/j0qTgKK9XeD9huMeE3s/OptD6DlY36bNgxSW87rsIx/nboyn+eJQA5tvhMP48lhLDZ6rDkRT1jsizxDYskQf4V//nsOoycuV6nTKDnneITGR1tn4AqDRbiwHSKho4GuBaM=" affine-2.0.0/AUTHORS.txt000066400000000000000000000003011271766707600146440ustar00rootroot00000000000000Authors ======= - Sean Gillies - Steven Ring - Mike Toews - Kevin Wurster - Todd Small affine-2.0.0/CHANGES.txt000066400000000000000000000026021271766707600145750ustar00rootroot00000000000000CHANGES ======= 2.0.0 (2016-05-20) ------------------ - Final release. 2.0b2 (2016-05-16) ------------------ - Bug fix: restore ``Affine __rmul__`` even though it permits dubious vector * matrix expressions (#27). 2.0b1 (2016-05-16) ------------------ - Breaking change: precision used in properties like ``is_conformal`` is no longer a global module attribute, but an Affine class or instance attribute (#19, #20). - Breaking change: ``is_degenerate`` property is now exact and not subject to a level of precision (#23). - Breaking change: we have reversed our sense of rotation, a positive angle now rotates a point counter-clockwise about the pivot point (#25). - Bug fix: a bug in matrix-vector multiplication had been reversing the direction of rotation and is now fixed (#25). 1.3.0 (2016-04-08) ------------------ - is_degenerate predicate is precise, not approximate (#22). 1.2.0 (2015-06-01) ------------------ - Enable pickling of Affine objects (#14). - Sort out the mixed up shearing parameters (#12). 1.1.0 (2014-11-13) ------------------ - Add loadsw/dumpsw world file utilities (#6). - Travis-CI and Coveralls config and web hooks added (#10). 1.0.1 (2014-10-20) ------------------ - set_epsilon() now actually sets module EPSILON (#4). - add AUTHORS.txt. 1.0 (2014-05-27) ---------------- - Code ported from Casey Duncan's Planar package. - from_gdal() class method added. affine-2.0.0/LICENSE.txt000066400000000000000000000027551271766707600146200ustar00rootroot00000000000000Copyright (c) 2014, Sean C. Gillies All rights reserved. Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met: * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer. * 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. * Neither the name of Sean C. Gillies nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission. 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 OWNER 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. affine-2.0.0/README.rst000066400000000000000000000056741271766707600144670ustar00rootroot00000000000000Affine ====== Matrices describing affine transformation of the plane. .. image:: https://travis-ci.org/sgillies/affine.svg?branch=master :target: https://travis-ci.org/sgillies/affine .. image:: https://coveralls.io/repos/sgillies/affine/badge.svg :target: https://coveralls.io/r/sgillies/affine The Affine package is derived from Casey Duncan's Planar package. Please see the copyright statement in `affine/__init__.py `__. Usage ----- The 3x3 augmented affine transformation matrix for transformations in two dimensions is illustrated below. .. :: | x' | | a b c | | x | | y' | = | d e f | | y | | 1 | | 0 0 1 | | 1 | Matrices can be created by passing the values ``a, b, c, d, e, f`` to the ``affine.Affine`` constructor or by using its ``identity()``, ``translation()``, ``scale()``, ``shear()``, and ``rotation()`` class methods. .. code-block:: pycon >>> from affine import Affine >>> Affine.identity() Affine(1.0, 0.0, 0.0, 0.0, 1.0, 0.0) >>> Affine.translation(1.0, 5.0) Affine(1.0, 0.0, 1.0, 0.0, 1.0, 5.0) >>> Affine.scale(2.0) Affine(2.0, 0.0, 0.0, 0.0, 2.0, 0.0) >>> Affine.shear(45.0, 45.0) # decimal degrees Affine(1.0, 0.9999999999999999, 0.0, 0.9999999999999999, 1.0, 0.0) >>> Affine.rotation(45.0) # decimal degrees Affine(0.7071067811865476, 0.7071067811865475, 0.0, -0.7071067811865475, 0.7071067811865476, 0.0) These matrices can be applied to ``(x, y)`` tuples to obtain transformed coordinates ``(x', y')``. .. code-block:: pycon >>> Affine.translation(1.0, 5.0) * (1.0, 1.0) (2.0, 6.0) >>> Affine.rotation(45.0) * (1.0, 1.0) (1.1102230246251565e-16, 1.414213562373095) They may also be multiplied together to combine transformations. .. code-block:: pycon >>> Affine.translation(1.0, 5.0) * Affine.rotation(45.0) Affine(0.7071067811865476, 0.7071067811865475, 1.0, -0.7071067811865475, 0.7071067811865476, 5.0) Usage with GIS data packages ---------------------------- Georeferenced raster datasets use affine transformations to map from image coordinates to world coordinates. The ``affine.Affine.from_gdal()`` class method helps convert `GDAL GeoTransform `__, sequences of 6 numbers in which the first and fourth are the x and y offsets and the second and sixth are the x and y pixel sizes. Using a GDAL dataset transformation matrix, the world coordinates ``(x, y)`` corresponding to the top left corner of the pixel 100 rows down from the origin can be easily computed. .. code-block:: pycon >>> geotransform = (-237481.5, 425.0, 0.0, 237536.4, 0.0, -425.0) >>> fwd = Affine.from_gdal(*geotransform) >>> col, row = 0, 100 >>> fwd * (col, row) (-237481.5, 195036.4) The reverse transformation is obtained using the ``~`` operator. .. code-block:: pycon >>> rev = ~fwd >>> rev * fwd * (col, row) (0.0, 99.99999999999999) affine-2.0.0/affine/000077500000000000000000000000001271766707600142145ustar00rootroot00000000000000affine-2.0.0/affine/__init__.py000066400000000000000000000402261271766707600163310ustar00rootroot00000000000000"""Affine transformation matrices The 3x3 augmented affine transformation matrix for transformations in two dimensions is illustrated below. | x' | | a b c | | x | | y' | = | d e f | | y | | 1 | | 0 0 1 | | 1 | The Affine package is derived from Casey Duncan's Planar package. See the copyright statement below. """ ############################################################################# # Copyright (c) 2010 by Casey Duncan # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are met: # # * Redistributions of source code must retain the above copyright notice, # this list of conditions and the following disclaimer. # * 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. # * Neither the name(s) of the copyright holders nor the names of its # contributors may be used to endorse or promote products derived from this # software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 HOLDERS 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. ############################################################################# from __future__ import division from collections import namedtuple import math __all__ = ['Affine'] __author__ = "Sean Gillies" __version__ = "2.0.0" EPSILON = 1e-5 class TransformNotInvertibleError(Exception): """The transform could not be inverted""" # Define assert_unorderable() depending on the language # implicit ordering rules. This keeps things consistent # across major Python versions try: 3 > "" except TypeError: # pragma: no cover # No implicit ordering (newer Python) def assert_unorderable(a, b): """Assert that a and b are unorderable""" return NotImplemented else: # pragma: no cover # Implicit ordering by default (older Python) # We must raise an exception ourselves # To prevent nonsensical ordering def assert_unorderable(a, b): """Assert that a and b are unorderable""" raise TypeError("unorderable types: %s and %s" % (type(a).__name__, type(b).__name__)) def cached_property(func): """Special property decorator that caches the computed property value in the object's instance dict the first time it is accessed. """ name = func.__name__ doc = func.__doc__ def getter(self, name=name): try: return self.__dict__[name] except KeyError: self.__dict__[name] = value = func(self) return value getter.func_name = name return property(getter, doc=doc) def cos_sin_deg(deg): """Return the cosine and sin for the given angle in degrees. With special-case handling of multiples of 90 for perfect right angles. """ deg = deg % 360.0 if deg == 90.0: return 0.0, 1.0 elif deg == 180.0: return -1.0, 0 elif deg == 270.0: return 0, -1.0 rad = math.radians(deg) return math.cos(rad), math.sin(rad) class Affine( namedtuple('Affine', ('a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i'))): """Two dimensional affine transform for 2D linear mapping. Parallel lines are preserved by these transforms. Affine transforms can perform any combination of translations, scales/flips, shears, and rotations. Class methods are provided to conveniently compose transforms from these operations. Internally the transform is stored as a 3x3 transformation matrix. The transform may be constructed directly by specifying the first two rows of matrix values as 6 floats. Since the matrix is an affine transform, the last row is always ``(0, 0, 1)``. N.B.: multiplication of a transform and an (x, y) vector *always* returns the column vector that is the matrix multiplication product of the transform and (x, y) as a column vector, no matter which is on the left or right side. This is obviously not the case for matrices and vectors in general, but provides a convenience for users of this class. :param members: 6 floats for the first two matrix rows. :type members: float """ precision = EPSILON def __new__(self, *members): if len(members) == 6: mat3x3 = [x * 1.0 for x in members] + [0.0, 0.0, 1.0] return tuple.__new__(Affine, mat3x3) else: raise TypeError( "Expected 6 coefficients, found %d" % len(members)) @classmethod def from_gdal(cls, c, a, b, f, d, e): """Use same coefficient order as GDAL's GetGeoTransform(). :param c, a, b, f, d, e: 6 floats ordered by GDAL. :rtype: Affine """ members = [a, b, c, d, e, f] mat3x3 = [x * 1.0 for x in members] + [0.0, 0.0, 1.0] return tuple.__new__(cls, mat3x3) @classmethod def identity(cls): """Return the identity transform. :rtype: Affine """ return identity @classmethod def translation(cls, xoff, yoff): """Create a translation transform from an offset vector. :param xoff: Translation x offset. :type xoff: float :param yoff: Translation y offset. :type yoff: float :rtype: Affine """ return tuple.__new__( cls, (1.0, 0.0, xoff, 0.0, 1.0, yoff, 0.0, 0.0, 1.0)) @classmethod def scale(cls, *scaling): """Create a scaling transform from a scalar or vector. :param scaling: The scaling factor. A scalar value will scale in both dimensions equally. A vector scaling value scales the dimensions independently. :type scaling: float or sequence :rtype: Affine """ if len(scaling) == 1: sx = sy = float(scaling[0]) else: sx, sy = scaling return tuple.__new__( cls, (sx, 0.0, 0.0, 0.0, sy, 0.0, 0.0, 0.0, 1.0)) @classmethod def shear(cls, x_angle=0, y_angle=0): """Create a shear transform along one or both axes. :param x_angle: Shear angle in degrees parallel to the x-axis. :type x_angle: float :param y_angle: Shear angle in degrees parallel to the y-axis. :type y_angle: float :rtype: Affine """ mx = math.tan(math.radians(x_angle)) my = math.tan(math.radians(y_angle)) return tuple.__new__( cls, (1.0, mx, 0.0, my, 1.0, 0.0, 0.0, 0.0, 1.0)) @classmethod def rotation(cls, angle, pivot=None): """Create a rotation transform at the specified angle. A pivot point other than the coordinate system origin may be optionally specified. :param angle: Rotation angle in degrees, counter-clockwise about the pivot point. :type angle: float :param pivot: Point to rotate about, if omitted the rotation is about the origin. :type pivot: sequence :rtype: Affine """ ca, sa = cos_sin_deg(angle) if pivot is None: return tuple.__new__( cls, (ca, -sa, 0.0, sa, ca, 0.0, 0.0, 0.0, 1.0)) else: px, py = pivot return tuple.__new__( cls, (ca, -sa, px - px * ca + py * sa, sa, ca, py - px * sa - py * ca, 0.0, 0.0, 1.0)) def __str__(self): """Concise string representation.""" return ("|% .2f,% .2f,% .2f|\n" "|% .2f,% .2f,% .2f|\n" "|% .2f,% .2f,% .2f|") % self def __repr__(self): """Precise string representation.""" return ("Affine(%r, %r, %r,\n" " %r, %r, %r)") % self[:6] def to_gdal(self): """Return same coefficient order as GDAL's SetGeoTransform(). :rtype: tuple """ return (self.c, self.a, self.b, self.f, self.d, self.e) @property def xoff(self): """Alias for 'c'""" return self.c @property def yoff(self): """Alias for 'f'""" return self.f @cached_property def determinant(self): """The determinant of the transform matrix. This value is equal to the area scaling factor when the transform is applied to a shape. """ a, b, c, d, e, f, g, h, i = self return a * e - b * d @property def is_identity(self): """True if this transform equals the identity matrix, within rounding limits. """ return self is identity or self.almost_equals(identity, self.precision) @property def is_rectilinear(self): """True if the transform is rectilinear. i.e., whether a shape would remain axis-aligned, within rounding limits, after applying the transform. """ a, b, c, d, e, f, g, h, i = self return ((abs(a) < self.precision and abs(e) < self.precision) or (abs(d) < self.precision and abs(b) < self.precision)) @property def is_conformal(self): """True if the transform is conformal. i.e., if angles between points are preserved after applying the transform, within rounding limits. This implies that the transform has no effective shear. """ a, b, c, d, e, f, g, h, i = self return abs(a * b + d * e) < self.precision @property def is_orthonormal(self): """True if the transform is orthonormal. Which means that the transform represents a rigid motion, which has no effective scaling or shear. Mathematically, this means that the axis vectors of the transform matrix are perpendicular and unit-length. Applying an orthonormal transform to a shape always results in a congruent shape. """ a, b, c, d, e, f, g, h, i = self return (self.is_conformal and abs(1.0 - (a * a + d * d)) < self.precision and abs(1.0 - (b * b + e * e)) < self.precision) @cached_property def is_degenerate(self): """True if this transform is degenerate. Which means that it will collapse a shape to an effective area of zero. Degenerate transforms cannot be inverted. """ return self.determinant == 0.0 @property def column_vectors(self): """The values of the transform as three 2D column vectors""" a, b, c, d, e, f, _, _, _ = self return (a, d), (b, e), (c, f) def almost_equals(self, other, precision=EPSILON): """Compare transforms for approximate equality. :param other: Transform being compared. :type other: Affine :return: True if absolute difference between each element of each respective transform matrix < ``self.precision``. """ for i in (0, 1, 2, 3, 4, 5): if abs(self[i] - other[i]) >= precision: return False return True def __gt__(self, other): return assert_unorderable(self, other) __ge__ = __lt__ = __le__ = __gt__ # Override from base class. We do not support entrywise # addition, subtraction or scalar multiplication because # the result is not an affine transform def __add__(self, other): raise TypeError("Operation not supported") __iadd__ = __add__ def __mul__(self, other): """Apply the transform using matrix multiplication, creating a resulting object of the same type. A transform may be applied to another transform, a vector, vector array, or shape. :param other: The object to transform. :type other: Affine, :class:`~planar.Vec2`, :class:`~planar.Vec2Array`, :class:`~planar.Shape` :rtype: Same as ``other`` """ sa, sb, sc, sd, se, sf, _, _, _ = self if isinstance(other, Affine): oa, ob, oc, od, oe, of, _, _, _ = other return tuple.__new__( Affine, (sa * oa + sb * od, sa * ob + sb * oe, sa * oc + sb * of + sc, sd * oa + se * od, sd * ob + se * oe, sd * oc + se * of + sf, 0.0, 0.0, 1.0)) else: try: vx, vy = other except Exception: return NotImplemented return (vx * sa + vy * sb + sc, vx * sd + vy * se + sf) def __rmul__(self, other): # We should not be called if other is an affine instance # This is just a guarantee, since we would potentially # return the wrong answer in that case. assert not isinstance(other, Affine) return self.__mul__(other) def __imul__(self, other): if isinstance(other, Affine) or isinstance(other, tuple): return self.__mul__(other) else: return NotImplemented def itransform(self, seq): """Transform a sequence of points or vectors in place. :param seq: Mutable sequence of :class:`~planar.Vec2` to be transformed. :returns: None, the input sequence is mutated in place. """ if self is not identity and self != identity: sa, sb, sc, sd, se, sf, _, _, _ = self for i, (x, y) in enumerate(seq): seq[i] = (x * sa + y * sd + sc, x * sb + y * se + sf) def __invert__(self): """Return the inverse transform. :raises: :except:`TransformNotInvertible` if the transform is degenerate. """ if self.is_degenerate: raise TransformNotInvertibleError( "Cannot invert degenerate transform") idet = 1.0 / self.determinant sa, sb, sc, sd, se, sf, _, _, _ = self ra = se * idet rb = -sb * idet rd = -sd * idet re = sa * idet return tuple.__new__( Affine, (ra, rb, -sc * ra - sf * rb, rd, re, -sc * rd - sf * re, 0.0, 0.0, 1.0)) __hash__ = tuple.__hash__ # hash is not inherited in Py 3 def __getnewargs__(self): # Required for unpickling. # Normal unpickling creates a situation where __new__ receives all 9 # elements rather than the 6 that are required for the constructor. # This method ensures that only the 6 are provided. return self.a, self.b, self.c, self.d, self.e, self.f identity = Affine(1, 0, 0, 0, 1, 0) """The identity transform""" # Miscellaneous utilities def loadsw(s): """Returns Affine from the contents of a world file string. This method also translates the coefficients from from center- to corner-based coordinates. :param s: str with 6 floats ordered in a world file. :rtype: Affine """ if not hasattr(s, 'split'): raise TypeError("Cannot split input string") coeffs = s.split() if len(coeffs) != 6: raise ValueError("Expected 6 coefficients, found %d" % len(coeffs)) a, d, b, e, c, f = [float(x) for x in coeffs] center = tuple.__new__(Affine, [a, b, c, d, e, f, 0.0, 0.0, 1.0]) return center * Affine.translation(-0.5, -0.5) def dumpsw(obj): """Return string for a world file. This method also translates the coefficients from from corner- to center-based coordinates. :rtype: str """ center = obj * Affine.translation(0.5, 0.5) return '\n'.join(repr(getattr(center, x)) for x in list('adbecf')) + '\n' # vim: ai ts=4 sts=4 et sw=4 tw=78 affine-2.0.0/affine/tests/000077500000000000000000000000001271766707600153565ustar00rootroot00000000000000affine-2.0.0/affine/tests/__init__.py000066400000000000000000000000001271766707600174550ustar00rootroot00000000000000affine-2.0.0/affine/tests/test_pickle.py000066400000000000000000000013501271766707600202350ustar00rootroot00000000000000""" Validate that instances of `affine.Affine()` can be pickled and unpickled. """ import pickle from multiprocessing import Pool import affine def test_pickle(): a = affine.Affine(1, 2, 3, 4, 5, 6) assert pickle.loads(pickle.dumps(a)) == a def _mp_proc(x): # A helper function - needed for test_with_multiprocessing() # Can't be defined inside the test because multiprocessing needs # everything to be in __main__ assert isinstance(x, affine.Affine) return x def test_with_multiprocessing(): a1 = affine.Affine(1, 2, 3, 4, 5, 6) a2 = affine.Affine(6, 5, 4, 3, 2, 1) results = Pool(2).map(_mp_proc, [a1, a2]) for expected, actual in zip([a1, a2], results): assert expected == actual affine-2.0.0/affine/tests/test_rotation.py000066400000000000000000000024511271766707600206300ustar00rootroot00000000000000import math from affine import Affine def test_rotation_angle(): """A positive angle rotates a vector counter clockwise (1.0, 0.0): | | | | 0---------* Affine.rotation(45.0) * (1.0, 0.0) == (0.707..., 0.707...) | | * | | 0---------- """ x, y = Affine.rotation(45.0) * (1.0, 0.0) assert round(x, 14) == round(math.sqrt(2.0) / 2.0, 14) assert round(y, 14) == round(math.sqrt(2.0) / 2.0, 14) def test_rotation_matrix(): """A rotation matrix has expected elements | cos(a) -sin(a) | | sin(a) cos(a) | """ rot = Affine.rotation(90.0) assert round(rot.a, 15) == round(math.cos(math.pi/2.0), 15) assert round(rot.b, 15) == round(-math.sin(math.pi/2.0), 15) assert rot.c == 0.0 assert round(rot.d, 15) == round(math.sin(math.pi/2.0), 15) assert round(rot.e, 15) == round(math.cos(math.pi/2.0), 15) assert rot.f == 0.0 def test_rotation_matrix_pivot(): """A rotation matrix with pivot has expected elements""" rot = Affine.rotation(90.0, pivot=(1.0, 1.0)) exp = (Affine.translation(1.0, 1.0) * Affine.rotation(90.0) * Affine.translation(-1.0, -1.0)) for r, e in zip(rot, exp): assert round(r, 15) == round(e, 15) affine-2.0.0/affine/tests/test_transform.py000066400000000000000000000407631271766707600210140ustar00rootroot00000000000000############################################################################# # Planar is Copyright (c) 2010 by Casey Duncan # All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions are met: # # * Redistributions of source code must retain the above copyright notice, # this list of conditions and the following disclaimer. # * 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. # * Neither the name(s) of the copyright holders nor the names of its # contributors may be used to endorse or promote products derived from this # software without specific prior written permission. # # THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS 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 HOLDERS 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. ############################################################################# """Transform unit tests""" from __future__ import division import math import unittest from textwrap import dedent from nose.tools import assert_equal, assert_almost_equal, raises from affine import Affine, EPSILON def seq_almost_equal(t1, t2, error=0.00001): assert len(t1) == len(t2), "%r != %r" % (t1, t2) for m1, m2 in zip(t1, t2): assert abs(m1 - m2) <= error, "%r != %r" % (t1, t2) class PyAffineTestCase(unittest.TestCase): @raises(TypeError) def test_zero_args(self): Affine() @raises(TypeError) def test_wrong_arg_type(self): Affine(None) @raises(TypeError) def test_args_too_few(self): Affine(1, 2) @raises(TypeError) def test_args_too_many(self): Affine(*range(10)) @raises(TypeError) def test_args_members_wrong_type(self): Affine(0, 2, 3, None, None, "") def test_len(self): t = Affine(1, 2, 3, 4, 5, 6) assert_equal(len(t), 9) def test_slice_last_row(self): t = Affine(1, 2, 3, 4, 5, 6) assert_equal(t[-3:], (0, 0, 1)) def test_members_are_floats(self): t = Affine(1, 2, 3, 4, 5, 6) for m in t: assert isinstance(m, float), repr(m) def test_getitem(self): t = Affine(1, 2, 3, 4, 5, 6) assert_equal(t[0], 1) assert_equal(t[1], 2) assert_equal(t[2], 3) assert_equal(t[3], 4) assert_equal(t[4], 5) assert_equal(t[5], 6) assert_equal(t[6], 0) assert_equal(t[7], 0) assert_equal(t[8], 1) assert_equal(t[-1], 1) @raises(TypeError) def test_getitem_wrong_type(self): t = Affine(1, 2, 3, 4, 5, 6) t['foobar'] def test_str(self): assert_equal( str(Affine(1.111, 2.222, 3.333, -4.444, -5.555, 6.666)), "| 1.11, 2.22, 3.33|\n|-4.44,-5.55, 6.67|\n| 0.00, 0.00, 1.00|") def test_repr(self): assert_equal( repr(Affine(1.111, 2.222, 3.456, 4.444, 5.5, 6.25)), ("Affine(1.111, 2.222, 3.456,\n" " 4.444, 5.5, 6.25)")) def test_identity_constructor(self): ident = Affine.identity() assert isinstance(ident, Affine) assert_equal( tuple(ident), (1, 0, 0, 0, 1, 0, 0, 0, 1)) assert ident.is_identity def test_translation_constructor(self): trans = Affine.translation(2, -5) assert isinstance(trans, Affine) assert_equal( tuple(trans), (1, 0, 2, 0, 1, -5, 0, 0, 1)) def test_scale_constructor(self): scale = Affine.scale(5) assert isinstance(scale, Affine) assert_equal( tuple(scale), (5, 0, 0, 0, 5, 0, 0, 0, 1)) scale = Affine.scale(-1, 2) assert_equal( tuple(scale), (-1, 0, 0, 0, 2, 0, 0, 0, 1)) assert_equal(tuple(Affine.scale(1)), tuple(Affine.identity())) def test_shear_constructor(self): shear = Affine.shear(30) assert isinstance(shear, Affine) mx = math.tan(math.radians(30)) seq_almost_equal( tuple(shear), (1, mx, 0, 0, 1, 0, 0, 0, 1)) shear = Affine.shear(-15, 60) mx = math.tan(math.radians(-15)) my = math.tan(math.radians(60)) seq_almost_equal( tuple(shear), (1, mx, 0, my, 1, 0, 0, 0, 1)) shear = Affine.shear(y_angle=45) seq_almost_equal( tuple(shear), (1, 0, 0, 1, 1, 0, 0, 0, 1)) def test_rotation_constructor(self): rot = Affine.rotation(60) assert isinstance(rot, Affine) r = math.radians(60) s, c = math.sin(r), math.cos(r) assert_equal( tuple(rot), (c, -s, 0, s, c, 0, 0, 0, 1)) rot = Affine.rotation(337) r = math.radians(337) s, c = math.sin(r), math.cos(r) seq_almost_equal( tuple(rot), (c, -s, 0, s, c, 0, 0, 0, 1)) assert_equal(tuple(Affine.rotation(0)), tuple(Affine.identity())) def test_rotation_constructor_quadrants(self): assert_equal( tuple(Affine.rotation(0)), (1, 0, 0, 0, 1, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(90)), (0, -1, 0, 1, 0, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(180)), (-1, 0, 0, 0, -1, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(-180)), (-1, 0, 0, 0, -1, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(270)), (0, 1, 0, -1, 0, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(-90)), (0, 1, 0, -1, 0, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(360)), (1, 0, 0, 0, 1, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(450)), (0, -1, 0, 1, 0, 0, 0, 0, 1)) assert_equal( tuple(Affine.rotation(-450)), (0, 1, 0, -1, 0, 0, 0, 0, 1)) def test_rotation_constructor_with_pivot(self): assert_equal(tuple(Affine.rotation(60)), tuple(Affine.rotation(60, pivot=(0, 0)))) rot = Affine.rotation(27, pivot=(2, -4)) r = math.radians(27) s, c = math.sin(r), math.cos(r) assert_equal( tuple(rot), (c, -s, 2 - 2 * c - 4 * s, s, c, -4 - 2 * s + 4 * c, 0, 0, 1)) assert_equal(tuple(Affine.rotation(0, (-3, 2))), tuple(Affine.identity())) @raises(TypeError) def test_rotation_contructor_wrong_arg_types(self): Affine.rotation(1, 1) def test_determinant(self): assert_equal(Affine.identity().determinant, 1) assert_equal(Affine.scale(2).determinant, 4) assert_equal(Affine.scale(0).determinant, 0) assert_equal(Affine.scale(5, 1).determinant, 5) assert_equal(Affine.scale(-1, 1).determinant, -1) assert_equal(Affine.scale(-1, 0).determinant, 0) assert_almost_equal(Affine.rotation(77).determinant, 1) assert_almost_equal(Affine.translation(32, -47).determinant, 1) def test_is_rectilinear(self): assert Affine.identity().is_rectilinear assert Affine.scale(2.5, 6.1).is_rectilinear assert Affine.translation(4, -1).is_rectilinear assert Affine.rotation(90).is_rectilinear assert not Affine.shear(4, -1).is_rectilinear assert not Affine.rotation(-26).is_rectilinear def test_is_conformal(self): assert Affine.identity().is_conformal assert Affine.scale(2.5, 6.1).is_conformal assert Affine.translation(4, -1).is_conformal assert Affine.rotation(90).is_conformal assert Affine.rotation(-26).is_conformal assert not Affine.shear(4, -1).is_conformal def test_is_orthonormal(self): assert Affine.identity().is_orthonormal assert Affine.translation(4, -1).is_orthonormal assert Affine.rotation(90).is_orthonormal assert Affine.rotation(-26).is_orthonormal assert not Affine.scale(2.5, 6.1).is_orthonormal assert not Affine.scale(.5, 2).is_orthonormal assert not Affine.shear(4, -1).is_orthonormal def test_is_degenerate(self): assert not Affine.identity().is_degenerate assert not Affine.translation(2, -1).is_degenerate assert not Affine.shear(0, -22.5).is_degenerate assert not Affine.rotation(88.7).is_degenerate assert not Affine.scale(0.5).is_degenerate assert Affine.scale(0).is_degenerate assert Affine.scale(-10, 0).is_degenerate assert Affine.scale(0, 300).is_degenerate assert Affine.scale(0).is_degenerate assert Affine.scale(0).is_degenerate def test_column_vectors(self): a, b, c = Affine(2, 3, 4, 5, 6, 7).column_vectors assert isinstance(a, tuple) assert isinstance(b, tuple) assert isinstance(c, tuple) assert_equal(a, (2, 5)) assert_equal(b, (3, 6)) assert_equal(c, (4, 7)) def test_almost_equals(self): EPSILON = 1e-5 E = EPSILON * 0.5 t = Affine(1.0, E, 0, -E, 1.0 + E, E) assert t.almost_equals(Affine.identity()) assert Affine.identity().almost_equals(t) assert t.almost_equals(t) t = Affine(1.0, 0, 0, -EPSILON, 1.0, 0) assert not t.almost_equals(Affine.identity()) assert not Affine.identity().almost_equals(t) assert t.almost_equals(t) def test_almost_equals_2(self): EPSILON = 1e-10 E = EPSILON * 0.5 t = Affine(1.0, E, 0, -E, 1.0 + E, E) assert t.almost_equals(Affine.identity(), precision=EPSILON) assert Affine.identity().almost_equals(t, precision=EPSILON) assert t.almost_equals(t, precision=EPSILON) t = Affine(1.0, 0, 0, -EPSILON, 1.0, 0) assert not t.almost_equals(Affine.identity(), precision=EPSILON) assert not Affine.identity().almost_equals(t, precision=EPSILON) assert t.almost_equals(t, precision=EPSILON) def test_equality(self): t1 = Affine(1, 2, 3, 4, 5, 6) t2 = Affine(6, 5, 4, 3, 2, 1) t3 = Affine(1, 2, 3, 4, 5, 6) assert t1 == t3 assert not t1 == t2 assert t2 == t2 assert not t1 != t3 assert not t2 != t2 assert t1 != t2 assert not t1 == 1 assert t1 != 1 @raises(TypeError) def test_gt(self): Affine(1, 2, 3, 4, 5, 6) > Affine(6, 5, 4, 3, 2, 1) @raises(TypeError) def test_lt(self): Affine(1, 2, 3, 4, 5, 6) < Affine(6, 5, 4, 3, 2, 1) @raises(TypeError) def test_add(self): Affine(1, 2, 3, 4, 5, 6) + Affine(6, 5, 4, 3, 2, 1) @raises(TypeError) def test_sub(self): Affine(1, 2, 3, 4, 5, 6) - Affine(6, 5, 4, 3, 2, 1) def test_mul_by_identity(self): t = Affine(1, 2, 3, 4, 5, 6) assert_equal(tuple(t * Affine.identity()), tuple(t)) def test_mul_transform(self): t = Affine.rotation(5) * Affine.rotation(29) assert isinstance(t, Affine) seq_almost_equal(t, Affine.rotation(34)) t = Affine.scale(3, 5) * Affine.scale(2) seq_almost_equal(t, Affine.scale(6, 10)) def test_itransform(self): pts = [(4, 1), (-1, 0), (3, 2)] r = Affine.scale(-2).itransform(pts) assert r is None, r assert_equal(pts, [(-8, -2), (2, 0), (-6, -4)]) @raises(TypeError) def test_mul_wrong_type(self): Affine(1, 2, 3, 4, 5, 6) * None @raises(TypeError) def test_mul_sequence_wrong_member_types(self): class NotPtSeq: @classmethod def from_points(cls, points): list(points) def __iter__(self): yield 0 Affine(1, 2, 3, 4, 5, 6) * NotPtSeq() def test_imul_transform(self): t = Affine.translation(3, 5) t *= Affine.translation(-2, 3.5) assert isinstance(t, Affine) seq_almost_equal(t, Affine.translation(1, 8.5)) def test_inverse(self): seq_almost_equal(~Affine.identity(), Affine.identity()) seq_almost_equal( ~Affine.translation(2, -3), Affine.translation(-2, 3)) seq_almost_equal( ~Affine.rotation(-33.3), Affine.rotation(33.3)) t = Affine(1, 2, 3, 4, 5, 6) seq_almost_equal(~t * t, Affine.identity()) def test_cant_invert_degenerate(self): from affine import TransformNotInvertibleError t = Affine.scale(0) self.assertRaises(TransformNotInvertibleError, lambda: ~t) @raises(TypeError) def test_bad_type_world(self): from affine import loadsw # wrong type, i.e don't use readlines() loadsw(['1.0', '0.0', '0.0', '1.0', '0.0', '0.0']) @raises(ValueError) def test_bad_value_world(self): from affine import loadsw # wrong number of parameters loadsw('1.0\n0.0\n0.0\n1.0\n0.0\n0.0\n0.0') def test_simple_world(self): from affine import loadsw, dumpsw s = '1.0\n0.0\n0.0\n-1.0\n100.5\n199.5\n' a = loadsw(s) self.assertEqual( a, Affine( 1.0, 0.0, 100.0, 0.0, -1., 200.0)) self.assertEqual(dumpsw(a), s) def test_real_world(self): from affine import loadsw, dumpsw s = dedent('''\ 39.9317755024 30.0907511581 30.0907511576 -39.9317755019 2658137.2266720217 5990821.7039887439''') # no EOL a1 = loadsw(s) self.assertTrue(a1.almost_equals( Affine( 39.931775502364644, 30.090751157602412, 2658102.2154086917, 30.090751157602412, -39.931775502364644, 5990826.624500916))) a1out = dumpsw(a1) self.assertTrue(isinstance(a1out, str)) a2 = loadsw(a1out) self.assertTrue(a1.almost_equals(a2)) # We're using pytest for tests added after 1.0 and don't need unittest # test case classes. def test_gdal(): t = Affine.from_gdal(-237481.5, 425.0, 0.0, 237536.4, 0.0, -425.0) assert t.c == t.xoff == -237481.5 assert t.a == 425.0 assert t.b == 0.0 assert t.f == t.yoff == 237536.4 assert t.d == 0.0 assert t.e == -425.0 assert tuple(t) == (425.0, 0.0, -237481.5, 0.0, -425.0, 237536.4, 0, 0, 1.0) assert t.to_gdal() == (-237481.5, 425.0, 0.0, 237536.4, 0.0, -425.0) def test_imul_number(): t = Affine(1, 2, 3, 4, 5, 6) try: t *= 2.0 except TypeError: assert True def test_mul_tuple(): t = Affine(1, 2, 3, 4, 5, 6) t * (2.0, 2.0) def test_rmul_tuple(): t = Affine(1, 2, 3, 4, 5, 6) (2.0, 2.0) * t def test_transform_precision(): t = Affine.rotation(45.0) assert t.precision == EPSILON t.precision = 1e-10 assert t.precision == 1e-10 assert Affine.rotation(0.0).precision == EPSILON def test_associative(): point = (12, 5) trans = Affine.translation(-10., -5.) rot90 = Affine.rotation(90.) result1 = rot90 * (trans * point) result2 = (rot90 * trans) * point seq_almost_equal(result1, (0., 2.)) seq_almost_equal(result1, result2) def test_roundtrip(): point = (12, 5) trans = Affine.translation(3, 4) rot37 = Affine.rotation(37.) point_prime = (trans * rot37) * point roundtrip_point = ~(trans * rot37) * point_prime seq_almost_equal(point, roundtrip_point) if __name__ == '__main__': unittest.main() # vim: ai ts=4 sts=4 et sw=4 tw=78 affine-2.0.0/setup.py000077500000000000000000000016741271766707600145110ustar00rootroot00000000000000from codecs import open as codecs_open from setuptools import setup, find_packages # Parse the version from the affine module. with open('affine/__init__.py') as f: for line in f: if "__version__" in line: version = line.split("=")[1].strip() version = version.strip('"').strip("'") break with codecs_open('README.rst', encoding='utf-8') as f: readme = f.read() setup(name='affine', version=version, description="Matrices describing affine transformation of the plane", long_description=readme, classifiers=[], keywords='affine transformation matrix', author='Sean Gillies', author_email='sean@mapbox.com', url='https://github.com/sgillies/affine', license='BSD', packages=find_packages(exclude=['ez_setup', 'examples', 'tests']), include_package_data=True, zip_safe=False, extras_require = {'test': ['pytest']} ) affine-2.0.0/tox.ini000066400000000000000000000003031271766707600142730ustar00rootroot00000000000000[tox] envlist = py27,py34,py35 [testenv] usedevelop = true deps = nose pytest-cov responses commands = python -m pytest affine/tests --cov affine --cov-report term-missing