Source code for fontTools.misc.transform

"""Affine 2D transformation matrix class.

The Transform class implements various transformation matrix operations,
both on the matrix itself, as well as on 2D coordinates.

Transform instances are effectively immutable: all methods that operate on the
transformation itself always return a new instance. This has as the
interesting side effect that Transform instances are hashable, ie. they can be
used as dictionary keys.

This module exports the following symbols:

	Transform -- this is the main class
	Identity  -- Transform instance set to the identity transformation
	Offset    -- Convenience function that returns a translating transformation
	Scale     -- Convenience function that returns a scaling transformation

Examples:

	>>> t = Transform(2, 0, 0, 3, 0, 0)
	>>> t.transformPoint((100, 100))
	(200, 300)
	>>> t = Scale(2, 3)
	>>> t.transformPoint((100, 100))
	(200, 300)
	>>> t.transformPoint((0, 0))
	(0, 0)
	>>> t = Offset(2, 3)
	>>> t.transformPoint((100, 100))
	(102, 103)
	>>> t.transformPoint((0, 0))
	(2, 3)
	>>> t2 = t.scale(0.5)
	>>> t2.transformPoint((100, 100))
	(52.0, 53.0)
	>>> import math
	>>> t3 = t2.rotate(math.pi / 2)
	>>> t3.transformPoint((0, 0))
	(2.0, 3.0)
	>>> t3.transformPoint((100, 100))
	(-48.0, 53.0)
	>>> t = Identity.scale(0.5).translate(100, 200).skew(0.1, 0.2)
	>>> t.transformPoints([(0, 0), (1, 1), (100, 100)])
	[(50.0, 100.0), (50.550167336042726, 100.60135501775433), (105.01673360427253, 160.13550177543362)]
	>>>
"""

from __future__ import print_function, division, absolute_import
from fontTools.misc.py23 import *

__all__ = ["Transform", "Identity", "Offset", "Scale"]


_EPSILON = 1e-15
_ONE_EPSILON = 1 - _EPSILON
_MINUS_ONE_EPSILON = -1 + _EPSILON


def _normSinCos(v):
	if abs(v) < _EPSILON:
		v = 0
	elif v > _ONE_EPSILON:
		v = 1
	elif v < _MINUS_ONE_EPSILON:
		v = -1
	return v


[docs]class Transform(object): """2x2 transformation matrix plus offset, a.k.a. Affine transform. Transform instances are immutable: all transforming methods, eg. rotate(), return a new Transform instance. Examples: >>> t = Transform() >>> t <Transform [1 0 0 1 0 0]> >>> t.scale(2) <Transform [2 0 0 2 0 0]> >>> t.scale(2.5, 5.5) <Transform [2.5 0 0 5.5 0 0]> >>> >>> t.scale(2, 3).transformPoint((100, 100)) (200, 300) """ def __init__(self, xx=1, xy=0, yx=0, yy=1, dx=0, dy=0): """Transform's constructor takes six arguments, all of which are optional, and can be used as keyword arguments: >>> Transform(12) <Transform [12 0 0 1 0 0]> >>> Transform(dx=12) <Transform [1 0 0 1 12 0]> >>> Transform(yx=12) <Transform [1 0 12 1 0 0]> >>> """ self.__affine = xx, xy, yx, yy, dx, dy
[docs] def transformPoint(self, p): """Transform a point. Example: >>> t = Transform() >>> t = t.scale(2.5, 5.5) >>> t.transformPoint((100, 100)) (250.0, 550.0) """ (x, y) = p xx, xy, yx, yy, dx, dy = self.__affine return (xx*x + yx*y + dx, xy*x + yy*y + dy)
[docs] def transformPoints(self, points): """Transform a list of points. Example: >>> t = Scale(2, 3) >>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)]) [(0, 0), (0, 300), (200, 300), (200, 0)] >>> """ xx, xy, yx, yy, dx, dy = self.__affine return [(xx*x + yx*y + dx, xy*x + yy*y + dy) for x, y in points]
[docs] def translate(self, x=0, y=0): """Return a new transformation, translated (offset) by x, y. Example: >>> t = Transform() >>> t.translate(20, 30) <Transform [1 0 0 1 20 30]> >>> """ return self.transform((1, 0, 0, 1, x, y))
[docs] def scale(self, x=1, y=None): """Return a new transformation, scaled by x, y. The 'y' argument may be None, which implies to use the x value for y as well. Example: >>> t = Transform() >>> t.scale(5) <Transform [5 0 0 5 0 0]> >>> t.scale(5, 6) <Transform [5 0 0 6 0 0]> >>> """ if y is None: y = x return self.transform((x, 0, 0, y, 0, 0))
[docs] def rotate(self, angle): """Return a new transformation, rotated by 'angle' (radians). Example: >>> import math >>> t = Transform() >>> t.rotate(math.pi / 2) <Transform [0 1 -1 0 0 0]> >>> """ import math c = _normSinCos(math.cos(angle)) s = _normSinCos(math.sin(angle)) return self.transform((c, s, -s, c, 0, 0))
[docs] def skew(self, x=0, y=0): """Return a new transformation, skewed by x and y. Example: >>> import math >>> t = Transform() >>> t.skew(math.pi / 4) <Transform [1 0 1 1 0 0]> >>> """ import math return self.transform((1, math.tan(y), math.tan(x), 1, 0, 0))
[docs] def transform(self, other): """Return a new transformation, transformed by another transformation. Example: >>> t = Transform(2, 0, 0, 3, 1, 6) >>> t.transform((4, 3, 2, 1, 5, 6)) <Transform [8 9 4 3 11 24]> >>> """ xx1, xy1, yx1, yy1, dx1, dy1 = other xx2, xy2, yx2, yy2, dx2, dy2 = self.__affine return self.__class__( xx1*xx2 + xy1*yx2, xx1*xy2 + xy1*yy2, yx1*xx2 + yy1*yx2, yx1*xy2 + yy1*yy2, xx2*dx1 + yx2*dy1 + dx2, xy2*dx1 + yy2*dy1 + dy2)
[docs] def reverseTransform(self, other): """Return a new transformation, which is the other transformation transformed by self. self.reverseTransform(other) is equivalent to other.transform(self). Example: >>> t = Transform(2, 0, 0, 3, 1, 6) >>> t.reverseTransform((4, 3, 2, 1, 5, 6)) <Transform [8 6 6 3 21 15]> >>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6)) <Transform [8 6 6 3 21 15]> >>> """ xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine xx2, xy2, yx2, yy2, dx2, dy2 = other return self.__class__( xx1*xx2 + xy1*yx2, xx1*xy2 + xy1*yy2, yx1*xx2 + yy1*yx2, yx1*xy2 + yy1*yy2, xx2*dx1 + yx2*dy1 + dx2, xy2*dx1 + yy2*dy1 + dy2)
[docs] def inverse(self): """Return the inverse transformation. Example: >>> t = Identity.translate(2, 3).scale(4, 5) >>> t.transformPoint((10, 20)) (42, 103) >>> it = t.inverse() >>> it.transformPoint((42, 103)) (10.0, 20.0) >>> """ if self.__affine == (1, 0, 0, 1, 0, 0): return self xx, xy, yx, yy, dx, dy = self.__affine det = xx*yy - yx*xy xx, xy, yx, yy = yy/det, -xy/det, -yx/det, xx/det dx, dy = -xx*dx - yx*dy, -xy*dx - yy*dy return self.__class__(xx, xy, yx, yy, dx, dy)
[docs] def toPS(self): """Return a PostScript representation: >>> t = Identity.scale(2, 3).translate(4, 5) >>> t.toPS() '[2 0 0 3 8 15]' >>> """ return "[%s %s %s %s %s %s]" % self.__affine
def __len__(self): """Transform instances also behave like sequences of length 6: >>> len(Identity) 6 >>> """ return 6 def __getitem__(self, index): """Transform instances also behave like sequences of length 6: >>> list(Identity) [1, 0, 0, 1, 0, 0] >>> tuple(Identity) (1, 0, 0, 1, 0, 0) >>> """ return self.__affine[index] def __ne__(self, other): return not self.__eq__(other) def __eq__(self, other): """Transform instances are comparable: >>> t1 = Identity.scale(2, 3).translate(4, 6) >>> t2 = Identity.translate(8, 18).scale(2, 3) >>> t1 == t2 1 >>> But beware of floating point rounding errors: >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6) >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3) >>> t1 <Transform [0.2 0 0 0.3 0.08 0.18]> >>> t2 <Transform [0.2 0 0 0.3 0.08 0.18]> >>> t1 == t2 0 >>> """ xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine xx2, xy2, yx2, yy2, dx2, dy2 = other return (xx1, xy1, yx1, yy1, dx1, dy1) == \ (xx2, xy2, yx2, yy2, dx2, dy2) def __hash__(self): """Transform instances are hashable, meaning you can use them as keys in dictionaries: >>> d = {Scale(12, 13): None} >>> d {<Transform [12 0 0 13 0 0]>: None} >>> But again, beware of floating point rounding errors: >>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6) >>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3) >>> t1 <Transform [0.2 0 0 0.3 0.08 0.18]> >>> t2 <Transform [0.2 0 0 0.3 0.08 0.18]> >>> d = {t1: None} >>> d {<Transform [0.2 0 0 0.3 0.08 0.18]>: None} >>> d[t2] Traceback (most recent call last): File "<stdin>", line 1, in ? KeyError: <Transform [0.2 0 0 0.3 0.08 0.18]> >>> """ return hash(self.__affine) def __bool__(self): """Returns True if transform is not identity, False otherwise. >>> bool(Identity) False >>> bool(Transform()) False >>> bool(Scale(1.)) False >>> bool(Scale(2)) True >>> bool(Offset()) False >>> bool(Offset(0)) False >>> bool(Offset(2)) True """ return self.__affine != Identity.__affine __nonzero__ = __bool__ def __repr__(self): return "<%s [%g %g %g %g %g %g]>" % ((self.__class__.__name__,) \ + self.__affine)
Identity = Transform()
[docs]def Offset(x=0, y=0): """Return the identity transformation offset by x, y. Example: >>> Offset(2, 3) <Transform [1 0 0 1 2 3]> >>> """ return Transform(1, 0, 0, 1, x, y)
[docs]def Scale(x, y=None): """Return the identity transformation scaled by x, y. The 'y' argument may be None, which implies to use the x value for y as well. Example: >>> Scale(2, 3) <Transform [2 0 0 3 0 0]> >>> """ if y is None: y = x return Transform(x, 0, 0, y, 0, 0)
if __name__ == "__main__": import sys import doctest sys.exit(doctest.testmod().failed)