f184f75486
git-svn-id: svn://svn.code.sf.net/p/fonttools/code/trunk@454 4cde692c-a291-49d1-8350-778aa11640f8
286 lines
6.9 KiB
Python
Executable File
286 lines
6.9 KiB
Python
Executable File
"""Affine 2D transformation matrix class.
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The Transform class implements various transformation matrix operations,
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both on the matrix itself, as well as on 2D coordinates.
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Transform instances are effectively immutable: all methods that operate on the
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transformation itself always return a new instance. This has as the
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interesting side effect that Transform instances are hashable, ie. they can be
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used as dictionary keys.
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This module exports the following symbols:
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Transform -- this is the main class
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Identity -- Transform instance set to the identity transformation
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Offset -- Convenience function that returns a translating transformation
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Scale -- Convenience function that returns a scaling transformation
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Examples:
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>>> t = Transform(2, 0, 0, 3, 0, 0)
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>>> t.transformPoint((100, 100))
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(200, 300)
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>>> t = Scale(2, 3)
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>>> t.transformPoint((100, 100))
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(200, 300)
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>>> t.transformPoint((0, 0))
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(0, 0)
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>>> t = Offset(2, 3)
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>>> t.transformPoint((100, 100))
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(102, 103)
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>>> t.transformPoint((0, 0))
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(2, 3)
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>>> t2 = t.scale(0.5)
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>>> t2.transformPoint((100, 100))
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(52.0, 53.0)
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>>> import math
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>>> t3 = t2.rotate(math.pi / 2)
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>>> t3.transformPoint((0, 0))
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(2.0, 3.0)
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>>> t3.transformPoint((100, 100))
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(-48.0, 53.0)
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>>> t = Identity.scale(0.5).translate(100, 200).skew(0.1, 0.2)
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>>> t.transformPoints([(0, 0), (1, 1), (100, 100)])
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[(50.0, 100.0), (50.550167336042726, 100.60135501775433), (105.01673360427253, 160.13550177543362)]
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>>>
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"""
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__all__ = ["Transform", "Identity", "Offset", "Scale"]
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_EPSILON = 1e-15
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_ONE_EPSILON = 1 - _EPSILON
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_MINUS_ONE_EPSILON = -1 + _EPSILON
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def _normSinCos(v):
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if abs(v) < _EPSILON:
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v = 0
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elif v > _ONE_EPSILON:
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v = 1
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elif v < _MINUS_ONE_EPSILON:
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v = -1
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return v
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class Transform:
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"""2x2 transformation matrix plus offset, a.k.a. Affine transform.
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Transform instances are immutable: all transforming methods, eg.
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rotate(), return a new Transform instance.
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Examples:
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>>> t = Transform()
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>>> t
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<Transform [1 0 0 1 0 0]>
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>>> t.scale(2)
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<Transform [2 0 0 2 0 0]>
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>>> t.scale(2.5, 5.5)
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<Transform [2.5 0.0 0.0 5.5 0 0]>
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>>>
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>>> t.scale(2, 3).transformPoint((100, 100))
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(200, 300)
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"""
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def __init__(self, xx=1, xy=0, yx=0, yy=1, dx=0, dy=0):
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self.__affine = xx, xy, yx, yy, dx, dy
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def transformPoint(self, (x, y)):
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"""Transform a point.
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Example:
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>>> t = Transform()
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>>> t = t.scale(2.5, 5.5)
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>>> t.transformPoint((100, 100))
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(250.0, 550.0)
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"""
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xx, xy, yx, yy, dx, dy = self.__affine
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return (xx*x + yx*y + dx, xy*x + yy*y + dy)
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def transformPoints(self, points):
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"""Transform a list of points.
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Example:
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>>> t = Scale(2, 3)
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>>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)])
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[(0, 0), (0, 300), (200, 300), (200, 0)]
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>>>
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"""
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xx, xy, yx, yy, dx, dy = self.__affine
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return [(xx*x + yx*y + dx, xy*x + yy*y + dy) for x, y in points]
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def translate(self, x=0, y=0):
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"""Return a new transformation, translated (offset) by x, y.
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Example:
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>>> t = Transform()
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>>> t.translate(20, 30)
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<Transform [1 0 0 1 20 30]>
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>>>
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"""
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return self.transform((1, 0, 0, 1, x, y))
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def scale(self, x=1, y=None):
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"""Return a new transformation, scaled by x, y. The 'y' argument
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may be None, which implies to use the x value for y as well.
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Example:
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>>> t = Transform()
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>>> t.scale(5)
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<Transform [5 0 0 5 0 0]>
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>>> t.scale(5, 6)
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<Transform [5 0 0 6 0 0]>
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>>>
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"""
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if y is None:
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y = x
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return self.transform((x, 0, 0, y, 0, 0))
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def rotate(self, angle):
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"""Return a new transformation, rotated by 'angle' (radians).
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Example:
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>>> import math
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>>> t = Transform()
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>>> t.rotate(math.pi / 2)
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<Transform [0 1 -1 0 0 0]>
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>>>
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"""
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import math
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c = _normSinCos(math.cos(angle))
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s = _normSinCos(math.sin(angle))
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return self.transform((c, s, -s, c, 0, 0))
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def skew(self, x=0, y=0):
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"""Return a new transformation, skewed by x and y.
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Example:
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>>> import math
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>>> t = Transform()
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>>> t.skew(math.pi / 4)
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<Transform [1.0 0.0 1.0 1.0 0 0]>
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>>>
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"""
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import math
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return self.transform((1, math.tan(y), math.tan(x), 1, 0, 0))
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def transform(self, other):
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"""Return a new transformation, transformed by another
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transformation.
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Example:
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>>> t = Transform(2, 0, 0, 3, 1, 6)
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>>> t.transform((4, 3, 2, 1, 5, 6))
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<Transform [8 9 4 3 11 24]>
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>>>
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"""
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xx1, xy1, yx1, yy1, dx1, dy1 = other
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xx2, xy2, yx2, yy2, dx2, dy2 = self.__affine
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return self.__class__(
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xx1*xx2 + xy1*yx2,
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xx1*xy2 + xy1*yy2,
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yx1*xx2 + yy1*yx2,
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yx1*xy2 + yy1*yy2,
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xx2*dx1 + yx2*dy1 + dx2,
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xy2*dx1 + yy2*dy1 + dy2)
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def reverseTransform(self, other):
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"""Return a new transformation, which is the other transformation
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transformed by self. self.reverseTransform(other) is equivalent to
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other.transform(self).
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Example:
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>>> t = Transform(2, 0, 0, 3, 1, 6)
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>>> t.reverseTransform((4, 3, 2, 1, 5, 6))
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<Transform [8 6 6 3 21 15]>
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>>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6))
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<Transform [8 6 6 3 21 15]>
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>>>
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"""
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xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine
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xx2, xy2, yx2, yy2, dx2, dy2 = other
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return self.__class__(
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xx1*xx2 + xy1*yx2,
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xx1*xy2 + xy1*yy2,
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yx1*xx2 + yy1*yx2,
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yx1*xy2 + yy1*yy2,
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xx2*dx1 + yx2*dy1 + dx2,
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xy2*dx1 + yy2*dy1 + dy2)
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def inverse(self):
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"""Return the inverse transformation.
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Example:
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>>> t = Transform(2, 0, 0, 3, 1, 6)
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>>> t.inverse()
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<Transform [0.5 0.0 0.0 0.333333333333 -0.5 -2.0]>
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>>>
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"""
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if self.__affine == (1, 0, 0, 1, 0, 0):
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return self
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xx, xy, yx, yy, dx, dy = self.__affine
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det = float(xx*yy - yx*xy)
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xx, xy, yx, yy = yy/det, -xy/det, -yx/det, xx/det
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dx, dy = -xx*dx - yx*dy, -xy*dx - yy*dy
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return self.__class__(xx, xy, yx, yy, dx, dy)
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def toPS(self):
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return "[%s %s %s %s %s %s]" % self.__affine
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def __len__(self):
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return 6
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def __getitem__(self, index):
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return self.__affine[index]
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def __getslice__(self, i, j):
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return self.__affine[i:j]
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def __cmp__(self, other):
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xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine
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xx2, xy2, yx2, yy2, dx2, dy2 = other
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return cmp((xx1, xy1, yx1, yy1, dx1, dy1),
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(xx2, xy2, yx2, yy2, dx2, dy2))
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def __hash__(self):
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return hash(self.__affine)
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def __repr__(self):
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return "<%s [%s %s %s %s %s %s]>" % ((self.__class__.__name__,)
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+ tuple(map(str, self.__affine)))
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Identity = Transform()
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def Offset(x=0, y=0):
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"""Return the identity transformation offset by x, y.
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Example:
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>>> Offset(2, 3)
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<Transform [1 0 0 1 2 3]>
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>>>
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"""
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return Transform(1, 0, 0, 1, x, y)
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def Scale(x, y=None):
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"""Return the identity transformation scaled by x, y. The 'y' argument
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may be None, which implies to use the x value for y as well.
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Example:
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>>> Scale(2, 3)
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<Transform [2 0 0 3 0 0]>
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>>>
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"""
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if y is None:
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y = x
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return Transform(x, 0, 0, y, 0, 0)
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def _test():
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import doctest, fontTools.misc.transform
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return doctest.testmod(fontTools.misc.transform)
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if __name__ == "__main__":
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_test()
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