dbc9d132c0
This removes some boilerplate code, and also helps when using static type checkers like mypy. The typing.NamedTuple class was added with python 3.6 which is our min required python, so we are good.
356 lines
8.4 KiB
Python
356 lines
8.4 KiB
Python
"""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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from typing import NamedTuple
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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(NamedTuple):
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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 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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Transform's constructor takes six arguments, all of which are
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optional, and can be used as keyword arguments:
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>>> Transform(12)
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<Transform [12 0 0 1 0 0]>
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>>> Transform(dx=12)
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<Transform [1 0 0 1 12 0]>
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>>> Transform(yx=12)
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<Transform [1 0 12 1 0 0]>
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Transform instances also behave like sequences of length 6:
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>>> len(Identity)
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6
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>>> list(Identity)
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[1, 0, 0, 1, 0, 0]
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>>> tuple(Identity)
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(1, 0, 0, 1, 0, 0)
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Transform instances are comparable:
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>>> t1 = Identity.scale(2, 3).translate(4, 6)
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>>> t2 = Identity.translate(8, 18).scale(2, 3)
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>>> t1 == t2
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1
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But beware of floating point rounding errors:
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>>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
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>>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
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>>> t1
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<Transform [0.2 0 0 0.3 0.08 0.18]>
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>>> t2
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<Transform [0.2 0 0 0.3 0.08 0.18]>
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>>> t1 == t2
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0
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Transform instances are hashable, meaning you can use them as
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keys in dictionaries:
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>>> d = {Scale(12, 13): None}
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>>> d
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{<Transform [12 0 0 13 0 0]>: None}
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But again, beware of floating point rounding errors:
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>>> t1 = Identity.scale(0.2, 0.3).translate(0.4, 0.6)
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>>> t2 = Identity.translate(0.08, 0.18).scale(0.2, 0.3)
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>>> t1
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<Transform [0.2 0 0 0.3 0.08 0.18]>
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>>> t2
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<Transform [0.2 0 0 0.3 0.08 0.18]>
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>>> d = {t1: None}
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>>> d
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{<Transform [0.2 0 0 0.3 0.08 0.18]>: None}
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>>> d[t2]
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Traceback (most recent call last):
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File "<stdin>", line 1, in ?
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KeyError: <Transform [0.2 0 0 0.3 0.08 0.18]>
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"""
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xx: float = 1
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xy: float = 0
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yx: float = 0
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yy: float = 1
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dx: float = 0
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dy: float = 0
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def transformPoint(self, p):
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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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(x, y) = p
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xx, xy, yx, yy, dx, dy = self
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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
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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 1 1 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
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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
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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 = Identity.translate(2, 3).scale(4, 5)
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>>> t.transformPoint((10, 20))
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(42, 103)
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>>> it = t.inverse()
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>>> it.transformPoint((42, 103))
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(10.0, 20.0)
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>>>
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"""
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if self == Identity:
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return self
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xx, xy, yx, yy, dx, dy = self
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det = 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 a PostScript representation:
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>>> t = Identity.scale(2, 3).translate(4, 5)
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>>> t.toPS()
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'[2 0 0 3 8 15]'
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>>>
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"""
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return "[%s %s %s %s %s %s]" % self
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def __bool__(self):
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"""Returns True if transform is not identity, False otherwise.
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>>> bool(Identity)
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False
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>>> bool(Transform())
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False
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>>> bool(Scale(1.))
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False
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>>> bool(Scale(2))
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True
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>>> bool(Offset())
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False
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>>> bool(Offset(0))
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False
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>>> bool(Offset(2))
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True
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"""
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return self != Identity
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__nonzero__ = __bool__
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def __repr__(self):
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return "<%s [%g %g %g %g %g %g]>" % ((self.__class__.__name__,) + self)
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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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if __name__ == "__main__":
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import sys
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import doctest
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sys.exit(doctest.testmod().failed)
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