3 The Transform class implements various transformation matrix operations,
6 Transform instances are effectively immutable: all methods that operate on the
8 interesting side effect that Transform instances are hashable, ie. they can be
13 Transform
16 	Transform instance set to the identity transformation
27 	>>> t = Transform(2, 0, 0, 3, 0, 0)
60 __all__ = ["Transform", "Identity", "Offset", "Scale", "DecomposedTransform"]
78 class Transform(NamedTuple):  class
79     """2x2 transformation matrix plus offset, a.k.a. Affine transform.
80     Transform instances are immutable: all transforming methods, eg.
81     rotate(), return a new Transform instance.
85             >>> t = Transform()
87             <Transform [1 0 0 1 0 0]>
89             <Transform [2 0 0 2 0 0]>
91             <Transform [2.5 0 0 5.5 0 0]>
96     Transform's constructor takes six arguments, all of which are
99             >>> Transform(12)
100             <Transform [12 0 0 1 0 0]>
101             >>> Transform(dx=12)
102             <Transform [1 0 0 1 12 0]>
103             >>> Transform(yx=12)
104             <Transform [1 0 12 1 0 0]>
106     Transform instances also behave like sequences of length 6::
115     Transform instances are comparable::
127             <Transform [0.2 0 0 0.3 0.08 0.18]>
129             <Transform [0.2 0 0 0.3 0.08 0.18]>
133     Transform instances are hashable, meaning you can use them as
138             {<Transform [12 0 0 13 0 0]>: None}
145             <Transform [0.2 0 0 0.3 0.08 0.18]>
147             <Transform [0.2 0 0 0.3 0.08 0.18]>
150             {<Transform [0.2 0 0 0.3 0.08 0.18]>: None}
154             KeyError: <Transform [0.2 0 0 0.3 0.08 0.18]>
165         """Transform a point.
169                 >>> t = Transform()
179         """Transform a list of points.
192         """Transform an (dx, dy) vector, treating translation as zero.
196                 >>> t = Transform(2, 0, 0, 2, 10, 20)
206         """Transform a list of (dx, dy) vector, treating translation as zero.
209                 >>> t = Transform(2, 0, 0, 2, 10, 20)
221                 >>> t = Transform()
223                 <Transform [1 0 0 1 20 30]>
226         return self.transform((1, 0, 0, 1, x, y))
233                 >>> t = Transform()
235                 <Transform [5 0 0 5 0 0]>
237                 <Transform [5 0 0 6 0 0]>
242         return self.transform((x, 0, 0, y, 0, 0))
249                 >>> t = Transform()
251                 <Transform [0 1 -1 0 0 0]>
258         return self.transform((c, s, -s, c, 0, 0))
265                 >>> t = Transform()
267                 <Transform [1 0 1 1 0 0]>
272         return self.transform((1, math.tan(y), math.tan(x), 1, 0, 0))
274     def transform(self, other):  member in Transform
279                 >>> t = Transform(2, 0, 0, 3, 1, 6)
280                 >>> t.transform((4, 3, 2, 1, 5, 6))
281                 <Transform [8 9 4 3 11 24]>
298         other.transform(self).
301                 >>> t = Transform(2, 0, 0, 3, 1, 6)
303                 <Transform [8 6 6 3 21 15]>
304                 >>> Transform(4, 3, 2, 1, 5, 6).transform((2, 0, 0, 3, 1, 6))
305                 <Transform [8 6 6 3 21 15]>
356         """Returns True if transform is not identity, False otherwise.
362                 >>> bool(Transform())
381 Identity = Transform()
389             <Transform [1 0 0 1 2 3]>
392     return Transform(1, 0, 0, 1, x, y)
401             <Transform [2 0 0 3 0 0]>
406     return Transform(x, 0, 0, y, 0, 0)
426     def fromTransform(self, transform):  argument
429         a, b, c, d, x, y = transform
472         """Return the Transform() equivalent of this transformation.
476                 <Transform [2 0 0 2 0 0]>
479         t = Transform()