Skip to content

Instantly share code, notes, and snippets.

@madig
Created April 29, 2020 09:56
Show Gist options
  • Save madig/459ba7775aff7b9f3ba16e0aff7b65cc to your computer and use it in GitHub Desktop.
Save madig/459ba7775aff7b9f3ba16e0aff7b65cc to your computer and use it in GitHub Desktop.
transform named tuple
"""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)]
>>>
"""
_EPSILON = 1e-15
_ONE_EPSILON = 1 - _EPSILON
_MINUS_ONE_EPSILON = -1 + _EPSILON
import typing as t
def _normSinCos(v):
if abs(v) < _EPSILON:
v = 0
elif v > _ONE_EPSILON:
v = 1
elif v < _MINUS_ONE_EPSILON:
v = -1
return v
class Transform(t.NamedTuple):
"""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)
"""
xx: float = 1
xy: float = 0
yx: float = 0
yy: float = 1
dx: float = 0
dy: float = 0
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
return (xx * x + yx * y + dx, xy * x + yy * y + dy)
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
return [(xx * x + yx * y + dx, xy * x + yy * y + dy) for x, y in points]
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))
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))
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))
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))
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
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,
)
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
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,
)
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 == (1, 0, 0, 1, 0, 0):
return self
xx, xy, yx, yy, dx, dy = self
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)
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
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[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
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)
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 != Identity.__affine
def __nonzero__(self):
return bool(self)
def __repr__(self):
return "<%s [%g %g %g %g %g %g]>" % ((self.__class__.__name__,) + self)
Identity = Transform()
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)
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)
def test(transf: t.Tuple[float, float, float, float, float, float]):
pass
test(Transform(1, 2, 3, 4, 5, 6))
test((1, 2, 3, 4, 5, 6))
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment