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-rw-r--r--Lib/fontTools/misc/transform.py93
1 files changed, 69 insertions, 24 deletions
diff --git a/Lib/fontTools/misc/transform.py b/Lib/fontTools/misc/transform.py
index 997598f5..94e1f622 100644
--- a/Lib/fontTools/misc/transform.py
+++ b/Lib/fontTools/misc/transform.py
@@ -10,12 +10,16 @@ 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
+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:
+:Example:
>>> t = Transform(2, 0, 0, 3, 0, 0)
>>> t.transformPoint((100, 100))
@@ -72,7 +76,8 @@ class Transform(NamedTuple):
Transform instances are immutable: all transforming methods, eg.
rotate(), return a new Transform instance.
- Examples:
+ :Example:
+
>>> t = Transform()
>>> t
<Transform [1 0 0 1 0 0]>
@@ -85,7 +90,8 @@ class Transform(NamedTuple):
(200, 300)
Transform's constructor takes six arguments, all of which are
- optional, and can be used as keyword arguments:
+ optional, and can be used as keyword arguments::
+
>>> Transform(12)
<Transform [12 0 0 1 0 0]>
>>> Transform(dx=12)
@@ -93,7 +99,8 @@ class Transform(NamedTuple):
>>> Transform(yx=12)
<Transform [1 0 12 1 0 0]>
- Transform instances also behave like sequences of length 6:
+ Transform instances also behave like sequences of length 6::
+
>>> len(Identity)
6
>>> list(Identity)
@@ -101,13 +108,15 @@ class Transform(NamedTuple):
>>> tuple(Identity)
(1, 0, 0, 1, 0, 0)
- Transform instances are comparable:
+ 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:
+ 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
@@ -118,12 +127,14 @@ class Transform(NamedTuple):
0
Transform instances are hashable, meaning you can use them as
- keys in dictionaries:
+ 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:
+ 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
@@ -149,7 +160,8 @@ class Transform(NamedTuple):
def transformPoint(self, p):
"""Transform a point.
- Example:
+ :Example:
+
>>> t = Transform()
>>> t = t.scale(2.5, 5.5)
>>> t.transformPoint((100, 100))
@@ -162,7 +174,8 @@ class Transform(NamedTuple):
def transformPoints(self, points):
"""Transform a list of points.
- Example:
+ :Example:
+
>>> t = Scale(2, 3)
>>> t.transformPoints([(0, 0), (0, 100), (100, 100), (100, 0)])
[(0, 0), (0, 300), (200, 300), (200, 0)]
@@ -171,10 +184,36 @@ class Transform(NamedTuple):
xx, xy, yx, yy, dx, dy = self
return [(xx*x + yx*y + dx, xy*x + yy*y + dy) for x, y in points]
+ def transformVector(self, v):
+ """Transform an (dx, dy) vector, treating translation as zero.
+
+ :Example:
+
+ >>> t = Transform(2, 0, 0, 2, 10, 20)
+ >>> t.transformVector((3, -4))
+ (6, -8)
+ >>>
+ """
+ (dx, dy) = v
+ xx, xy, yx, yy = self[:4]
+ return (xx*dx + yx*dy, xy*dx + yy*dy)
+
+ def transformVectors(self, vectors):
+ """Transform a list of (dx, dy) vector, treating translation as zero.
+
+ :Example:
+ >>> t = Transform(2, 0, 0, 2, 10, 20)
+ >>> t.transformVectors([(3, -4), (5, -6)])
+ [(6, -8), (10, -12)]
+ >>>
+ """
+ xx, xy, yx, yy = self[:4]
+ return [(xx*dx + yx*dy, xy*dx + yy*dy) for dx, dy in vectors]
+
def translate(self, x=0, y=0):
"""Return a new transformation, translated (offset) by x, y.
- Example:
+ :Example:
>>> t = Transform()
>>> t.translate(20, 30)
<Transform [1 0 0 1 20 30]>
@@ -186,7 +225,7 @@ class Transform(NamedTuple):
"""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:
+ :Example:
>>> t = Transform()
>>> t.scale(5)
<Transform [5 0 0 5 0 0]>
@@ -201,7 +240,7 @@ class Transform(NamedTuple):
def rotate(self, angle):
"""Return a new transformation, rotated by 'angle' (radians).
- Example:
+ :Example:
>>> import math
>>> t = Transform()
>>> t.rotate(math.pi / 2)
@@ -216,7 +255,7 @@ class Transform(NamedTuple):
def skew(self, x=0, y=0):
"""Return a new transformation, skewed by x and y.
- Example:
+ :Example:
>>> import math
>>> t = Transform()
>>> t.skew(math.pi / 4)
@@ -230,7 +269,7 @@ class Transform(NamedTuple):
"""Return a new transformation, transformed by another
transformation.
- Example:
+ :Example:
>>> t = Transform(2, 0, 0, 3, 1, 6)
>>> t.transform((4, 3, 2, 1, 5, 6))
<Transform [8 9 4 3 11 24]>
@@ -251,7 +290,7 @@ class Transform(NamedTuple):
transformed by self. self.reverseTransform(other) is equivalent to
other.transform(self).
- Example:
+ :Example:
>>> t = Transform(2, 0, 0, 3, 1, 6)
>>> t.reverseTransform((4, 3, 2, 1, 5, 6))
<Transform [8 6 6 3 21 15]>
@@ -272,7 +311,7 @@ class Transform(NamedTuple):
def inverse(self):
"""Return the inverse transformation.
- Example:
+ :Example:
>>> t = Identity.translate(2, 3).scale(4, 5)
>>> t.transformPoint((10, 20))
(42, 103)
@@ -290,7 +329,10 @@ class Transform(NamedTuple):
return self.__class__(xx, xy, yx, yy, dx, dy)
def toPS(self):
- """Return a PostScript representation:
+ """Return a PostScript representation
+
+ :Example:
+
>>> t = Identity.scale(2, 3).translate(4, 5)
>>> t.toPS()
'[2 0 0 3 8 15]'
@@ -300,6 +342,9 @@ class Transform(NamedTuple):
def __bool__(self):
"""Returns True if transform is not identity, False otherwise.
+
+ :Example:
+
>>> bool(Identity)
False
>>> bool(Transform())
@@ -326,7 +371,7 @@ Identity = Transform()
def Offset(x=0, y=0):
"""Return the identity transformation offset by x, y.
- Example:
+ :Example:
>>> Offset(2, 3)
<Transform [1 0 0 1 2 3]>
>>>
@@ -337,7 +382,7 @@ 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:
+ :Example:
>>> Scale(2, 3)
<Transform [2 0 0 3 0 0]>
>>>
generated by cgit v1.2.3 (git 2.25.1) at 2024-06-11 09:30:08 +0000