this module has been included in so many (in house) packages that it's time it gets a more central place.
git-svn-id: svn://svn.code.sf.net/p/fonttools/code/trunk@399 4cde692c-a291-49d1-8350-778aa11640f8
diff --git a/Lib/fontTools/misc/transform.py b/Lib/fontTools/misc/transform.py
new file mode 100755
index 0000000..d98a6b3
--- /dev/null
+++ b/Lib/fontTools/misc/transform.py
@@ -0,0 +1,117 @@
+"""Affine 2D transformation class."""
+
+
+_EPSILON = 1e-15
+_ONE_EPSILON = 1 - _EPSILON
+_MINUS_ONE_EPSILON = -1 + _EPSILON
+
+
+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:
+
+ """2x2 transformation matrix plus offset, a.k.a. Affine transform.
+ Transform instances are "immutable": all transforming methods, eg.
+ rotate(), return a new Transform instance."""
+
+ def __init__(self, xx=1, xy=0, yx=0, yy=1, dx=0, dy=0):
+ self.__affine = xx, xy, yx, yy, dx, dy
+
+ def transformPoint(self, (x, y)):
+ """Transform a point."""
+ xx, xy, yx, yy, dx, dy = self.__affine
+ return (xx*x + yx*y + dx, xy*x + yy*y + dy)
+
+ def translate(self, x=0, y=0):
+ return self.transform((1, 0, 0, 1, x, y))
+
+ def scale(self, x=1, y=None):
+ if y is None:
+ y = x
+ return self.transform((x, 0, 0, y, 0, 0))
+
+ def rotate(self, angle):
+ 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):
+ import math
+ return self.transform((1, math.tan(y), math.tan(x), 1, 0, 0))
+
+ def transform(self, other):
+ xx1, xy1, yx1, yy1, dx1, dy1 = other
+ xx2, xy2, yx2, yy2, dx2, dy2 = self.__affine
+ 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):
+ xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine
+ 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 transform."
+ if self.__affine == (1, 0, 0, 1, 0, 0):
+ return self
+ xx, xy, yx, yy, dx, dy = self.__affine
+ det = float(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 "[%s %s %s %s %s %s]" % self.__affine
+
+ def __len__(self):
+ return 6
+
+ def __getitem__(self, index):
+ return self.__affine[index]
+
+ def __getslice__(self, i, j):
+ return self.__affine[i:j]
+
+ def __cmp__(self, other):
+ xx1, xy1, yx1, yy1, dx1, dy1 = self.__affine
+ xx2, xy2, yx2, yy2, dx2, dy2 = other
+ return cmp((xx1, xy1, yx1, yy1, dx1, dy1),
+ (xx2, xy2, yx2, yy2, dx2, dy2))
+
+ def __hash__(self):
+ return hash(self.__affine)
+
+ def __repr__(self):
+ return "<%s [%s %s %s %s %s %s]>" % ((self.__class__.__name__,)
+ + tuple(map(str, self.__affine)))
+
+
+Identity = Transform()
+
+def Offset(x=0, y=0):
+ return Transform(1, 0, 0, 1, x, y)
+
+def Scale(x, y=None):
+ if y is None:
+ y = x
+ return Transform(x, 0, 0, y, 0, 0)