def scalebox(p1, p2):
p1 = Vector(p1)
p2 = Vector(p2)
x1, y1 = p1
x2, y2 = p2
return (Matrix.translate(p1) *
Matrix.scaleXY(x2 - x1, y2 - y1)).inverse()
#m = [[1.0/(x2-x1), 0, 0], [0, 1.0/(y2-y1), 0], [-x1, -y1, 1]]
#m = [[1.0/(x2-x1), 0, -1.0/x1], [0, 1.0/(y2-y1), -1.0/y1], [0, 0, 1]]
return Matrix(m)
def rotate(angle):
"""Return a rotate matrix, angle in radians anticlockwise"""
return Matrix(
numpy.array(
[[math.cos(angle), -math.sin(angle), 0],
[math.sin(angle), math.cos(angle), 0], [0, 0, 1]],
numpy.Float))
def scaleboxInverse(p1, p2):
#p1 = Vector(p1)
#p2 = Vector(p2)
x1, y1 = p1
x2, y2 = p2
#return (Matrix.translate(p1) * Matrix.scaleXY(x2-x1, y2-y1)).inverse()
#m = [[(x2-x1), 0, 0], [0, (y2-y1), 0], [x1, y1, 1]]
m = [[(x2 - x1), 0, x1], [0, (y2 - y1), y1], [0, 0, 1]]
return Matrix(m)
def __mul__(self, other):
"""Multiplies with a Matrix or point"""
#if type(other) == types.TupleType:
if issequence(other) and len(other) == 2:
x, y = other
if True:
x, y = float(x), float(y)
vec = array([x, y, 1])
newvec = numpy.dot(self.matrix, vec)
newx = newvec[0] / newvec[2]
newy = newvec[1] / newvec[2]
return Vector((newx, newy))
else:
m = self.matrix
nx = m[0, 0] * x + m[0, 1] * y + m[0, 2]
ny = m[1, 0] * x + m[1, 1] * y + m[1, 2]
nw = m[2, 0] * x + m[2, 1] * y + m[2, 2]
return Vector((nx / nw, ny / nw))
elif type(other) == Matrix:
newmatrix = numpy.matrixmultiply(self.matrix, other.matrix)
return Matrix(newmatrix[0, 0], newmatrix[1, 1],
newmatrix[0, 2], newmatrix[1, 2])
else:
raise Exception, "can only multiply with 'point tuples', and Matrices"
def nolocation(self):
matrix = numpy.array(self.matrix)
matrix[0][2] = 0
matrix[1][2] = 0
return Matrix(matrix)
def shear(x, y):
"""Returns a shear matrix"""
return Matrix(
numpy.array([[1, x, 0], [y, 1, 0], [0, 0, 1]], numpy.Float))
def scaleXY(x, y):
"""Returns a non-uniform scale matrix"""
return Matrix(
numpy.array([[x, 0, 0], [0, y, 0], [0, 0, 1]], numpy.Float))
def scale(s):
"""Returns a uniform scale matrix"""
return Matrix(
numpy.array([[s, 0, 0], [0, s, 0], [0, 0, 1]], numpy.Float))
def translate(point):
"""Return a translation matrix"""
x, y = point
return Matrix(
numpy.array([[1, 0, x], [0, 1, y], [0, 0, 1]], numpy.Float))
def inverse(self):
"""Return the inverse of this matrix"""
return Matrix(linear_algebra.inverse(self.matrix))