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Code Editor : transform.py
'''functions for 2D affine transformations''' __all__ = ( 'nullTransform', 'translate', 'scale', 'rotate', 'skewX', 'skewY', 'mmult', 'inverse', 'zTransformPoint', 'transformPoint', 'transformPoints', 'zTransformPoints', ) from math import pi, cos, sin, tan # constructors for matrices: def nullTransform(): return (1, 0, 0, 1, 0, 0) def translate(dx, dy): return (1, 0, 0, 1, dx, dy) def scale(sx, sy): return (sx, 0, 0, sy, 0, 0) def rotate(angle): a = angle * pi/180 return (cos(a), sin(a), -sin(a), cos(a), 0, 0) def skewX(angle): a = angle * pi/180 return (1, 0, tan(a), 1, 0, 0) def skewY(angle): a = angle * pi/180 return (1, tan(a), 0, 1, 0, 0) def mmult(A, B): "A postmultiplied by B" # I checked this RGB # [a0 a2 a4] [b0 b2 b4] # [a1 a3 a5] * [b1 b3 b5] # [ 1 ] [ 1 ] # return (A[0]*B[0] + A[2]*B[1], A[1]*B[0] + A[3]*B[1], A[0]*B[2] + A[2]*B[3], A[1]*B[2] + A[3]*B[3], A[0]*B[4] + A[2]*B[5] + A[4], A[1]*B[4] + A[3]*B[5] + A[5]) def inverse(A): "For A affine 2D represented as 6vec return 6vec version of A**(-1)" # I checked this RGB det = float(A[0]*A[3] - A[2]*A[1]) R = [A[3]/det, -A[1]/det, -A[2]/det, A[0]/det] return tuple(R+[-R[0]*A[4]-R[2]*A[5],-R[1]*A[4]-R[3]*A[5]]) def zTransformPoint(A,v): "Apply the homogenous part of atransformation a to vector v --> A*v" return (A[0]*v[0]+A[2]*v[1],A[1]*v[0]+A[3]*v[1]) def transformPoint(A,v): "Apply transformation a to vector v --> A*v" return (A[0]*v[0]+A[2]*v[1]+A[4],A[1]*v[0]+A[3]*v[1]+A[5]) def transformPoints(matrix, V): r = [transformPoint(matrix,v) for v in V] if isinstance(V,tuple): r = tuple(r) return r def zTransformPoints(matrix, V): return list(map(lambda x,matrix=matrix: zTransformPoint(matrix,x), V))
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