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