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Mini Shell
Mini Shell
'''functions for 2D affine transformations'''
__all__ = (
'nullTransform',
'translate',
'scale',
'rotate',
'skewX',
'skewY',
'mmult',
'inverse',
'zTransformPoint',
'transformPoint',
'transformPoints',
'zTransformPoints',
)
from math import cos, sin, tan, radians
# 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 = radians(angle)
sina = sin(a)
cosa = cos(a)
return (cosa, sina, -sina, cosa, 0, 0)
def skewX(angle):
return (1, 0, tan(radians(angle)), 1, 0, 0)
def skewY(angle):
return (1, tan(radians(angle)), 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))
Zerion Mini Shell 1.0