interpolation.pyx
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# from interpolation cimport interpolate
import numpy as np
cimport numpy as np
cimport cython
from libc.math cimport floor, ceil, sqrt, fabs, round
from cython.parallel import prange
cdef double[64][64] temp = [
[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 2, -2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 9, -9,-9, 9, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-6, 6, 6,-6, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-6, 6, 6,-6, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 4, -4,-4, 4, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3,-6,-3, 0, 0, 0, 0, 6,-6, 3,-3, 0, 0, 0, 0, 4, 2, 2, 1, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 3, 3, 0, 0, 0, 0,-4, 4,-2, 2, 0, 0, 0, 0,-2,-2,-1,-1, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 4, 2, 0, 0, 0, 0,-3, 3,-3, 3, 0, 0, 0, 0,-2,-1,-2,-1, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2,-2,-2, 0, 0, 0, 0, 2,-2, 2,-2, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0],
[-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 9, -9, 0, 0,-9, 9, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-6, 6, 0, 0, 6,-6, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0, 0, 0,-1, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9,-9, 0, 0,-9, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 3, 0, 0,-6,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6,-6, 0, 0, 3,-3, 0, 0, 4, 2, 0, 0, 2, 1, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3,-3, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 4, 0, 0,-2, 2, 0, 0,-2,-2, 0, 0,-1,-1, 0, 0],
[ 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 9, 0,-9, 0,-9, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 3, 0,-6, 0,-3, 0, 6, 0,-6, 0, 3, 0,-3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 2, 0, 1, 0],
[-27, 27,27,-27,27,-27,-27,27,-18,-9,18, 9,18, 9,-18,-9,-18,18,-9, 9,18,-18, 9,-9,-18,18,18,-18,-9, 9, 9,-9,-12,-6,-6,-3,12, 6, 6, 3,-12,-6,12, 6,-6,-3, 6, 3,-12,12,-6, 6,-6, 6,-3, 3,-8,-4,-4,-2,-4,-2,-2,-1],
[18, -18,-18,18,-18,18,18,-18, 9, 9,-9,-9,-9,-9, 9, 9,12,-12, 6,-6,-12,12,-6, 6,12,-12,-12,12, 6,-6,-6, 6, 6, 6, 3, 3,-6,-6,-3,-3, 6, 6,-6,-6, 3, 3,-3,-3, 8,-8, 4,-4, 4,-4, 2,-2, 4, 4, 2, 2, 2, 2, 1, 1],
[-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 0,-3, 0, 3, 0, 3, 0,-4, 0, 4, 0,-2, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-2, 0,-1, 0,-1, 0],
[18, -18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6, 9,-9, 9,-9,-9, 9,-9, 9,12,-12,-12,12, 6,-6,-6, 6, 6, 3, 6, 3,-6,-3,-6,-3, 8, 4,-8,-4, 4, 2,-4,-2, 6,-6, 6,-6, 3,-3, 3,-3, 4, 2, 4, 2, 2, 1, 2, 1],
[-12, 12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-6, 6,-6, 6, 6,-6, 6,-6,-8, 8, 8,-8,-4, 4, 4,-4,-3,-3,-3,-3, 3, 3, 3, 3,-4,-4, 4, 4,-2,-2, 2, 2,-4, 4,-4, 4,-2, 2,-2, 2,-2,-2,-2,-2,-1,-1,-1,-1],
[ 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-6, 6, 0, 0, 6,-6, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 4, -4, 0, 0,-4, 4, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-6, 6, 0, 0, 6,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4,-2, 0, 0, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-3, 3, 0, 0,-3, 3, 0, 0,-2,-1, 0, 0,-2,-1, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4,-4, 0, 0,-4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0,-2,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2,-2, 0, 0, 2,-2, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0],
[-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0,-6, 0, 6, 0, 6, 0,-6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,-4, 0,-2, 0, 4, 0, 2, 0,-3, 0, 3, 0,-3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0,-2, 0,-1, 0,-2, 0,-1, 0],
[18, -18,-18,18,-18,18,18,-18,12, 6,-12,-6,-12,-6,12, 6,12,-12, 6,-6,-12,12,-6, 6, 9,-9,-9, 9, 9,-9,-9, 9, 8, 4, 4, 2,-8,-4,-4,-2, 6, 3,-6,-3, 6, 3,-6,-3, 6,-6, 3,-3, 6,-6, 3,-3, 4, 2, 2, 1, 4, 2, 2, 1],
[-12, 12,12,-12,12,-12,-12,12,-6,-6, 6, 6, 6, 6,-6,-6,-8, 8,-4, 4, 8,-8, 4,-4,-6, 6, 6,-6,-6, 6, 6,-6,-4,-4,-2,-2, 4, 4, 2, 2,-3,-3, 3, 3,-3,-3, 3, 3,-4, 4,-2, 2,-4, 4,-2, 2,-2,-2,-1,-1,-2,-2,-1,-1],
[ 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[ 0, 0, 0, 0, 0, 0, 0, 0, 4, 0,-4, 0,-4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 0,-2, 0,-2, 0, 2, 0,-2, 0, 2, 0,-2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0],
[-12, 12,12,-12,12,-12,-12,12,-8,-4, 8, 4, 8, 4,-8,-4,-6, 6,-6, 6, 6,-6, 6,-6,-6, 6, 6,-6,-6, 6, 6,-6,-4,-2,-4,-2, 4, 2, 4, 2,-4,-2, 4, 2,-4,-2, 4, 2,-3, 3,-3, 3,-3, 3,-3, 3,-2,-1,-2,-1,-2,-1,-2,-1],
[ 8, -8,-8, 8,-8, 8, 8,-8, 4, 4,-4,-4,-4,-4, 4, 4, 4,-4, 4,-4,-4, 4,-4, 4, 4,-4,-4, 4, 4,-4,-4, 4, 2, 2, 2, 2,-2,-2,-2,-2, 2, 2,-2,-2, 2, 2,-2,-2, 2,-2, 2,-2, 2,-2, 2,-2, 1, 1, 1, 1, 1, 1, 1, 1]
]
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef double interpolate(image_t[:, :, :] V, double x, double y, double z) nogil:
cdef double xd, yd, zd
cdef double c00, c10, c01, c11
cdef double c0, c1
cdef double c
cdef int x0 = <int>floor(x)
cdef int x1 = x0 + 1
cdef int y0 = <int>floor(y)
cdef int y1 = y0 + 1
cdef int z0 = <int>floor(z)
cdef int z1 = z0 + 1
if x0 == x1:
xd = 1.0
else:
xd = (x - x0) / (x1 - x0)
if y0 == y1:
yd = 1.0
else:
yd = (y - y0) / (y1 - y0)
if z0 == z1:
zd = 1.0
else:
zd = (z - z0) / (z1 - z0)
c00 = _G(V, x0, y0, z0)*(1 - xd) + _G(V, x1, y0, z0)*xd
c10 = _G(V, x0, y1, z0)*(1 - xd) + _G(V, x1, y1, z0)*xd
c01 = _G(V, x0, y0, z1)*(1 - xd) + _G(V, x1, y0, z1)*xd
c11 = _G(V, x0, y1, z1)*(1 - xd) + _G(V, x1, y1, z1)*xd
c0 = c00*(1 - yd) + c10*yd
c1 = c01*(1 - yd) + c11*yd
c = c0*(1 - zd) + c1*zd
return c
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef image_t _G(image_t[:, :, :] V, int x, int y, int z) nogil:
cdef int dz, dy, dx
dz = V.shape[0] - 1
dy = V.shape[1] - 1
dx = V.shape[2] - 1
if x < 0:
x = dx + x + 1
elif x > dx:
x = x - dx - 1
if y < 0:
y = dy + y + 1
elif y > dy:
y = y - dy - 1
if z < 0:
z = dz + z + 1
elif z > dz:
z = z - dz - 1
return V[z, y, x]
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef void calc_coef_tricub(image_t[:, :, :] V, double x, double y, double z, double [64] coef) nogil:
cdef int xi = <int>floor(x)
cdef int yi = <int>floor(y)
cdef int zi = <int>floor(z)
cdef double[64] _x
cdef int i, j
_x[0] = _G(V, xi, yi, zi)
_x[1] = _G(V, xi + 1, yi, zi)
_x[2] = _G(V, xi, yi + 1, zi)
_x[3] = _G(V, xi + 1, yi + 1, zi)
_x[4] = _G(V, xi, yi, zi + 1)
_x[5] = _G(V, xi + 1, yi, zi + 1)
_x[6] = _G(V, xi, yi + 1, zi + 1)
_x[7] = _G(V, xi + 1, yi + 1, zi + 1)
_x[8] = 0.5*(_G(V, xi+1,yi,zi) - _G(V, xi-1, yi, zi))
_x[9] = 0.5*(_G(V, xi+2,yi,zi) - _G(V, xi, yi, zi))
_x[10] = 0.5*(_G(V, xi+1, yi+1,zi) - _G(V, xi-1, yi+1, zi))
_x[11] = 0.5*(_G(V, xi+2, yi+1,zi) - _G(V, xi, yi+1, zi))
_x[12] = 0.5*(_G(V, xi+1, yi,zi+1) - _G(V, xi-1, yi, zi+1))
_x[13] = 0.5*(_G(V, xi+2, yi,zi+1) - _G(V, xi, yi, zi+1))
_x[14] = 0.5*(_G(V, xi+1, yi+1,zi+1) - _G(V, xi-1, yi+1, zi+1))
_x[15] = 0.5*(_G(V, xi+2, yi+1,zi+1) - _G(V, xi, yi+1, zi+1))
_x[16] = 0.5*(_G(V, xi, yi+1,zi) - _G(V, xi, yi-1, zi))
_x[17] = 0.5*(_G(V, xi+1, yi+1,zi) - _G(V, xi+1, yi-1, zi))
_x[18] = 0.5*(_G(V, xi, yi+2,zi) - _G(V, xi, yi, zi))
_x[19] = 0.5*(_G(V, xi+1, yi+2,zi) - _G(V, xi+1, yi, zi))
_x[20] = 0.5*(_G(V, xi, yi+1,zi+1) - _G(V, xi, yi-1, zi+1))
_x[21] = 0.5*(_G(V, xi+1, yi+1,zi+1) - _G(V, xi+1, yi-1, zi+1))
_x[22] = 0.5*(_G(V, xi, yi+2,zi+1) - _G(V, xi, yi, zi+1))
_x[23] = 0.5*(_G(V, xi+1, yi+2,zi+1) - _G(V, xi+1, yi, zi+1))
_x[24] = 0.5*(_G(V, xi, yi,zi+1) - _G(V, xi, yi, zi-1))
_x[25] = 0.5*(_G(V, xi+1, yi,zi+1) - _G(V, xi+1, yi, zi-1))
_x[26] = 0.5*(_G(V, xi, yi+1,zi+1) - _G(V, xi, yi+1, zi-1))
_x[27] = 0.5*(_G(V, xi+1, yi+1,zi+1) - _G(V, xi+1, yi+1, zi-1))
_x[28] = 0.5*(_G(V, xi, yi,zi+2) - _G(V, xi, yi, zi))
_x[29] = 0.5*(_G(V, xi+1, yi,zi+2) - _G(V, xi+1, yi, zi))
_x[30] = 0.5*(_G(V, xi, yi+1,zi+2) - _G(V, xi, yi+1, zi))
_x[31] = 0.5*(_G(V, xi+1, yi+1,zi+2) - _G(V, xi+1, yi+1, zi))
_x [32] = 0.25*(_G(V, xi+1, yi+1, zi) - _G(V, xi-1, yi+1, zi) - _G(V, xi+1, yi-1, zi) + _G(V, xi-1, yi-1, zi))
_x [33] = 0.25*(_G(V, xi+2, yi+1, zi) - _G(V, xi, yi+1, zi) - _G(V, xi+2, yi-1, zi) + _G(V, xi, yi-1, zi))
_x [34] = 0.25*(_G(V, xi+1, yi+2, zi) - _G(V, xi-1, yi+2, zi) - _G(V, xi+1, yi, zi) + _G(V, xi-1, yi, zi))
_x [35] = 0.25*(_G(V, xi+2, yi+2, zi) - _G(V, xi, yi+2, zi) - _G(V, xi+2, yi, zi) + _G(V, xi, yi, zi))
_x [36] = 0.25*(_G(V, xi+1, yi+1, zi+1) - _G(V, xi-1, yi+1, zi+1) - _G(V, xi+1, yi-1, zi+1) + _G(V, xi-1, yi-1, zi+1))
_x [37] = 0.25*(_G(V, xi+2, yi+1, zi+1) - _G(V, xi, yi+1, zi+1) - _G(V, xi+2, yi-1, zi+1) + _G(V, xi, yi-1, zi+1))
_x [38] = 0.25*(_G(V, xi+1, yi+2, zi+1) - _G(V, xi-1, yi+2, zi+1) - _G(V, xi+1, yi, zi+1) + _G(V, xi-1, yi, zi+1))
_x [39] = 0.25*(_G(V, xi+2, yi+2, zi+1) - _G(V, xi, yi+2, zi+1) - _G(V, xi+2, yi, zi+1) + _G(V, xi, yi, zi+1))
_x [40] = 0.25*(_G(V, xi+1, yi, zi+1) - _G(V, xi-1, yi, zi+1) - _G(V, xi+1, yi, zi-1) + _G(V, xi-1, yi, zi-1))
_x [41] = 0.25*(_G(V, xi+2, yi, zi+1) - _G(V, xi, yi, zi+1) - _G(V, xi+2, yi, zi-1) + _G(V, xi, yi, zi-1))
_x [42] = 0.25*(_G(V, xi+1, yi+1, zi+1) - _G(V, xi-1, yi+1, zi+1) - _G(V, xi+1, yi+1, zi-1) + _G(V, xi-1, yi+1, zi-1))
_x [43] = 0.25*(_G(V, xi+2, yi+1, zi+1) - _G(V, xi, yi+1, zi+1) - _G(V, xi+2, yi+1, zi-1) + _G(V, xi, yi+1, zi-1))
_x [44] = 0.25*(_G(V, xi+1, yi, zi+2) - _G(V, xi-1, yi, zi+2) - _G(V, xi+1, yi, zi) + _G(V, xi-1, yi, zi))
_x [45] = 0.25*(_G(V, xi+2, yi, zi+2) - _G(V, xi, yi, zi+2) - _G(V, xi+2, yi, zi) + _G(V, xi, yi, zi))
_x [46] = 0.25*(_G(V, xi+1, yi+1, zi+2) - _G(V, xi-1, yi+1, zi+2) - _G(V, xi+1, yi+1, zi) + _G(V, xi-1, yi+1, zi))
_x [47] = 0.25*(_G(V, xi+2, yi+1, zi+2) - _G(V, xi, yi+1, zi+2) - _G(V, xi+2, yi+1, zi) + _G(V, xi, yi+1, zi))
_x [48] = 0.25*(_G(V, xi, yi+1, zi+1) - _G(V, xi, yi-1, zi+1) - _G(V, xi, yi+1, zi-1) + _G(V, xi, yi-1, zi-1))
_x [49] = 0.25*(_G(V, xi+1, yi+1, zi+1) - _G(V, xi+1, yi-1, zi+1) - _G(V, xi+1, yi+1, zi-1) + _G(V, xi+1, yi-1, zi-1))
_x [50] = 0.25*(_G(V, xi, yi+2, zi+1) - _G(V, xi, yi, zi+1) - _G(V, xi, yi+2, zi-1) + _G(V, xi, yi, zi-1))
_x [51] = 0.25*(_G(V, xi+1, yi+2, zi+1) - _G(V, xi+1, yi, zi+1) - _G(V, xi+1, yi+2, zi-1) + _G(V, xi+1, yi, zi-1))
_x [52] = 0.25*(_G(V, xi, yi+1, zi+2) - _G(V, xi, yi-1, zi+2) - _G(V, xi, yi+1, zi) + _G(V, xi, yi-1, zi))
_x [53] = 0.25*(_G(V, xi+1, yi+1, zi+2) - _G(V, xi+1, yi-1, zi+2) - _G(V, xi+1, yi+1, zi) + _G(V, xi+1, yi-1, zi))
_x [54] = 0.25*(_G(V, xi, yi+2, zi+2) - _G(V, xi, yi, zi+2) - _G(V, xi, yi+2, zi) + _G(V, xi, yi, zi))
_x [55] = 0.25*(_G(V, xi+1, yi+2, zi+2) - _G(V, xi+1, yi, zi+2) - _G(V, xi+1, yi+2, zi) + _G(V, xi+1, yi, zi))
_x[56] = 0.125*(_G(V, xi+1, yi+1, zi+1) - _G(V, xi-1, yi+1, zi+1) - _G(V, xi+1, yi-1, zi+1) + _G(V, xi-1, yi-1, zi+1) - _G(V, xi+1, yi+1, zi-1) + _G(V, xi-1,yi+1,zi-1)+_G(V, xi+1,yi-1,zi-1)-_G(V, xi-1,yi-1,zi-1))
_x[57] = 0.125*(_G(V, xi+2, yi+1, zi+1) - _G(V, xi, yi+1, zi+1) - _G(V, xi+2, yi-1, zi+1) + _G(V, xi, yi-1, zi+1) - _G(V, xi+2, yi+1, zi-1) + _G(V, xi,yi+1,zi-1)+_G(V, xi+2,yi-1,zi-1)-_G(V, xi,yi-1,zi-1))
_x[58] = 0.125*(_G(V, xi+1, yi+2, zi+1) - _G(V, xi-1, yi+2, zi+1) - _G(V, xi+1, yi, zi+1) + _G(V, xi-1, yi, zi+1) - _G(V, xi+1, yi+2, zi-1) + _G(V, xi-1,yi+2,zi-1)+_G(V, xi+1,yi,zi-1)-_G(V, xi-1,yi,zi-1))
_x[59] = 0.125*(_G(V, xi+2, yi+2, zi+1) - _G(V, xi, yi+2, zi+1) - _G(V, xi+2, yi, zi+1) + _G(V, xi, yi, zi+1) - _G(V, xi+2, yi+2, zi-1) + _G(V, xi,yi+2,zi-1)+_G(V, xi+2,yi,zi-1)-_G(V, xi,yi,zi-1))
_x[60] = 0.125*(_G(V, xi+1, yi+1, zi+2) - _G(V, xi-1, yi+1, zi+2) - _G(V, xi+1, yi-1, zi+2) + _G(V, xi-1, yi-1, zi+2) - _G(V, xi+1, yi+1, zi) + _G(V, xi-1,yi+1,zi)+_G(V, xi+1,yi-1,zi)-_G(V, xi-1,yi-1,zi))
_x[61] = 0.125*(_G(V, xi+2, yi+1, zi+2) - _G(V, xi, yi+1, zi+2) - _G(V, xi+2, yi-1, zi+2) + _G(V, xi, yi-1, zi+2) - _G(V, xi+2, yi+1, zi) + _G(V, xi,yi+1,zi)+_G(V, xi+2,yi-1,zi)-_G(V, xi,yi-1,zi))
_x[62] = 0.125*(_G(V, xi+1, yi+2, zi+2) - _G(V, xi-1, yi+2, zi+2) - _G(V, xi+1, yi, zi+2) + _G(V, xi-1, yi, zi+2) - _G(V, xi+1, yi+2, zi) + _G(V, xi-1,yi+2,zi)+_G(V, xi+1,yi,zi)-_G(V, xi-1,yi,zi))
_x[63] = 0.125*(_G(V, xi+2, yi+2, zi+2) - _G(V, xi, yi+2, zi+2) - _G(V, xi+2, yi, zi+2) + _G(V, xi, yi, zi+2) - _G(V, xi+2, yi+2, zi) + _G(V, xi,yi+2,zi)+_G(V, xi+2,yi,zi)-_G(V, xi,yi,zi))
for j in prange(64):
coef[j] = 0.0
for i in xrange(64):
coef[j] += (temp[j][i] * _x[i])
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef double tricub_interpolate(image_t[:, :, :] V, double x, double y, double z) nogil:
# From: Tricubic interpolation in three dimensions. Lekien and Marsden
cdef double[64] coef
cdef double result = 0.0
calc_coef_tricub(V, x, y, z, coef)
cdef int i, j, k
cdef int xi = <int>floor(x)
cdef int yi = <int>floor(y)
cdef int zi = <int>floor(z)
for i in xrange(4):
for j in xrange(4):
for k in xrange(4):
result += (coef[i+4*j+16*k] * ((x-xi)**i) * ((y-yi)**j) * ((z-zi)**k))
# return V[<int>z, <int>y, <int>x]
# with gil:
# print result
return result
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef double cubicInterpolate(double p[4], double x) nogil:
return p[1] + 0.5 * x*(p[2] - p[0] + x*(2.0*p[0] - 5.0*p[1] + 4.0*p[2] - p[3] + x*(3.0*(p[1] - p[2]) + p[3] - p[0])))
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef double bicubicInterpolate (double p[4][4], double x, double y) nogil:
cdef double arr[4]
arr[0] = cubicInterpolate(p[0], y)
arr[1] = cubicInterpolate(p[1], y)
arr[2] = cubicInterpolate(p[2], y)
arr[3] = cubicInterpolate(p[3], y)
return cubicInterpolate(arr, x)
@cython.boundscheck(False) # turn of bounds-checking for entire function
@cython.cdivision(True)
@cython.wraparound(False)
cdef double tricubicInterpolate(image_t[:, :, :] V, double x, double y, double z) nogil:
# From http://www.paulinternet.nl/?page=bicubic
cdef double p[4][4][4]
cdef int xi = <int>floor(x)
cdef int yi = <int>floor(y)
cdef int zi = <int>floor(z)
cdef int i, j, k
for i in xrange(4):
for j in xrange(4):
for k in xrange(4):
p[i][j][k] = _G(V, xi + i -1, yi + j -1, zi + k - 1)
cdef double arr[4]
arr[0] = bicubicInterpolate(p[0], y-yi, z-zi)
arr[1] = bicubicInterpolate(p[1], y-yi, z-zi)
arr[2] = bicubicInterpolate(p[2], y-yi, z-zi)
arr[3] = bicubicInterpolate(p[3], y-yi, z-zi)
return cubicInterpolate(arr, x-xi)
def tricub_interpolate_py(image_t[:, :, :] V, double x, double y, double z):
return tricub_interpolate(V, x, y, z)
def tricub_interpolate2_py(image_t[:, :, :] V, double x, double y, double z):
return tricubicInterpolate(V, x, y, z)
def trilin_interpolate_py(image_t[:, :, :] V, double x, double y, double z):
return interpolate(V, x, y, z)