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September 21, 2024 14:30
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| #!/usr/bin/python3 | |
| import numpy as np | |
| from math import pi | |
| def shear_xy(f1, f2): | |
| m = np.eye(3) | |
| m[0][2] = f1 | |
| m[1][2] = f2 | |
| return m | |
| def shear_yz(f1, f2): | |
| m = np.eye(3) | |
| m[1][0] = f1 | |
| m[2][0] = f2 | |
| return m | |
| def shear_xz(f1, f2): | |
| m = np.eye(3) | |
| m[0][1] = f1 | |
| m[2][1] = f2 | |
| return m | |
| def rotate_z(a): | |
| m = np.eye(3) | |
| m[0][0] = np.cos(a) | |
| m[0][1] = -np.sin(a) | |
| m[1][0] = -m[0][1] | |
| m[1][1] = m[0][0] | |
| return m | |
| def rotation(k, theta): | |
| # https://en.wikipedia.org/wiki/Rodrigues%27_rotation_formula | |
| K = np.zeros((3,3)) | |
| K[0,1] = -k[2] | |
| K[0,2] = k[1] | |
| K[1,2] = -k[0] | |
| K[1,0] = -K[0,1] | |
| K[2,0] = -K[0,2] | |
| K[2,1] = -K[1,2] | |
| I = np.eye(3) | |
| R = I + np.sin(theta) * K + (1 - np.cos(theta)) * (K @ K) | |
| return R | |
| def decompose_shear(m): | |
| """ | |
| (%i4) sxy . syz . sxz; | |
| [ f1 f4 + 1 f1 (f6 + f4 f5) + f5 f1 ] | |
| [ ] | |
| (%o4) [ f2 f4 + f3 f2 (f6 + f4 f5) + f3 f5 + 1 f2 ] | |
| [ ] | |
| [ f4 f6 + f4 f5 1 ] | |
| """ | |
| A = np.zeros((3,2)) | |
| A[0][0] = 1 + m[2][0]*m[0][2] | |
| A[0][1] = m[0][2] | |
| A[1][0] = m[1][0] | |
| A[1][1] = m[1][2] | |
| A[2][0] = m[2][0] | |
| A[2][1] = 1.0 | |
| B = np.array([m[0][1], m[1][1] - 1, m[2][1]]) | |
| x, res, rank, sing = np.linalg.lstsq(A, B, rcond=None) | |
| f5, f6 = list(x) | |
| f1 = m[0][2] | |
| f2 = m[1][2] | |
| f3 = m[1][0] - m[1][2]*m[2][0] | |
| f4 = m[2][0] | |
| sxy_ans = shear_xy(f1, f2) | |
| syz_ans = shear_yz(f3, f4) | |
| sxz_ans = shear_xz(f5, f6) | |
| return sxy_ans, syz_ans, sxz_ans | |
| if __name__ == "__main__": | |
| R = rotation([1,1,2], pi/3) | |
| m = np.linalg.inv(R) @ shear_yz(0.3, 0.7) @ R | |
| print("M:") | |
| print(m) | |
| sxy_ans, syz_ans, sxz_ans = decompose_shear(m) | |
| print("ShearXY:") | |
| print(sxy_ans) | |
| print("ShearYZ:") | |
| print(syz_ans) | |
| print("ShearXZ:") | |
| print(sxz_ans) | |
| res = sxy_ans @ syz_ans @ sxz_ans | |
| print("Res:") | |
| print(res) |
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