numpy :在三维欧几里得坐标中给定2组4个点的变换矩阵

import numpy as np

# 假设我们有两组4个点的坐标
points_src = np.array([[x1, y1, z1], [x2, y2, z2], [x3, y3, z3], [x4, y4, z4]])
points_tgt = np.array([[u1, v1, w1], [u2, v2, w2], [u3, v3, w3], [u4, v4, w4]])

# 构建设计矩阵
def build_design_matrix(src, tgt):
    A = []
    for i in range(len(src)):
        x, y, z = src[i]
        u, v, w = tgt[i]
        A.append([x, y, z, 1, 0, 0, 0, 0, -u*x, -u*y, -u*z, -u])
        A.append([0, 0, 0, 0, x, y, z, 1, -v*x, -v*y, -v*z, -v])
        A.append([0, 0, 0, 0, 0, 0, 0, 0, x, y, z, 1])
    return np.array(A)

A = build_design_matrix(points_src, points_tgt)

# 构建目标向量
b = tgt.reshape(-1)

# 使用最小二乘法求解变换矩阵
transform_matrix, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)

print("变换矩阵:\n", transform_matrix.reshape(4, 4))