请用python编写8点法相对定向

相对定向是数字摄影测量的重要内容之一，8点法相对定向是一种经典的相对定向方法。以下是一个简单的Python实现：

import numpy as np

# 定义8个点的像片坐标和地面坐标
image_points = np.array([[x1, y1], [x2, y2], [x3, y3], [x4, y4], [x5, y5], [x6, y6], [x7, y7], [x8, y8]])
ground_points = np.array([[X1, Y1, Z1], [X2, Y2, Z2], [X3, Y3, Z3], [X4, Y4, Z4], [X5, Y5, Z5], [X6, Y6, Z6], [X7, Y7, Z7], [X8, Y8, Z8]])

# 计算像平面与地面坐标系的旋转矩阵R和平移向量t
A = np.zeros((16, 6))
b = np.zeros((16, 1))
for i in range(0, 8):
    A[i*2, 0] = image_points[i, 0]
    A[i*2, 1] = image_points[i, 1]
    A[i*2, 2] = 1
    A[i*2, 3] = 0
    A[i*2, 4] = 0
    A[i*2, 5] = 0
    b[i*2] = ground_points[i, 0]
    A[i*2+1, 0] = 0
    A[i*2+1, 1] = 0
    A[i*2+1, 2] = 0
    A[i*2+1, 3] = image_points[i, 0]
    A[i*2+1, 4] = image_points[i, 1]
    A[i*2+1, 5] = 1
    b[i*2+1] = ground_points[i, 1]
x, residuals, rank, s = np.linalg.lstsq(A, b, rcond=None)
R1 = np.array([[x[0], x[1], x[2]], [x[3], x[4], x[5]], [0, 0, 1]])
t1 = np.array([[x[6]], [x[7]], [0]])

# 计算地面坐标系到相机坐标系的旋转矩阵R2和平移向量t2
B = np.zeros((16, 6))
c = np.zeros((16, 1))
for i in range(0, 8):
    B[i*2, 0] = ground_points[i, 0]
    B[i*2, 1] = ground_points[i, 1]
    B[i*2, 2] = ground_points[i, 2]
    B[i*2, 3] = 0
    B[i*2, 4] = 0
    B[i*2, 5] = 0
    c[i*2] = image_points[i, 0]
    B[i*2+1, 0] = 0
    B[i*2+1, 1] = 0
    B[i*2+1, 2] = 0
    B[i*2+1, 3] = ground_points[i, 0]
    B[i*2+1, 4] = ground_points[i, 1]
    B[i*2+1, 5] = ground_points[i, 2]
    c[i*2+1] = image_points[i, 1]
y, residuals, rank, s = np.linalg.lstsq(B, c, rcond=None)
R2 = np.array([[y[0], y[1], y[2]], [y[3], y[4], y[5]], [y[6], y[7], y[8]]])
t2 = np.array([[y[9]], [y[10]], [y[11]]])

# 计算相机坐标系到像平面的投影矩阵P
P = np.zeros((3, 4))
P[0:3, 0:3] = R2.T @ R1
P[0:3, 3] = -R2.T @ R1 @ t1 + t2

# 输出结果
print("R1：")
print(R1)
print("t1：")
print(t1)
print("R2：")
print(R2)
print("t2：")
print(t2)
print("P：")
print(P)

上述代码中，`image_points`是8个点在像片坐标系下的坐标，`ground_points`是8个点在地面坐标系下的坐标。通过最小二乘法求解旋转矩阵和平移向量，最终计算出相机坐标系到像平面的投影矩阵P。