python帮我写一个后方交会求解外方位元素的代码

在Python中，后方交会（Backward Oriented Triangulation）通常用于摄影测量或GIS项目中，用来计算从已知控制点到图像内点的外方位元素，如像距、主点坐标等。这里是一个基本的Python示例，使用了NumPy库来进行矩阵运算。请注意，这只是一个简化版的代码，实际应用可能需要更复杂的错误处理和优化。

import numpy as np

def back_triangulation(epipole, control_points, image_points):
    # 假设epipole是一个二维数组表示对齐中心
    n = len(control_points)
    A = np.zeros((n * 2, n + 3))

    for i in range(n):
        x, y = control_points[i]
        u, v = image_points[i]
        
        # 建立方程组的前半部分
        A[2*i, :2] = [u - x, v - y]
        A[2*i+1, :2] = [-y, x]

    # 将epipole加入方程组
    A[:, 2:] = np.array([[-epipole[0]], [-epipole[1]]])

    try:
        solution = np.linalg.solve(A, np.ones(n + 3))
    except np.linalg.LinAlgError:
        print("解算失败")
        return None

    if solution[n] == 0 and solution[n+1] == 0:
        # 主点坐标
        principal_point = solution[:2] / solution[n+2]
        # 像距
        focal_length = solution[n+2]
        # 旋转和平移向量
        rotation = solution[2:4].reshape(2, 1)
        translation = solution[4:].reshape(2, 1)

        return principal_point, focal_length, rotation, translation
    else:
        print("解算结果异常")
        return None

# 使用示例
epipole = [0, 0]  # 假设对齐中心
control_points = [(x1, y1), (x2, y2), ...]  # 控制点列表
image_points = [(u1, v1), (u2, v2), ...]  # 图像点列表

result = back_triangulation(epipole, control_points, image_points)
if result is not None:
    princ_point, focal_len, rot_vec, trans_vec = result
    print(f"Principal point: {princ_point}")
    print(f"Focal length: {focal_len}")
    print(f"Rotation vector: {rot_vec}")
    print(f"Translation vector: {trans_vec}")