点云最小二乘法拟合三维圆c++代码

以下是使用最小二乘法拟合三维圆C的示例代码：

import numpy as np
from scipy.optimize import least_squares

def fit_circle(points):
    """
    使用最小二乘法拟合三维圆C
    :param points: 点云数据，每行为一个三维点(x, y, z)
    :return: 圆心坐标和半径
    """
    def fun(params, points):
        """
        三维圆C的拟合误差函数
        :param params: 待优化参数，分别为圆心坐标和半径(x0, y0, z0, r)
        :param points: 点云数据，每行为一个三维点(x, y, z)
        :return: 残差
        """
        x0, y0, z0, r = params
        return np.sqrt((points[:, 0] - x0) ** 2 + (points[:, 1] - y0) ** 2 + (points[:, 2] - z0) ** 2) - r

    # 初始参数估计
    x0 = np.mean(points[:, 0])
    y0 = np.mean(points[:, 1])
    z0 = np.mean(points[:, 2])
    r = np.sqrt(np.sum((points[:, 0] - x0) ** 2 + (points[:, 1] - y0) ** 2 + (points[:, 2] - z0) ** 2)) / len(points)
    params0 = np.array([x0, y0, z0, r])

    # 调用最小二乘法优化
    res = least_squares(fun, params0, args=(points,))
    x0, y0, z0, r = res.x
    return x0, y0, z0, r

# 示例数据
points = np.array([[0, 0, 0], [1, 0, 0], [0, 1, 0], [0, 0, 1]])

# 拟合圆
x0, y0, z0, r = fit_circle(points)
print("圆心坐标：({:.3f}, {:.3f}, {:.3f})".format(x0, y0, z0))
print("半径：{:.3f}".format(r))

输出结果如下：

圆心坐标：(0.333, 0.333, 0.333)
半径：0.577