把下面的代码转成C++实现import numpy as np from scipy.optimize import leastsq # 5个点的坐标 points = np.array([(349.816803, -56.949635), (345.811920, -56.854336), (341.920746, -57.405914), (353.892120, -57.741192), (357.636841, -59.161972)]) # 拟合圆的函数 def circle_func(params, x, y): a, b, r = params return (x - a) ** 2 + (y - b) ** 2 - r ** 2 # 最小二乘法拟合圆 def fit_circle(points): x = points[:, 0] y = points[:, 1] # 初始值为点集的中心和最大距离的一半 a0, b0 = np.mean(x), np.mean(y) r0 = np.max(np.sqrt((x - a0) ** 2 + (y - b0) ** 2)) / 2 params, flag = leastsq(circle_func, [a0, b0, r0], args=(x, y)) a, b, r = params return (a, b, r) # 求舍弃误差最大的点 def find_outlier(points): _, _, r = fit_circle(points) max_distance = 0 outlier = None for i, point in enumerate(points): distance = np.sqrt((point[0] - a) ** 2 + (point[1] - b) ** 2) - r if distance > max_distance: max_distance = distance outlier = i return outlier # 拟合圆和求舍弃误差最大的点 a, b, r = fit_circle(points) outlier = find_outlier(points) print("最佳圆心为：({:.2f}, {:.2f})".format(a, b)) print("最佳半径为：{:.2f}".format(r)) print("舍弃误差最大的点为：{}".format(points[outlier]))

以下是将代码转成C++的实现：

#include <iostream>
#include <cmath>
#include <Eigen/Core>
#include <Eigen/Dense>
#include <unsupported/Eigen/NonLinearOptimization>
#include <unsupported/Eigen/NumericalDiff>

using namespace Eigen;

// 5个点的坐标
MatrixXd points(5, 2);
points << 349.816803, -56.949635,
          345.811920, -56.854336,
          341.920746, -57.405914,
          353.892120, -57.741192,
          357.636841, -59.161972;

// 拟合圆的函数
template<typename T>
void circle_func(const T* params, const T& x, const T& y, T* fvec) {
    const T& a = params[0];
    const T& b = params[1];
    const T& r = params[2];
    fvec[0] = (x - a) * (x - a) + (y - b) * (y - b) - r * r;
}

// 最小二乘法拟合圆
struct CircleFitFunctor : Eigen::NumericalDiff< CircleFitFunctor >
{
    int operator()(const Eigen::VectorXd& params, Eigen::VectorXd& fvec) const {
        for (int i = 0; i < points.rows(); ++i) {
            circle_func(params.data(), points(i, 0), points(i, 1), fvec.data() + i);
        }
        return 0;
    }
};

// 求舍弃误差最大的点
int find_outlier() {
    double a, b, r;
    // 拟合圆
    CircleFitFunctor functor;
    LevenbergMarquardt<CircleFitFunctor> lm(functor);
    VectorXd params(3);
    params << points.col(0).mean(), points.col(1).mean(), (points.colwise() - params.head<2>().transpose()).rowwise().norm().maxCoeff() / 2;
    lm.minimize(params);
    a = params[0];
    b = params[1];
    r = params[2];
    // 求舍弃误差最大的点
    double max_distance = 0;
    int outlier = -1;
    for (int i = 0; i < points.rows(); ++i) {
        double distance = (points(i, 0) - a) * (points(i, 0) - a) + (points(i, 1) - b) * (points(i, 1) - b) - r * r;
        if (distance > max_distance) {
            max_distance = distance;
            outlier = i;
        }
    }
    return outlier;
}

int main() {
    // 拟合圆和求舍弃误差最大的点
    double a, b, r;
    a = points.col(0).mean();
    b = points.col(1).mean();
    r = (points.colwise() - Vector2d(a, b)).rowwise().norm().maxCoeff() / 2;
    std::cout << "最佳圆心为：(" << a << ", " << b << ")" << std::endl;
    std::cout << "最佳半径为：" << r << std::endl;
    int outlier = find_outlier();
    std::cout << "舍弃误差最大的点为：" << points.row(outlier) << std::endl;
    return 0;
}