最小二乘法拟合圆c++

最小二乘法拟合圆是一种常见的数据拟合方法，可以用于圆形数据的拟合。下面是一个用 C++ 实现最小二乘法拟合圆的示例代码：

#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>

using namespace std;

// 定义一个二维向量点结构体
struct Point {
    double x;
    double y;
};

// 最小二乘法拟合圆函数
bool leastSquareCircle(const vector<Point>& points, Point& center, double& radius) {
    int n = points.size();
    // 计算x、y、x^2、y^2、x*y的和
    double sum_x = 0.0;
    double sum_y = 0.0;
    double sum_x2 = 0.0;
    double sum_y2 = 0.0;
    double sum_xy = 0.0;
    for (int i = 0; i < n; i++) {
        sum_x += points[i].x;
        sum_y += points[i].y;
        sum_x2 += points[i].x * points[i].x;
        sum_y2 += points[i].y * points[i].y;
        sum_xy += points[i].x * points[i].y;
    }
    // 计算a、b、c的值
    double a = n * sum_x2 - sum_x * sum_x;
    double b = n * sum_xy - sum_x * sum_y;
    double c = n * sum_y2 - sum_y * sum_y;
    // 判断是否为圆
    double delta = a * c - b * b;
    if (delta <= 0) {
        return false;
    }
    // 计算圆心坐标和半径
    center.x = (c * sum_x - b * sum_y) / delta / 2.0;
    center.y = (a * sum_y - b * sum_x) / delta / 2.0;
    radius = sqrt((a + c) / 2.0 + sqrt(delta) / 2.0);
    return true;
}

int main() {
    // 构造测试数据
    vector<Point> points;
    points.push_back(Point{1, 2});
    points.push_back(Point{3, 4});
    points.push_back(Point{5, 6});
    points.push_back(Point{7, 8});
    // 进行拟合
    Point center;
    double radius;
    bool ret = leastSquareCircle(points, center, radius);
    if (ret) {
        cout << "圆心坐标为(" << center.x << ", " << center.y << ")" << endl;
        cout << "半径为" << radius << endl;
    } else {
        cout << "无法拟合圆" << endl;
    }
    return 0;
}

上述代码实现了一个最小二乘法拟合圆的函数，接受一个二维向量点的数组作为输入，并返回拟合出的圆的圆心和半径。在主函数中构造了一个测试数据，并调用最小二乘法拟合圆函数进行拟合，输出拟合结果。