用C#寫最小區域法擬合圓心座標和半徑

以下是使用C#语言实现最小二乘法拟合圆的示例代码，假设已有一组样本点(x,y)，我们需要拟合出一条圆形的曲线，找到圆心坐标以及半径：

using System;
using System.Collections.Generic;
using System.Linq;

namespace CircleFitting
{
    class Program
    {
        static void Main(string[] args)
        {
            // 假设已有一组样本点(x,y)
            double[] x = { 1, 2, 3, 4, 5 };
            double[] y = { 1, 3, 5, 7, 9 };

            // 初始化参数
            double X = 0, Y = 0, XX = 0, YY = 0, XY = 0, YYXX = 0, YXXX = 0, YXXY = 0, YYY = 0, YYYX = 0, YYYXX = 0;

            // 计算参数
            for (int i = 0; i < x.Length; i++)
            {
                double xi = x[i];
                double yi = y[i];
                X += xi;
                Y += yi;
                XX += xi * xi;
                YY += yi * yi;
                XY += xi * yi;
                YYXX += yi * yi * xi * xi;
                YXXX += yi * xi * xi * xi;
                YXXY += yi * xi * xi * yi;
                YYY += yi * yi * yi;
                YYYX += yi * yi * yi * xi;
                YYYXX += yi * yi * yi * xi * xi;
            }

            double N = x.Length;
            double C = N * XX - X * X;
            double D = N * XY - X * Y;
            double E = N * YY - Y * Y;
            double G = 0.5 * (C * E - D * D);

            // 计算圆心坐标和半径
            double cx = (E * X - D * Y) / (2 * G);
            double cy = (C * Y - D * X) / (2 * G);
            double radius = Math.Sqrt(cx * cx + cy * cy + G / N);

            Console.WriteLine($"The center of the circle is ({cx}, {cy}), and the radius is {radius}.");
        }
    }
}

这段代码中，我们首先定义了一组样本点(x,y)，然后通过最小二乘法的思想，求出了参数C、D、E、G以及圆心坐标(cx,cy)和半径(radius)。最后输出圆心坐标和半径的值即可。