C#使用最小二乘法对多个离散点进行圆拟合

        /// <summary>
        /// 最小二乘法拟合圆,计算拟合圆半径和拟合圆圆心
        /// </summary>
        /// <param name="points">拟合点</param>
        /// <returns>返回拟合圆的计算结果</returns>
        public double[] FittingCircleByLeastSquare(List<Point> points)
        {
            //最小二乘法拟合圆
            ///https://blog.csdn.net/qq_31253399/article/details/107306569
            double U_i = 0, V_i = 0, U_c = 0, V_c = 0;
            double X = points.Average(p => p.X), Y = points.Average(p => p.Y);
            double S_uuu = 0, S_vvv = 0, S_uvv = 0, S_uuv = 0;
            double S_uu = 0, S_vv = 0, S_uv = 0;
            for (int i = 0; i < points.Count; i++)
            {
                U_i = points[i].X - X;
                V_i = points[i].Y - Y;
                S_uuu += Math.Pow(U_i, 3);
                S_uuv += Math.Pow(U_i, 2) * V_i;
                S_uuu += Math.Pow(U_i, 3);
                S_uvv += Math.Pow(V_i, 2) * U_i;
                S_uu += Math.Pow(U_i, 2);
                S_vv += Math.Pow(V_i, 2);
                S_uv += U_i * V_i;
            }
            U_c = (S_uuv * S_uv - S_uuu * S_vv - S_uvv * S_vv + S_uv * S_vvv) / 2 * (S_uv * S_uv - S_uu * S_vv);
            V_c = (S_uuu * S_uv - S_uuv * S_uu - S_uu * S_vvv + S_uv * S_uvv) / 2 * (S_uv * S_uv - S_uu * S_vv);
            //计算拟合圆圆心坐标
            double X_c = U_c + X;
            double Y_c = V_c + Y;
            //计算R
            double R = points.Sum(p => ((p.X - X_c) * (p.X - X_c) + (p.Y - X_c) * (p.Y - Y_c)));
            return new double[3] { X_c, Y_c, R };
        }