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 };

        }

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