最小二乘法拟合圆,计算拟合圆半径和拟合圆圆心

///
        /// 最小二乘法拟合圆,计算拟合圆半径和拟合圆圆心
        ///
        ///
        ///
        /// 圆心X
        /// 圆心Y
        /// 半径
        public static void FittingCircle(double[] X, double[] Y, out double cent_x, out double cent_y, out double radius)
        {
            cent_x = 0;
            cent_y = 0;
            radius = 0;
            if (X.Length < 3)
            {
                return;
            }
            double sum_x = 0.0f, sum_y = 0.0f;
            double sum_x2 = 0.0f, sum_y2 = 0.0f;
            double sum_x3 = 0.0f, sum_y3 = 0.0f;
            double sum_xy = 0.0f, sum_x1y2 = 0.0f, sum_x2y1 = 0.0f;
            int N = X.Length;
            double x, y, x2, y2;
            for (int i = 0; i < N; i++)
            {
                x = X[i];
                y = Y[i];
                x2 = x * x;
                y2 = y * y;
                sum_x += x;
                sum_y += y;
                sum_x2 += x2;
                sum_y2 += y2;
                sum_x3 += x2 * x;
                sum_y3 += y2 * y;
                sum_xy += x * y;
                sum_x1y2 += x * y2;
                sum_x2y1 += x2 * y;
            }
            double C, D, E, G, H;
            double a, b, c;
            C = N * sum_x2 - sum_x * sum_x;
            D = N * sum_xy - sum_x * sum_y;
            E = N * sum_x3 + N * sum_x1y2 - (sum_x2 + sum_y2) * sum_x;
            G = N * sum_y2 - sum_y * sum_y;
            H = N * sum_x2y1 + N * sum_y3 - (sum_x2 + sum_y2) * sum_y;
            a = (H * D - E * G) / (C * G - D * D);
            b = (H * C - E * D) / (D * D - G * C);
            c = -(a * sum_x + b * sum_y + sum_x2 + sum_y2) / N;
            cent_x = a / (-2);
            cent_y = b / (-2);
            radius = Math.Sqrt(a * a + b * b - 4 * c) / 2;
        }