C# 多点最小二乘法拟合平面算法

　　　　　/// <summary>
        /// 实现三阶行列式求值计算
        /// </summary>
        /// <param name="x1"></param>
        /// <param name="y1"></param>
        /// <param name="z1"></param>
        /// <param name="x2"></param>
        /// <param name="y2"></param>
        /// <param name="z2"></param>
        /// <param name="x3"></param>
        /// <param name="y3"></param>
        /// <param name="z3"></param>
        /// <returns></returns>
        private double gDeterm3(double x1,
                                double y1,
                                double z1,
                                double x2,
                                double y2,
                                double z2,
                                double x3,
                                double y3,
                                double z3)
        {
            return x1 * y2 * z3 +
                   y1 * z2 * x3 +
                   z1 * x2 * y3 -
                   z1 * y2 * x3 -
                   y1 * x2 * z3 -
                   x1 * z2 * y3;
        }


        
        private void button1_Click(object sender, EventArgs e)
        {   //初始化坐标值
            double[] xArr = new double[16] { 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3 };
            double[] yArr = new double[16] { 0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3 };
            double[] zArr = new double[16] { 5, 4, 1, 1, 9, 7, 3, -1, 9, 5, 2, -3, 1, -2, 0, 3 };
            //初始化需要的变量
            double x1 = 0d, x2 = 0d, y1 = 0d, y2 = 0d, z1 = 0d, xz = 0d, yz = 0d, xy = 0d, r = 0d;

　　　　　　  //计算
            for (int i = 0; i < xArr.Length; i++)
            {
                x1 += xArr[i];
                x2 += xArr[i] * xArr[i];
                xz += xArr[i] * zArr[i];

                y1 += yArr[i];
                y2 += yArr[i] * yArr[i];
                yz += yArr[i] * zArr[i];

                z1 += zArr[i];
                xy += xArr[i] * yArr[i];
            }
            string res = "";
            r = gDeterm3(x2, xy, x1, xy, y2, y1, x1, y1, xArr.Length);
            res += "R ="+r+",";
            if (r != 0) {
                res += "A =" + gDeterm3(xz, xy, x1, yz, y2, y1, z1, y1, xArr.Length) / r + ",";
                res += "B =" + gDeterm3(x2, xz, x1, xy, yz, y1, x1, z1, xArr.Length) / r + ",";
                res += "C =" + gDeterm3(x2, xy, xz, xy, y2, yz, x1, y1, z1) / r;
            }
            this.label1.Text = res;
        }