已知空间上若干点（xi, yi, zi）, 求空间上包含这些点的最小球半径 R, 以及球心坐标。

思路：球心与这些点的最大距离为半径， 球心与最大距离点生成向量，将球心朝着该向量方向移动若干距离，再计算半径的变化。

namespace Test_BST
{
    public class Program
    {
        static void Main(string[] args)
        {
            // 初始化输入点
            List<Point> originPoints = new List<Point>() { ............};
            double radius = AnnealAlgorithm(originPoints);
        }

        private struct Point
        {
            public double x;
            public double y;
            public double z;
        }

        // square of a number
        private static double Sqr(double x) { return x * x; }

        // 两点之间的距离
        private static double Dist(Point A, Point B)
        {
            return Math.Sqrt(Sqr(A.x - B.x) + Sqr(A.y - B.y) + Sqr(A.z - B.z));
        }

        // 求最大半径
        private static double GetMaxRadius(Point p0, List<Point> pts)
        {
            double maxRadius = 0;
            foreach (var point in pts)
            {
                double radius = Dist(p0, point);
                maxRadius = radius > maxRadius ? radius : maxRadius;
            }

            return maxRadius;
        }

        private static double AnnealAlgorithm(List<Point> originPts)
        {
            Point center = new Point();
            center.x = 0;
            center.y = 0;
            center.z = 0;

            // 将初始化中心点设置为所有点的代数平均位置
            foreach (var pt in originPts)
            {
                center.x += pt.x;
                center.y += pt.y;
                center.z += pt.z;
            }
            center.x /= originPts.Count;
            center.y /= originPts.Count;
            center.z /= originPts.Count;

            double temp = 1e3; // 初始温度
            double coolingFactor = 0.98; // 降温因子
            double ans = GetMaxRadius(center, originPts); // 当前最小半径
            var random = new Random();

            while (temp > 1e-5)
            {
                Point newCenter = new Point();
                double max_r = 0;
                // 找到与当前中心点距离最远的点，将中心向着改点移动
                for (int i = 0; i < originPts.Count; i++)
                {
                    double r = Dist(center, originPts[i]);
                    if (r > max_r)
                    {
                        newCenter.x = (originPts[i].x - center.x) / r;
                        newCenter.y = (originPts[i].y - center.y) / r;
                        newCenter.z = (originPts[i].z - center.z) / r;
                        max_r = r;
                    }
                }
                newCenter.x = center.x + newCenter.x * temp;
                newCenter.y = center.y + newCenter.y * temp;
                newCenter.z = center.z + newCenter.z * temp;

                // 移动后的最大半径
                double tmp = GetMaxRadius(newCenter, originPts);

                if (tmp < ans) 
                {
                    center.x += newCenter.x * temp;
                    center.y += newCenter.y * temp;
                    center.z += newCenter.z * temp;
                }
                else if (Math.Exp((ans -tmp)/temp) > random.NextDouble() )
                {
                    center.x += newCenter.x * temp;
                    center.y += newCenter.y * temp;
                    center.z += newCenter.z * temp;
                }

                temp *= coolingFactor;
            }
            double miniRadius = GetMaxRadius(center, originPts);
            Console.WriteLine("the cooridnate of the center is {0}, the radius value is {1}", center, miniRadius));

            return miniRadius;
        }
    }
}