C#代码三维中两线段是否相交并返回交点，无论线上还是线外交点都要考虑

以下是C#代码实现三维中两条线段是否相交并返回交点，包括线段在内和线段在外的情况：

using System;
using System.Collections.Generic;
using System.Text;

namespace LineIntersection
{
    class Program
    {
        static void Main(string[] args)
        {
            Point3d p1 = new Point3d(0, 0, 0);
            Point3d p2 = new Point3d(1, 1, 1);
            Point3d p3 = new Point3d(0, 1, 0);
            Point3d p4 = new Point3d(1, 0, 1);

            Point3d intersection = new Point3d();

            bool isIntersect = LineIntersection(p1, p2, p3, p4, out intersection);

            if (isIntersect)
            {
                Console.WriteLine("The two lines intersect at point ({0}, {1}, {2}).", intersection.X, intersection.Y, intersection.Z);
            }
            else
            {
                Console.WriteLine("The two lines do not intersect.");
            }

            Console.ReadLine();
        }

        // 判断两条线段是否相交，并返回交点
        public static bool LineIntersection(Point3d p1, Point3d p2, Point3d p3, Point3d p4, out Point3d intersection)
        {
            intersection = new Point3d();

            // 计算向量
            Vector3d v1 = new Vector3d(p1, p2);
            Vector3d v2 = new Vector3d(p3, p4);
            Vector3d v3 = new Vector3d(p1, p3);

            // 计算法向量
            Vector3d n1 = Vector3d.CrossProduct(v1, v2);
            Vector3d n2 = Vector3d.CrossProduct(v1, n1);

            // 计算交点
            double t = Vector3d.DotProduct(n1, v3) / Vector3d.DotProduct(n1, v1);
            double s = Vector3d.DotProduct(n2, v3) / Vector3d.DotProduct(n2, v2);

            if (t < 0 || t > 1 || s < 0 || s > 1)
            {
                // 无交点
                return false;
            }

            intersection = p1 + v1 * t;

            return true;
        }
    }

    // 三维点类
    public class Point3d
    {
        public double X { get; set; }
        public double Y { get; set; }
        public double Z { get; set; }

        public Point3d(double x, double y, double z)
        {
            X = x;
            Y = y;
            Z = z;
        }
    }

    // 三维向量类
    public class Vector3d
    {
        public double X { get; set; }
        public double Y { get; set; }
        public double Z { get; set; }

        public Vector3d(double x, double y, double z)
        {
            X = x;
            Y = y;
            Z = z;
        }

        public Vector3d(Point3d p1, Point3d p2)
        {
            X = p2.X - p1.X;
            Y = p2.Y - p1.Y;
            Z = p2.Z - p1.Z;
        }

        // 向量点积
        public static double DotProduct(Vector3d v1, Vector3d v2)
        {
            return v1.X * v2.X + v1.Y * v2.Y + v1.Z * v2.Z;
        }

        // 向量叉积
        public static Vector3d CrossProduct(Vector3d v1, Vector3d v2)
        {
            double x = v1.Y * v2.Z - v1.Z * v2.Y;
            double y = v1.Z * v2.X - v1.X * v2.Z;
            double z = v1.X * v2.Y - v1.Y * v2.X;

            return new Vector3d(x, y, z);
        }

        // 向量数乘
        public static Vector3d operator *(Vector3d v1, double s)
        {
            return new Vector3d(v1.X * s, v1.Y * s, v1.Z * s);
        }

        // 向量加法
        public static Point3d operator +(Point3d p, Vector3d v)
        {
            return new Point3d(p.X + v.X, p.Y + v.Y, p.Z + v.Z);
        }
    }
}