如何判断两个三角形在2D空间中是否相交或包含？

在处理UV重叠、CPU的ZFighting检测时会遇到2D空间中的三角形相交问题， 网上普遍是3D空间的相交解法，因此写本文研究下，不过虽然实现了需求， 但解法较为暴力。 效果如图： （鼠标拖动区域处有一小三角形，与外部大三角形进行相交包含演示） 若两三角形存在线段相交，则两三角形相交，但三点都包含的情况下则无法囊括在内。 所以还需额外判断一次三点都包含的情况。 2D空间的三角形相交得从线段与线段相交做起，这里用之前的叉乘方法来检测： https://www.cnblogs.com/hont/p/6106043.html 点是否在多边形内用的是单双数检测法： https://www.cnblogs.com/hont/p/6105997.html 方法还是比较朴素的方法，但离线情况下使用无问题。 代码如下(Unity XZ空间)： using System.Collections; using System.Collections.Generic; using UnityEngine; public class RayVsTriangle : MonoBehaviour { public Transform a0; public Transform b0; public Transform c0; public Transform a1; public Transform b1; public Transform c1; private bool TriangleVsTriangle(Vector3 a0, Vector3 b0, Vector3 c0, Vector3 a1, Vector3 b1, Vector3 c1) { bool IsIntersect(Vector3 a, Vector3 b, Vector3 c, Vector3 d) { float crossA = Vector3.Cross(d - c, a - c).y; float crossB = Vector3.Cross(d - c, b - c).y; if (!(crossA > 0f ^ crossB > 0f)) return false; float crossC = Vector3.Cross(b - a, c - a).y; float crossD = Vector3.Cross(b - a, d - a).y; if (!(crossC > 0f ^ crossD > 0f)) return false; return true; } bool IsContain(Vector3 a, Vector3 b, Vector3 c, Vector3 p0) { const float kRaycastLen = 100000f; Vector3 comparePoint = (c + b) * 0.5f; Vector3 originPoint = p0; comparePoint += (comparePoint - originPoint).normalized * kRaycastLen; int count = 0; if (IsIntersect(a, b, originPoint, comparePoint)) ++count; if (IsIntersect(b, c, originPoint, comparePoint)) ++count; if (IsIntersect(c, a, originPoint, comparePoint)) ++count; return count % 2 == 1; } if (IsIntersect(a0, b0, a1, b1)) return true; if (IsIntersect(a0, b0, b1, c1)) return true; if (IsIntersect(a0, b0, c1, a1)) return true; if (IsIntersect(b0, c0, a1, b1)) return true; if (IsIntersect(b0, c0, b1, c1)) return true; if (IsIntersect(b0, c0, c1, a1)) return true; if (IsIntersect(c0, a0, a1, b1)) return true; if (IsIntersect(c0, a0, b1, c1)) return true; if (IsIntersect(c0, a0, c1, a1)) return true; if (IsContain(a1, b1, c1, a0) && IsContain(a1, b1, c1, b0) && IsContain(a1, b1, c1, c0)) return true; return false; } private void OnDrawGizmos() { bool isRed = TriangleVsTriangle(a0.position, b0.position, c0.position, a1.position, b1.position, c1.position); Gizmos.color = isRed ? Color.red : Color.white; Gizmos.DrawLine(a0.position, b0.position); Gizmos.DrawLine(b0.position, c0.position); Gizmos.DrawLine(c0.position, a0.position); Gizmos.DrawLine(a1.position, b1.position); Gizmos.DrawLine(b1.position, c1.position); Gizmos.DrawLine(c1.position, a1.position); } }