unity3d：两条线段相交并求交点坐标

àì夳堔傛蜴生んèń 2022-11-16 13:54 342阅读 0赞

public static float Cross(Vector2 a, Vector2 b)
        { 
            return a.x * b.y - b.x * a.y;
        }
    
        public static bool SegmentsInterPoint(Vector2 a, Vector2 b, Vector2 c, Vector2 d, ref Vector2 IntrPos)
        { 
    
            //v1×v2=x1y2-y1x2 
            //以线段ab为准，是否c，d在同一侧
            Vector2 ab = b - a;
            Vector2 ac = c - a;
            float abXac = Cross(ab,ac);
    
            Vector2 ad = d - a;
            float abXad = Cross(ab, ad);
    
            if (abXac * abXad >= 0)
            { 
                return false;
            }
    
            //以线段cd为准，是否ab在同一侧
            Vector2 cd = d - c;
            Vector2 ca = a - c;
            Vector2 cb = b - c;
    
            float cdXca = Cross(cd, ca);
            float cdXcb = Cross(cd, cb);
            if (cdXca * cdXcb >= 0)
            { 
                return false;
            }
            //计算交点坐标 
            float t = Cross(a -c, d -c) / Cross (d-c,b-a);
            float dx = t * (b.x - a.x);
            float dy = t * (b.y - a.y);
    
            IntrPos = new Vector2() {  x = a.x + dx, y = a.y + dy };
            return true;
        }

外积，又称叉积，是向量代数（解析几何）中的一个概念。两个向量v1(x1, y1)和v2(x2, y2)的外积v1×v2=x1y2-y1x2。如果由v1到v2是顺时针转动，外积为负，反之为正，为0表示二者方向相同（平行）。  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2x1b3lpa3Vu_size_16_color_FFFFFF_t_70]  
abxac \* abxad >= 0 说明以ab线段为准,c,d两点都在同一侧，说明两个线段不会相交  
cdxca \* cdxcb >=0 说明以cd线段为准，a，b两点都在同一侧，说明两个线段不会相交  
交点为o  
![在这里插入图片描述][20210407151356773.png]  
然后根据线段定义  
![在这里插入图片描述][20210407151435253.png]  
以a为起点，b-a为u， t为 ao/ab, 求出o点坐标  
![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2x1b3lpa3Vu_size_16_color_FFFFFF_t_70 1]

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[20210407151356773.png]: /images/20221022/70a164444a25489caa1e8695da5d768f.png
[20210407151435253.png]: /images/20221022/eebe56aa8a2b421a9b26629b9bfd5e57.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L2x1b3lpa3Vu_size_16_color_FFFFFF_t_70 1]: /images/20221022/e40a405f05b040359245769bba79f1ad.png