判断两条线段是否相交

思路：即利用叉积判断线段两端点是否都相互横跨

#include <iostream>

using namespace std;

struct point

{

     double x,y;

};

double min(double x,double y)

{

     return x<y?x:y;

}

double max(double x,double y)

{

     return x>y?x:y;

}

bool onsegment(point pi,point pj,point pk) //有可能在某线段上

{

     if(min(pi.x,pj.x)<=pk.x&&pk.x<=max(pi.x,pj.x))

     {

          if(min(pi.y,pj.y)<=pk.y&&pk.y<=max(pi.y,pj.y))

          {

               return true;

          }

     }

     return false;

}

double direction(point pi,point pj,point pk)//计算叉积

{

     return (pi.x-pk.x)*(pi.y-pj.y)-(pi.y-pk.y)*(pi.x-pj.x);

}

bool judge(point p1,point p2,point p3,point p4)//判断是否相交

{

     double d1 = direction(p3,p4,p1);

     double d2 = direction(p3,p4,p2);

     double d3 = direction(p1,p2,p3);

     double d4 = direction(p1,p2,p4);

     if(d1*d2<0&&d3*d4<0)

          return true;

     if(d1==0&&onsegment(p3,p4,p1))

     return true;

     if(d2==0&&onsegment(p3,p4,p2))

     return true;

     if(d3==0&&onsegment(p1,p2,p3))

     return true;

     if(d4==0&&onsegment(p1,p2,p4))

     return true;

     return false;

}

int main()

{

     point p1,p2,p3,p4;

     cin>>p1.x>>p1.y>>p2.x>>p2.y>>p3.x>>p3.y>>p4.x>>p4.y;

     if(judge(p1,p2,p3,p4))

     {

          cout<<"the two segments are interset"<<endl;

     }

     else

     {

          cout<<"the two segments are not interset"<<endl;

     }

    return 0;

}