判断两条线段是否相交（三种算法）

算法1：

 

 ///----------alg 1------------
 struct Point
 {
     double x, y;
 };

 bool between(double a, double X0, double X1)
 {
     double temp1= a-X0;
     double temp2= a-X1;
     if ( ( temp1<1e-8 && temp2>-1e-8 ) || ( temp2<1e-6 && temp1>-1e-8 ) )
     {
         return true;
     }
     else
     {
         return false;
     }
 }


 // 判断两条直线段是否有交点，有则计算交点的坐标
 // p1,p2是直线一的端点坐标
 // p3,p4是直线二的端点坐标
 bool detectIntersect(Point p1, Point p2, Point p3, Point p4)
 {
     double line_x,line_y; //交点
     if ( (fabs(p1.x-p2.x)<1e-6) && (fabs(p3.x-p4.x)<1e-6) )
     {
         return false;
     }
     else if ( (fabs(p1.x-p2.x)<1e-6) ) //如果直线段p1p2垂直与y轴
     {
         if (between(p1.x,p3.x,p4.x))
         {
             double k = (p4.y-p3.y)/(p4.x-p3.x);
             line_x = p1.x;
             line_y = k*(line_x-p3.x)+p3.y;

             if (between(line_y,p1.y,p2.y))
             {
                 return true;
             }
             else
             {
                 return false;
             }
         }
         else
         {
             return false;
         }
     }
     else if ( (fabs(p3.x-p4.x)<1e-6) ) //如果直线段p3p4垂直与y轴
     {
         if (between(p3.x,p1.x,p2.x))
         {
             double k = (p2.y-p1.y)/(p2.x-p1.x);
             line_x = p3.x;
             line_y = k*(line_x-p2.x)+p2.y;

             if (between(line_y,p3.y,p4.y))
             {
                 return true;
             }
             else
             {
                 return false;
             }
         }
         else
         {
             return false;
         }
     }
     else
     {
         double k1 = (p2.y-p1.y)/(p2.x-p1.x);
         double k2 = (p4.y-p3.y)/(p4.x-p3.x);

         if (fabs(k1-k2)<1e-6)
         {
             return false;
         }
         else
         {
             line_x = ((p3.y - p1.y) - (k2*p3.x - k1*p1.x)) / (k1-k2);
             line_y = k1*(line_x-p1.x)+p1.y;
         }

         if (between(line_x,p1.x,p2.x)&&between(line_x,p3.x,p4.x))
         {
             return true;
         }
         else
         {
             return false;
         }
     }
 }
 ///------------alg 1------------

 

 

算法2：

 ///------------alg 2------------
 //叉积
 double mult(Point a, Point b, Point c)
 {
     return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);
 }

 //aa, bb为一条线段两端点 cc, dd为另一条线段的两端点 相交返回true, 不相交返回false
 bool intersect(Point aa, Point bb, Point cc, Point dd)
 {
     if ( max(aa.x, bb.x)
     {
         return false;
     }
     if ( max(aa.y, bb.y)
     {
         return false;
     }
     if ( max(cc.x, dd.x)
     {
         return false;
     }
     if ( max(cc.y, dd.y)
     {
         return false;
     }
     if ( mult(cc, bb, aa)*mult(bb, dd, aa)<0 )
     {
         return false;
     }
     if ( mult(aa, dd, cc)*mult(dd, bb, cc)<0 )
     {
         return false;
     }
     return true;
 }
 ///------------alg 2------------

  

 

 

算法3：http://dec3.jlu.edu.cn/webcourse/t000096/graphics/chapter5/01_1.

html

 ///------------alg 3------------
 double determinant(double v1, double v2, double v3, double v4)  // 行列式
 {
     return (v1*v3-v2*v4);
 }

 bool intersect3(Point aa, Point bb, Point cc, Point dd)
 {
     double delta = determinant(bb.x-aa.x, cc.x-dd.x, bb.y-aa.y, cc.y-dd.y);
     if ( delta<=(1e-6) && delta>=-(1e-6) )  // delta=0，表示两线段重合或平行
     {
         return false;
     }
     double namenda = determinant(cc.x-aa.x, cc.x-dd.x, cc.y-aa.y, cc.y-dd.y) / delta;
     if ( namenda>1 || namenda<0 )
     {
         return false;
     }
     double miu = determinant(bb.x-aa.x, cc.x-aa.x, bb.y-aa.y, cc.y-aa.y) / delta;
     if ( miu>1 || miu<0 )
     {
         return false;
     }
     return true;
 }
 ///------------alg 3------------

 

main函数测试：

 

 int main()
 {
     Point p1, p2, p3, p4;
     p1.x = 1;
     p1.y = 4;
     p2.x = 3;
     p2.y = 0;
     p3.x = 0;
     p3.y = 1;
     p4.x = 4;
     p4.y = 3;


     int i=0, j=0;
     bool flag = false;
     flag = intersect3(p1, p2, p3, p4);

     // alg 2
     time_t seconds1 = time (NULL);
     for ( ; i!=20000; ++i )
     {
         for ( j=0; j!=60000; ++j )
         {
             flag = detectIntersect(p1, p2, p3, p4);
         }
     }
     time_t seconds2 = time (NULL);

     cout << "Time used in alg 1:" << seconds2-seconds1 << " seconds." << endl;

     // alg 2
     time_t seconds3 = time (NULL);
     i=0;
     j=0;
     for ( ; i!=20000; ++i )
     {
         for ( j=0; j!=60000; ++j )
         {
             flag = intersect(p1, p2, p3, p4);
         }
     }
     time_t seconds4 = time (NULL);
     cout << "Time used in alg 2:" << seconds4-seconds3 << " seconds." << endl;

     // alg 3
     time_t seconds5 = time (NULL);
     i=0;
     j=0;
     for ( ; i!=20000; ++i )
     {
         for ( j=0; j!=60000; ++j )
         {
             flag = intersect3(p1, p2, p3, p4);
         }
     }
     time_t seconds6 = time (NULL);
     cout << "Time used in alg 3:" << seconds6-seconds5 << " seconds." << endl;
     return 0;
 }

  

 VS2008编译器环境下测试结果：

Debug模式下： 

alg 1: 315 seconds;

alg 2: 832 seconds;

alg 3: 195 seconds;

 

Release模式下： 

alg 1: 157 seconds;

alg 2: 169 seconds;

alg 3: 122 seconds;

 

 

结论： 使用算法3，时间复杂度最低。