线段相交

转载地址：http://blog.csdn.net/rickliuxiao/article/details/6259322

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)<min(cc.x, dd.x) )  
        {  
            return false;  
        }  
        if ( max(aa.y, bb.y)<min(cc.y, dd.y) )  
        {  
            return false;  
        }  
        if ( max(cc.x, dd.x)<min(aa.x, bb.x) )  
        {  
            return false;  
        }  
        if ( max(cc.y, dd.y)<min(aa.y, bb.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;  
    }