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falsebool 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.

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///------------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 2time_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 2time_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 3time_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。