计算几何之线段相交问题模板

1.定义一个点的结构体：

const double eps=1e-6;//精度struct point{    int x,y;//一般是double比较好，个人喜好}node[100];

线段相交不同于直线相交，需要判断多次：
2.叉积：

double cross(point a,point b,point c){    return (c.x-a.x)*(b.y-a.y)-(b.x-a.x)*(c.y-a.y);}

3.快速排斥实验：

bool quick_check(point a,point b,point c,point d){    if(min(a.x,b.x)<=max(c.x,d.x)&&min(c.x,d.x)<=max(a.x,b.x)&&min(a.y,b.y)<=max(c.y,d.y)&&min(c.y,d.y)<=max(a.y,b.y))        return 1;    else return 0;}

4.跨立实验（一般和快速排斥一起用，进而排除特殊情况）

bool kua_li(point a,point b,point c,point d){    if(!quick_check(a,b,c,d)) return 0;    if(cross(a,b,c)*cross(a,b,d)>=-eps) return 0;    if(cross(c,d,a)*cross(c,d,b)>=-eps) return 0;     return 1;}

5.求线段交点（使用叉积）：

point intersection(point a,point b,point c,point d){    point inter;    inter.x=(cross(a,b,d)*c.x+cross(a,b,c)*d.x)/(cross(a,b,d)-cross(a,b,c));    inter.y=(cross(a,b,d)*c.y+cross(a,b,c)*d.y)/(cross(a,b,d)-cross(a,b,c));    return inter;}