uva 191 Intersection

题目：判断线段是否与矩形相交。

分析：计算几何，简单题。先判断线段在矩形内的情况，然后判断线段与四边关系即可。

注意：线段在矩形内部属于相交，线段与边平行时的特判。

/*线段相交 */#include <iostream>#include <cstdio>#include <cstdlib>#define deff 1e-6//#define Tusing namespace std;struct Point{  double x;double y;};int direction(Point* pi,Point* pj,Point* pk){    Point p1,p2;    p1.x = pk->x - pi->x;    p1.y = pk->y - pi->y;    p2.x = pj->x - pi->x;    p2.y = pj->y - pi->y;    double cross = p1.x*p2.y - p2.x*p1.y;    if(cross > deff)        return 1;    else if(cross < -deff)        return -1;    else        return 0;}bool onSegment(Point* pi,Point* pj,Point* pk){    double minx,miny,maxx,maxy;    if(pi->x > pj->x)    {        minx = pj->x; maxx = pi->x;    }    else    {        minx = pi->x; maxx = pj->x;    }    if(pi->y > pj->y)    {        miny = pj->y; maxy = pi->y;    }    else    {        miny = pi->y; maxy = pj->y;    }    return (minx <= pk->x)&&(maxx >= pk->x)&&(miny <=pk->y)&&(maxy >= pk->y);}bool segmentIntersect(Point* p1,Point* p2,Point* p3,Point* p4){    int d1 = direction(p3,p4,p1);    int d2 = direction(p3,p4,p2);    int d3 = direction(p1,p2,p3);    int d4 = direction(p1,p2,p4);    if(d1*d2 < 0&&d3*d4 < 0)    {       // printf("1\n");         return true;    }    if(!d1 && onSegment(p3,p4,p1))    {        //printf("2\n");        return true;    }    if(!d2 && onSegment(p3,p4,p2))        {           // printf("3\n");            return true;        }    if(!d3 && onSegment(p1,p2,p3))        {           // printf("4\n");            return true;        }    if(!d4 && onSegment(p1,p2,p4))        {           // printf("5\n");            return true;        }    return false;}//判断线段是否在矩形内bool inRectangle(Point* p1,Point* p2,Point* p3,Point* p4){    return onSegment(p3,p4,p1)&&onSegment(p3,p4,p2);}int main(){    #ifdef T     freopen("in.txt","r",stdin);     freopen("out.txt","w",stdout);    #endif    Point p1,p2,p3,p4,p5,p6;    bool b1,b2,b3,b4;    int n;   // int cas = 0;    scanf("%d",&n);    while(n--)    {       // printf("cas = %d\n",cas++);        scanf("%lf %lf %lf %lf",&p1.x,&p1.y,&p2.x,&p2.y);        scanf("%lf %lf %lf %lf",&p3.x,&p3.y,&p5.x,&p5.y);        if(inRectangle(&p1,&p2,&p3,&p5))        {             printf("T\n");             continue;        }        p4.x = p5.x;p4.y =p3.y;        p6.x = p3.x;p6.y =p5.y;        b1 = segmentIntersect(&p1,&p2,&p3,&p4);b2 = segmentIntersect(&p1,&p2,&p4,&p5);        b3 = segmentIntersect(&p1,&p2,&p5,&p6);b4 = segmentIntersect(&p1,&p2,&p6,&p3);        if(b1||b2||b3||b4)         printf("T\n");         else            printf("F\n");    }   return 0;}