[POJ 1410] Intersection

#include<iostream>
#include<stdio.h>
#include<string>
#include<map>
#include<set>
#include<queue>
#include<stack>
#include<string.h>
#include<stdlib.h>
#include<math.h>
#include<algorithm>
#define PI 3.1415926
#define MOD 10000000007
#define N 1000005
#define INF 0x7fffffff
using namespace std;
typedef long long LL;
const double eps=1e-8;
//点
struct point
{
    double x,y;
};
//线段
struct line
{
    point p1,p2;
} l;
//面
struct poly
{
    int n;//几个面
    double area;
    point plist[15];
} rec;
//点乘
double dotdel(double x1,double y1,double x2,double y2)
{
    return x1*x2+y1*y2;
}
//叉乘
double crossmul(double x1,double y1,double x2,double y2)
{
    return x1*y2-x2*y1;
}
//判断是否为0，达到一定精度即认为成立
int cmpzero(double d)
{
    return (fabs(d)<eps)?0:(d>0?1:-1);
}
//右手螺旋定则，1:a在cd右侧，-1:a在cd左侧，0:三点共线
int cross(point a,point c,point d)
{
    return cmpzero(crossmul(a.x-c.x,a.y-c.y,d.x-c.x,d.y-c.y));
}
//在cross(a,c,d)==0的基础上，可判断点a是否在cd内部
int between(point a,point c,point d)
{
    return cmpzero(dotdel(c.x-a.x,c.y-a.y,d.x-a.x,d.y-a.y))!=1;
}
//两线段相交情况：0:不相交，1:规范相交，2:不规范相交（交于端点或重合）
int seg_intersect(point a,point b,point c,point d)
{
    int a_cd=cross(a,c,d);
    if(a_cd==0 && between(a,c,d))
        return 2;
    int b_cd=cross(b,c,d);
    if(a_cd==0 && between(a,c,d))
        return 2;
    int c_ab = cross(c, a, b);
    if (c_ab == 0 && between(c, a, b))
        return 2;
    int d_ab=cross(d,a,b);
    if(d_ab==0 && between(d,a,b))
        return 2;
    if((a_cd^b_cd)==-2 && (c_ab^d_ab)==-2)
        return 1;
    return 0;
}
//使用有向面积法判断点是否在多边形内
bool point_in_poly(point p)
{
    double s=0.0;
    for(int i=0; i<rec.n; i++)
        s+=fabs(crossmul(rec.plist[i].x-p.x,rec.plist[i].y-p.y,rec.plist[(i+1)%rec.n].x-p.x,
                         rec.plist[(i+1)%rec.n].y-p.y));
    if(cmpzero(s-rec.area)==0) return true;
    else return false;
}
//判断线段是否与多边形相交
bool rec_seg_intersect()
{
    if(point_in_poly(l.p1) && point_in_poly(l.p2))
        return 1;
    else if(seg_intersect(l.p1,l.p2,rec.plist[0],rec.plist[1])
            || seg_intersect(l.p1,l.p2,rec.plist[1],rec.plist[2])
            || seg_intersect(l.p1,l.p2,rec.plist[2],rec.plist[3])
            || seg_intersect(l.p1,l.p2,rec.plist[3],rec.plist[0]))
        return 1;
    return 0;
}
//计算多边形面积
void getarea()
{
    double s=rec.plist[0].y*(rec.plist[rec.n-1].x-rec.plist[1].x);
    for(int i=1; i<rec.n; i++)
        s+=rec.plist[i].y*(rec.plist[i-1].x-rec.plist[(i+1)%rec.n].x);
    rec.area=s;
}
int main()
{
    int T;
    double x1,y1,x2,y2,t;
    scanf("%d",&T);
    while(T--)
    {
        scanf("%lf%lf%lf%lf",&l.p1.x,&l.p1.y,&l.p2.x,&l.p2.y);
        scanf("%lf%lf%lf%lf",&x1,&y1,&x2,&y2);
        if(x1>x2)
        {
            t=x1;
            x1=x2;
            x2=t;
        }
        if(y2>y1)
        {
            t=y1;
            y1=y2;
            y2=t;
        }
        rec.n=4;
        rec.plist[0].x=x1;
        rec.plist[0].y=y1;
        rec.plist[1].x=x1;
        rec.plist[1].y=y2;
        rec.plist[2].x=x2;
        rec.plist[2].y=y2;
        rec.plist[3].x=x2;
        rec.plist[3].y=y1;
        getarea();
        puts(rec_seg_intersect()?"T":"F");
    }
    return 0;
}