计算几何 多边形相交、半平面交

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<complex>
#include<vector>
#include<deque>
using namespace std;
typedef long long LL;
#define INF 0x7fffffff
#define zero(x) (((x)>0?(x):(-x))<eps)
const double eps=1e-8;
const double pi=acos(-1.0);
int dcmp(double x) { return x<-eps?-1:x>eps?1:0;}
double sqr(double x) { return x*x;}
double mysqrt(double n) { return sqrt(max(0.0,n));}

struct point
{
    double x,y;
    point() {};
    point(double a,double b):x(a),y(b) {};
};
typedef point Vector;
//向量-向量
Vector operator -(const Vector &a, const Vector &b) {return Vector(a.x-b.x, a.y-b.y);}
//向量+向量
Vector operator +(const Vector &a, const Vector &b) {return Vector(a.x+b.x, a.y+b.y);}
//向量*常数
Vector operator *(const double &a, const Vector &b) {return Vector(a*b.x, a*b.y);}
Vector operator *(const Vector &a, const double &b) {return Vector(a.x*b, a.y*b);}
Vector operator /(const Vector &a, const double &b) {return Vector(a.x/b,a.y/b);}
//向量*向量 Dot
double dot(const Vector &a,const Vector &b) {return a.x*b.x+a.y*b.y;}
//向量X向量
double cross(const Vector &a,const Vector &b) {return a.x*b.y-a.y*b.x;}
//向量==向量
bool isequal(const Vector &a,const Vector &b) {return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;}
double Area(vector<point> p)
{
    int n=p.size();
    double area = 0;
    for(int i=1; i<n-1; ++i)
        area += cross(p[i]-p[0], p[i+1]-p[0]);
    return fabs(area/2);
}

//struct halfplane
//{
//    point a,b;
//    halfplane() {};
//    halfplane(point a,point b):a(a),b(b) {};
//};

typedef pair<point,point> halfplane;

inline double satisfy(point a,halfplane p)
{
    return dcmp(cross(a-p.first,p.second-p.first))<=0;
}
point crosspoint(const halfplane &a,const halfplane &b)
{
    double k=cross(b.first-b.second,a.first-b.second);
    k=k/(k-cross(b.first-b.second,a.second-b.second));
    return a.first+(a.second-a.first)*(k);
}
double arg(point p)
{
    return arg(complex<double>(p.x,p.y));
}
bool cmp(const halfplane &a,const halfplane &b)
{
    int res=dcmp(arg(a.second-a.first)-arg(b.second-b.first));
    return res==0? satisfy(a.first,b):res<0;
}
vector<point> halfplaneIntersection(vector<halfplane> v)
{
    sort(v.begin(),v.end(),cmp);
    deque<halfplane> q;
    deque<point> ans;
    q.push_back(v[0]);
    for(int i=1; i<v.size(); ++i)
    {
        if(dcmp(arg(v[i].second-v[i].first)-arg(v[i-1].second-v[i-1].first))==0)
        {
            continue;
        }
        while(ans.size()>0&&!satisfy(ans.back(),v[i]))
        {
            ans.pop_back();
            q.pop_back();
        }
        while(ans.size()>0&&!satisfy(ans.front(),v[i]))
        {
            ans.pop_front();
            q.pop_front();
        }
        ans.push_back(crosspoint(q.back(),v[i]));
        q.push_back(v[i]);
    }
    while(ans.size()>0&&!satisfy(ans.back(),q.front()))
    {
        ans.pop_back();
        q.pop_back();
    }
    while(ans.size()>0&&!satisfy(ans.front(),q.back()))
    {
        ans.pop_front();
        q.pop_front();
    }
    ans.push_back(crosspoint(q.back(),q.front()));
    return vector<point>(ans.begin(),ans.end());
}

vector<halfplane> hp;
vector<point> ans;
point p[100],q[100];

int main()
{
    double x1,Y1,x2,Y2;
    double x3,Y3,x4,Y4;
    while(scanf("%lf %lf %lf %lf",&x1,&Y1,&x2,&Y2)!=EOF)
    {
        scanf("%lf %lf %lf %lf",&x3,&Y3,&x4,&Y4);
        p[0]=point(x1,Y1);
        p[1]=point(x2,Y1);
        p[2]=point(x1,Y2);
        hp.clear();
        //要逆时针插入
        if(x1>x2&&Y1>Y2) {
            hp.push_back(halfplane(p[0],p[1]));
            hp.push_back(halfplane(p[1],p[2]));
            hp.push_back(halfplane(p[2],p[0]));
        }
        else if(x1>x2&&Y1<Y2) {
                hp.push_back(halfplane(p[1],p[0]));
            hp.push_back(halfplane(p[0],p[2]));
            hp.push_back(halfplane(p[2],p[1]));
        }
        else if(x1<x2&&Y1>Y2) {
            hp.push_back(halfplane(p[0],p[2]));
            hp.push_back(halfplane(p[2],p[1]));
            hp.push_back(halfplane(p[1],p[0]));
        }
        else if(x1<x2&&Y1<Y2) {
            hp.push_back(halfplane(p[0],p[1]));
            hp.push_back(halfplane(p[1],p[2]));
            hp.push_back(halfplane(p[2],p[0]));
        }

        q[0]=point(x3,Y3);
        q[1]=point(x4,Y3);
        q[2]=point(x4,Y4);
        q[3]=point(x3,Y4);
        hp.push_back(halfplane(q[0],q[1]));
        hp.push_back(halfplane(q[1],q[2]));
        hp.push_back(halfplane(q[2],q[3]));
        hp.push_back(halfplane(q[3],q[0]));

        ans =halfplaneIntersection(hp);
        printf("%.8f
",Area(ans));
    }
    return 0;
}