计算几何板子

#include <iostream>
#include <string.h>
#include <queue>
#include <stdio.h>
#include <algorithm>
#include <math.h>
typedef long long ll;
using namespace std;
const int maxn=1e4+10;
const int mod=998244353;
using namespace std;

const ll eps = 1e-8;
int sgn(ll x)
{
    if(fabs(x) < eps)return 0;
    if(x < 0) return -1;
    return 1;
}
struct Point
{
    ll x,y;
    Point(){}
    Point(ll _x,ll _y)
    {
        x = _x;y = _y;
    }
    Point operator -(const Point &b)const
    {
        return Point(x - b.x,y - b.y);
    }
    ll operator ^(const Point &b)const
    {
        return x*b.y - y*b.x;
    }
    ll operator *(const Point &b)const
    {
        return x*b.x + y*b.y;
    }
    ll operator ==(const Point &b)const
    {
        return x==b.x&&y==b.y;
    }

};
struct Line
{
    Point s,e;
    Line(){}
    Line(Point _s,Point _e)
    {
        s = _s;e = _e;
    }
};
ll xmult(Point p0,Point p1,Point p2) //p0p1 X p0p2
{
    return (p1-p0)^(p2-p0);
}
ll xmult(Point p0,Point p1,Point p2,Point p3) //p0p1 X p2p3
{
    return (p1-p0)^(p3-p2);
}
bool Seg_inter_line(Line l1,Line l2) //判断直线l1和线段l2是否相交
{
    return sgn(xmult(l2.s,l1.s,l1.e))*sgn(xmult(l2.e,l1.s,l1.e)) <= 0;
}
ll dist(Point a,Point b)
{
    return sqrt( (b - a)*(b - a) );
}
//多边形面积s的二倍（参数按逆时针给出）
ll get_mianji(Point *P,int num)
{
    ll ans=0;
    for(int i=0;i<num;i++)
    {
        ans+=P[i]^P[(i+1)%num];
    }
    return ans;
}
//多边形形面积e

//凸包s
Point tubao[maxn];
int num_tubao;
Point t(0,1e9+7);
bool cmp_jijiao(Point p1,Point p2)
{
    if(xmult(t, p1, p2)>0)
    {
        return 1;
    }
    else if(xmult(t, p1, p2)==0)
    {
        return dist(t, p1)<dist(t, p2);
    }
    else
        return 0;
}
void get_tubao(Point *P,int num)
{
    t.x=0;
    t.y=1e9+7;
    for(int i=0;i<num;i++)
    {
        if(P[i].y<t.y)
        {
            t=P[i];
        }
        else if(P[i].y==t.y)
        {
            t.x=min(P[i].x,t.x);
        }
    }
    sort(P, P+num, cmp_jijiao);
    num_tubao=2;
    tubao[0]=P[0];tubao[1]=P[1];
    for(int i=2;i<num;i++)
    {
        while(xmult(tubao[num_tubao-2], tubao[num_tubao-1], P[i])<0)
        {
            num_tubao--;
        }
        tubao[num_tubao]=P[i];
        num_tubao++;
        
    }
}
//凸包e

//旋转卡壳s（求最大四边形面积）
ll ro_ka(Point *P,int num)
{
    
    ll ans=0;
    //去掉重复的点s
    int num2=1;
    for(int i=1;i<num;i++)
    {
        if(P[i].x==P[i-1].x&&P[i].y==P[i-1].y)
        {
            continue;
        }
        else
        {
            P[num2]=P[i];
            num2++;
        }
    }
    num=num2;
    //去掉重复的点e
    for(int i=0;i<num;i++)
        P[i+num]=P[i];
    //检查是否凸包上的点全部共线s
    int flag=1;
    for(int i=2;i<num;i++)
    {
        if(xmult(P[0], P[1], P[2])!=0)
            flag=0;
    }
    if(flag==1)
        return 0;
    //检查是否凸包上的点全部共线e
    for(int i=0;i<num;i++){
        int l=i,r;
        for(int j=i+1;j<num;j++)
        {
            if(xmult(P[l], P[l+1], P[j],P[j+1])<0){
                r=j;
                break;
            }
        }
        for(int j=i+1;j<num;j++)
        {
            while(xmult(P[l], P[l+1], P[i],P[j])>0)
                l++;
            while(xmult(P[r], P[r+1], P[i],P[j])<0)
                r++;
            Point t[4]={P[i],P[l],P[j],P[r]};
            ans=max(ans,get_mianji(t, 4));
        }
    }
    return ans;
}
//旋转卡壳e

//坐标旋转s

Point rotate(Point p,double angle){
    Point v = p;
    double c = cos(angle), s = sin(angle);
    return Point(v.x*c - v.y*s , v.x*s + v.y*c);
}
//坐标旋转e

//半平面交s
Point dad_anticlock[maxn];//输入弄好就行了
Line dad_half_line[maxn],que[maxn];
    //得到极角角度
double getAngle(Point a) {
  return atan2(a.y, a.x);
}

    //得到极角角度
double getAngle(Line a) {
  return atan2(a.e.y - a.s.y, a.e.x - a.s.x);
}
bool onRight(Line a, Line b, Line c) {
  Point o = getIntersectPoint(b, c);
  if (((a.e - a.s) ^ (o - a.s)) < 0) return true;
  return false;
}
bool cmp_half(Line L1,Line L2)
{
    Point va = L1.e - L1.s, vb = L2.e - L2.s;
    double A =  getAngle(va), B = getAngle(vb);
    if (fabs((double)(A - B)) < eps) return ((va) ^ (L2.e - L1.s)) >= 0;
    return A < B;
}
bool Is_half(int num)
{
    for(int i=0;i<num;i++)
    {
        dad_half_line[i].s=dad_anticlock[i];
        dad_half_line[i].e=dad_anticlock[(i+1)%num];
    }
    sort(dad_half_line, dad_half_line+num, cmp_half);
    
    int head = 0, tail = 0, cnt = 0;//模拟双端队列
    //去重，极角相同时取最后一个。
    for (int i = 0; i < num - 1; i++) {
        if (fabs(getAngle(dad_half_line[i]) - getAngle(dad_half_line[i + 1])) < eps) {
            continue;
        }
        dad_half_line[cnt++] = dad_half_line[i];
    }
    dad_half_line[cnt++] = dad_half_line[num - 1];
    
    
    for (int i = 0; i < cnt; i++) {
        //判断新加入直线产生的影响
        while(tail - head > 1 && onRight(dad_half_line[i], que[tail - 1], que[tail - 2])) tail--;
        while(tail - head > 1 && onRight(dad_half_line[i], que[head], que[head + 1])) head++;
        que[tail++] = dad_half_line[i];
      }
      //最后判断最先加入的直线和最后的直线的影响
      while(tail - head > 1 && onRight(que[head], que[tail - 1], que[tail - 2])) tail--;
      while(tail - head > 1 && onRight(que[tail - 1], que[head], que[head + 1])) head++;
      if (tail - head < 3) return false;
      return true;
    
}

//半平面交e