计算几何小结计算几何小结

计算几何小结

计算几何是个好东西，写代码感觉在写LemonLime(不你没真正写过)，一层层堆叠起来，真(难)好(调)玩。

占坑

//@winlere
#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<assert.h>
#define pf(x) ((x)*(x))

using namespace std;  typedef long long ll;
inline int qr(){
	int ret=0,f=0,c=getchar();
	while(!isdigit(c))f|=c==45,c=getchar();
	while(isdigit(c)) ret=ret*10+c-48,c=getchar();
	return f?-ret:ret;
}

struct NODE{
	double x,y;
	NODE operator + (NODE b)const{return {x+b.x,y+b.y};}
	NODE operator - (NODE b)const{return {x-b.x,y-b.y};}
	NODE operator * (double b)const{return {x*b,y*b};}
	double operator % (NODE b)const{return x*b.y-y*b.x;}
	double operator ^ (NODE b)const{return sqrt(pf(x-b.x)+pf(y-b.y));}
	bool operator < (NODE b)const{return atan2(y,x)<atan2(b.y,b.x);}
	bool operator == (NODE b)const{return x==b.x&&y==b.y;}
};

double atan2(NODE a){return atan2(a.y,a.x);}

struct LINE{
	NODE vec,pt;
	LINE(NODE a,NODE b):vec(b-a),pt(a){}
	bool operator < (LINE b)const{return atan2(vec)==atan2(b.vec)?b.vec%(pt-b.pt)>0:vec<b.vec;}
	NODE operator * (LINE b)const{
		//no exist para
		NODE A=vec,B=b.vec,C=b.pt-pt;
		//if(B%A==0) return {1e9,1e9};
		double t=(B%C)/(B%A);
		//assert(t==t);
		return pt+vec*t;
	}
};

typedef vector<NODE> mat;
typedef vector<LINE> poly;
poly data;
const double bound=1000;
double sum(poly data){
	if(data.size()<3) return 0;
	double ret=0;
	sort(data.begin(),data.end());
	NODE x={0,0};
	for(int t=0,ed=data.size();t<ed;++t)
		ret+=(data[t]*data[(t-1+ed)%ed]-x)%(data[t]*data[(t+1)%ed]-x);	
	assert(ret==ret);
	return ret/2;
}

poly Surface(poly _data){
	sort(_data.begin(),_data.end());
	poly data;
	for(int t=0,r=0,ed=_data.size();r<ed;t=++r){
		while(r+1<ed&&atan2(_data[t].vec)==atan2(_data[r+1].vec)) ++r;
		data.push_back(_data[t]);
	}
	deque<LINE> q(data.begin(),data.begin()+2);
	for(int t=2,ed=data.size();t<ed;++t){
		while(q.size()>1){
			NODE m=q[q.size()-1]*q[q.size()-2];
			assert(m.x<=1e7);
			if(data[t].vec%(m-data[t].pt)<0) q.pop_back();
			else break;
		}
		while(q.size()>1){
			NODE m=q[0]*q[1];
			assert(m.x<=1e7);
			if(data[t].vec%(m-data[t].pt)<0) q.pop_front();
			else break;
		}
		q.push_back(data[t]);
	}
	while(q.size()>1){
		NODE m=q[q.size()-1]*q[q.size()-2];
		assert(m.x<=1e7);
		if(q.front().vec%(m-q.front().pt)<0) q.pop_back();
		else break;
	}
	while(q.size()>1){
		NODE m=q[0]*q[1];
		assert(m.x<=1e7);
		if(q.back().vec%(m-q.back().pt)<0) q.pop_front();
		else break;
	}
	return poly(q.begin(),q.end());
}

int main(){
	int n=qr();
	for(int t0=1;t0<=n;++t0){
		mat sav(qr());
		for(auto&t:sav) t.x=qr(),t.y=qr();
		for(int i=0,ed=sav.size();i<ed;++i)
			data.push_back(LINE(sav[i],sav[(i+1)%ed]));
		sort(data.begin(),data.end());
	}
	double k=sum(Surface(data));
	printf("%.5lf\n",k);
	return 0;
}