Educational Codeforces Round 2D. Area of Two Circles' Intersection（计算几何+圆相交的面积）

#define CF

#ifndef CF
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#else
#include<bits/stdc++.h>
#endif // CF
using namespace std;
#define LL long long
#define pb push_back
#define X first
#define Y second
#define cl(a,b) memset(a,b,sizeof(a))
typedef pair<long long ,long long > P;
const int maxn=2*100005;
const LL inf=1LL<<50;
const LL mod=1e9+7;

typedef long double db;
const db pi=acos(-1.0);

db Deg2Rad(db deg){return (deg*pi/180.0);}
db Rad2Deg(db rad){return (rad*180.0/pi);}
db Sin(db deg){return sin(Deg2Rad(deg));}
db ArcSin(db val){return Rad2Deg(asin(val));}
db ArcCos(db val){return Rad2Deg(acos(val));}
struct circle{
db x,y,r;
circle(){}
circle(db _x,db _y, db _r):x(_x),y(_y),r(_r){}
};
struct point{
db x,y;
point(){x=y=0;}
point(db a,db b){
x=a,y=b;
}
};
point Center(const circle&c){
return point(c.x,c.y);
}
db Distance(const point&a,const point&b){
return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
db Area(const circle& x){
return pi*x.r*x.r;
}
db commonArea(const circle&A,const circle &B){
db area=0.0;
const circle&M=(A.r>B.r)?A:B;
const circle&N=(A.r>B.r)?B:A;
db D=Distance(Center(M),Center(N));
if((D<M.r+N.r)&&(D>M.r-N.r)){
db cosM=(M.r*M.r+D*D-N.r*N.r)/(2.0*M.r*D);
db cosN=(N.r*N.r+D*D-M.r*M.r)/(2.0*N.r*D);
db alpha=2.0*ArcCos(cosM);
db beta= 2.0*ArcCos(cosN);
db TM=0.5*M.r*M.r*Sin(alpha);
db TN=0.5*N.r*N.r*Sin(beta);
db FM=(alpha/360.0)*Area(M);
db FN=(beta/360.0)*Area(N);
area=FM+FN-TM-TN;
}
else if(D<=M.r-N.r){
area=Area(N);
}
return area;
}
int main(){
db x1,x2,y1,y2,r1,r2;
cin>>x1>>y1>>r1;
cin>>x2>>y2>>r2;
circle A(x1,y1,r1),B(x2,y2,r2);
cout.precision(9);
cout<<commonArea(A,B)<<endl;
return 0;
}