题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=5120
A ring is a 2-D figure bounded by two circles sharing the common center. The radius for these circles are denoted by r and R (r < R). For more details, refer to the gray part in the illustration below.
Matt just designed a new logo consisting of two rings with the same size in the 2-D plane. For his interests, Matt would like to know the area of the intersection of these two rings.
题意：求两个相同大小的圆环的面积交。
解法：几何，圆的面积交模板。画一个图应该就能发现公式：圆环面积交=大圆大圆面积交-2×大圆小圆面积交+小圆小圆面积交。
#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#define inf 0x7fffffff
#define exp 1e-10
#define PI 3.141592654
using namespace std;
typedef long long ll;
struct Point
{
double x,y;
Point (double x=,double y=):x(x),y(y){}
};
double dist(Point a,Point b)
{
double x=(a.x-b.x)*(a.x-b.x);
double y=(a.y-b.y)*(a.y-b.y);
return sqrt(x+y);
}
double Area_of_overlap(Point c1,double r1,Point c2,double r2)
{
double d=dist(c1,c2);
if (r1+r2<d+exp) return ;
if (d<fabs(r1-r2)+exp)
{
double r=min(r1,r2);
return PI*r*r;
}
double x=(d*d+r1*r1-r2*r2)/(*d);
double t1=acos(x/r1);
double t2=acos((d-x)/r2);
return r1*r1*t1+r2*r2*t2-d*r1*sin(t1);
}
int main()
{
int t,ncase=;
double r,R;
Point a,b;
scanf("%d",&t);
while (t--)
{
scanf("%lf%lf",&r,&R);
scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y);
double bb_area=Area_of_overlap(a,R,b,R);
double bs_area=Area_of_overlap(a,R,b,r);
double ss_area=Area_of_overlap(a,r,b,r);
printf("Case #%d: %.6lf\n",ncase++,bb_area-2.0*bs_area+ss_area);
}
return ;
}