hdu 5120 Intersection

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 ;
 }