hdu 5120 Intersection

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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 ;

 }