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。
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<cstdlib> 5 #include<cmath> 6 #include<algorithm> 7 #define inf 0x7fffffff 8 #define exp 1e-10 9 #define PI 3.141592654 10 using namespace std; 11 typedef long long ll; 12 struct Point 13 { 14 double x,y; 15 Point (double x=0,double y=0):x(x),y(y){} 16 }; 17 double dist(Point a,Point b) 18 { 19 double x=(a.x-b.x)*(a.x-b.x); 20 double y=(a.y-b.y)*(a.y-b.y); 21 return sqrt(x+y); 22 } 23 double Area_of_overlap(Point c1,double r1,Point c2,double r2) 24 { 25 double d=dist(c1,c2); 26 if (r1+r2<d+exp) return 0; 27 if (d<fabs(r1-r2)+exp) 28 { 29 double r=min(r1,r2); 30 return PI*r*r; 31 } 32 double x=(d*d+r1*r1-r2*r2)/(2*d); 33 double t1=acos(x/r1); 34 double t2=acos((d-x)/r2); 35 return r1*r1*t1+r2*r2*t2-d*r1*sin(t1); 36 } 37 int main() 38 { 39 int t,ncase=1; 40 double r,R; 41 Point a,b; 42 scanf("%d",&t); 43 while (t--) 44 { 45 scanf("%lf%lf",&r,&R); 46 scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y); 47 double bb_area=Area_of_overlap(a,R,b,R); 48 double bs_area=Area_of_overlap(a,R,b,r); 49 double ss_area=Area_of_overlap(a,r,b,r); 50 printf("Case #%d: %.6lf ",ncase++,bb_area-2.0*bs_area+ss_area); 51 } 52 return 0; 53 }