求两圆相交部分面积（C++)

 1 #include <iostream>
 2 using namespace std;
 3 #include<cmath>
 4 #include<stdio.h>
 5 #define PI 3.141593
 6 struct point//点
 7 {
 8     double x,y;
 9 };
10 struct circle//圆
11 {
12     point center;
13     double r;
14 };
15 float dist(point a,point b)//求圆心距
16 {
17     return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
18 }
19  
20 int main()
21 {
22     circle a,b;
23     while(cin>>a.center.x>>a.center.y>>a.r>>b.center.x>>b.center.y>>b.r)
24     {
25         if((dist(a.center,b.center)+min(a.r,b.r))<=max(a.r,b.r))//两圆内交或包含
26             {
27                 if(a.r<b.r) printf("%.3lf\n",PI*a.r*a.r);
28                 else printf("%.3lf\n",PI*b.r*b.r);
29             }
30         else if(dist(a.center,b.center)>=(a.r+b.r))//两圆外交或相离
31             cout<<"0.000"<<endl;
32         else
33         {
34             double length=dist(a.center,b.center);
35             double d1=2*acos((a.r*a.r+length*length-b.r*b.r)/(2*a.r*length)); //求两扇形圆心角
36             double d2=2*acos((b.r*b.r+length*length-a.r*a.r)/(2*b.r*length));
37             double area1=a.r*a.r*d1/2-a.r*a.r*sin(d1)/2;
38             //根据圆心角求扇形面积，减去三角形面积，得到相交部分面积
39             //扇形面积：S=PI*r*r*θ/(2*PI)  三角形面积：S=1/2*a*c*sin(B)
40             double area2=b.r*b.r*d2/2-b.r*b.r*sin(d2)/2;
41             double area=area1+area2;
42             printf("%.3lf\n",area);
43         }
44     }
45     return 0;
46 }