Tell me the area（计算几何--求两圆相交面积）

Problem Link：http://acm.hdu.edu.cn/showproblem.php?pid=1798

Tell me the area

Time Limit: 3000/1000 MS (Java/Others)    Memory Limit: 65536/32768 K (Java/Others)
Total Submission(s): 2828    Accepted Submission(s): 903

Problem Description

    There are two circles in the plane (shown in the below picture), there is a common area between the two circles. The problem is easy that you just tell me the common area.

 

Input

There are many cases. In each case, there are two lines. Each line has three numbers: the coordinates (X and Y) of the centre of a circle, and the radius of the circle.

 

Output

For each case, you just print the common area which is rounded to three digits after the decimal point. For more details, just look at the sample.

 

Sample Input

0 0 2 2 2 1

 

Sample Output

0.108

 

Author

wangye

 

Source

2008 “Insigma International Cup” Zhejiang Collegiate Programming Contest - Warm Up（4）

AC code：

#include
#include
#include
#include
#define PI acos(-1)

using namespace std;

int main()
{
	int T;
	double r1,r2,x1,x2,y1,y2,dr,r,A1,A2,p,s,s1,s2,ans;	
	while(scanf("%lf%lf%lf",&x1,&y1,&r1)!=EOF)
	{
		scanf("%lf%lf%lf",&x2,&y2,&r2);
		dr=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
		r=min(r1,r2);
		if(dr>=r1+r2)
			printf("0.000\n");
		else if(dr<=fabs(r1-r2) && dr>=0)
		{
			ans=PI*r*r;
			printf("%0.3lf\n",ans);
		}
		else
		{
			A1=acos((r1*r1+dr*dr-r2*r2)/(2*r1*dr));
			A2=acos((r2*r2+dr*dr-r1*r1)/(2*r2*dr));
			p=(r1+r2+dr)/2;
			s=sqrt(p*(p-r1)*(p-r2)*(p-dr));
			s1=s-PI*r2*r2*(A2/(2*PI));
			s2=s-PI*r1*r1*(A1/(2*PI));
			ans=2*(s-s1-s2);
			printf("%.3lf\n",ans);
		}		
	}
	return 0;
}