标签：

Intersection

Matt is a big fan of logo design. Recently he falls in love with logo made up by rings. The following figures are some famous examples you may know.


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.

2
2 3
0 0
0 0
2 3
0 0
5 0

Case #1: 15.707963
Case #2: 2.250778

2014ACM/ICPC亚洲区北京站-重现赛（感谢北师和上交）  

几何计算题，，，有点麻烦

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
int a1,a2,b1,b2;
double d,p;
double area;
double fun(int a,int b)
{
    double sa,sb;
	d=sqrt((a1-a2)*(a1-a2)+(b1-b2)*(b1-b2));//圆心距 
	double rr=min(a,b);
	if(d<=abs(a-b))   //内含或者内切
 	  area=acos(-1.0)*rr*rr;
	else if(d>=a+b)//外切或不相交 
	      area=0.0;
	else{//相交求面积 
  	   p=(a+b+d)/2.0;//海伦公式里边的P 
	   sa=acos((a*a+d*d-b*b)/(2.0*a*d));//c^2=a^2+b^2-2*a*b*cos;求出圆心角 
	   sb=acos((b*b+d*d-a*a)/(2.0*b*d)); //同上      
  	   area=sa*a*a+sb*b*b-2*sqrt(p*(p-a)*(p-b)*(p-d));//两个扇形面积和就减去三角形面积，得相交部分面积 
	}
    return area;
}
int main()
{
	int t,k=0;
	int R,r;
	double s1,s2,s3,sum;
	while(scanf("%d",&t)!=EOF){
		while(t--){
		 k++;
		 scanf("%d%d%d%d%d%d",&R,&r,&a1,&b1,&a2,&b2);
		 s1=fun(R,R); s2=fun(r,r); s3=fun(R,r);//环的可以看作是两个圆，可以看出规律，，两个环相交的面积就等于
		 		//两个大圆相交的面积减去两次大圆和小圆相交的面积，再加上两个小圆相交的面积 
		 if(R>r)  sum=s1-2*s3+s2;
		 else sum=s2-2*s3+s1;
		 printf("Case #%d: %.6lf\n",k,sum);
		}
	}
	return 0;
} 

hdu 5120 Intersection

标签：

原文地址：http://blog.csdn.net/ling_du/article/details/47186947