HDU5120

这题求的是圆环相交的面积，画图可知圆环相交面积=大交大-2×大交小+小交小

这题需要用到圆的相交面积公式

题目链接：http://acm.hust.edu.cn/vjudge/contest/view.action?cid=93642#problem/I

AC代码：

 1 #include <stdio.h>
 2 #include <string.h>
 3 #include <math.h>
 4 #include <algorithm>
 5 #define exp 1e-10
 6 #define PI 3.141592654
 7 using namespace std;
 8 typedef long long LL;
 9 struct point
10 {
11     double x,y;
12     point(double x=0,double y=0):x(x),y(y){}
13 }a,b;
14 
15 double dist(point a,point b)
16 {
17     double x=(a.x-b.x)*(a.x-b.x);
18     double y=(a.y-b.y)*(a.y-b.y);
19     return sqrt(x+y);
20 }
21 
22 double overlap(point c1,double r1,point c2,double r2)
23 {
24     double d=dist(c1,c2);
25     if(r1+r2<d+exp)
26     {
27         return 0;
28     }
29     if(d<fabs(r1-r2)+exp)
30     {
31         double r=min(r1,r2);
32         return PI*r*r;
33     }
34     double x=(d*d+r1*r1-r2*r2)/(2*d);
35     double t1=acos(x/r1);
36     double t2=acos((d-x)/r2);
37     return r1*r1*t1+r2*r2*t2-d*r1*sin(t1);
38 }
39 
40 int main()
41 {
42     int T,f;
43     f=0;
44     double r,R;
45     scanf("%d",&T);
46     while(T--)
47     {
48         f++;
49         scanf("%lf%lf",&r,&R);
50         scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y);
51         double big=overlap(a,R,b,R);
52         double bigsmall=overlap(a,R,b,r);
53         double small=overlap(a,r,b,r);
54         printf("Case #%d: %.6lf
",f,big-2*bigsmall+small);
55     }
56     return 0;
57 }

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