hdu 5120 Intersection

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\n",ncase++,bb_area-2.0*bs_area+ss_area);

51     }

52     return 0;

53 }