S = A大B大 - A大B小 - A小B大 + A小B小。（A表示A环，大表示大圆，B同）。然后直接套模板，，，，
1 #include <stdio.h>
2 #include <algorithm>
3 #include <string.h>
4 #include <cmath>
5 using namespace std;
6
7 const double eps = 1e-8;
8 const double PI = acos(-1.0);
9
10 int sgn(double x)
11 {
12 if(fabs(x) < eps) return 0;
13 if(x < 0) return - 1;
14 else return 1;
15 }
16 struct Point
17 {
18 double x, y;
19 Point(){}
20 Point(double _x, double _y)
21 {
22 x = _x; y = _y;
23 }
24 Point operator -( const Point &b) const
25 {
26 return Point(x - b. x, y - b. y);
27 }
28
29 double operator ^ (const Point &b) const
30 {
31 return x*b. y - y*b. x;
32 }
33
34 double operator * (const Point &b) const
35 {
36 return x*b. x + y*b. y;
37 }
38
39 void transXY(double B)
40 {
41 double tx = x,ty = y;
42 x = tx* cos(B) - ty*sin(B);
43 y = tx* sin(B) + ty*cos(B);
44 }
45 };
46
47 double dist( Point a, Point b)
48 {
49 return sqrt((a-b)*(a- b));
50 }
51
52 double Ac(Point c1, double r1, Point c2, double r2)
53 {
54 double d = dist(c1,c2);
55 if(r1 + r2 < d + eps) return 0;
56 if(d < fabs(r1 - r2) + eps)
57 {
58 double r = min(r1,r2);
59 return PI*r*r;
60 }
61 double x = (d*d + r1*r1 - r2*r2)/(2*d);
62 double t1 = acos(x / r1);
63 double t2 = acos((d - x)/r2);
64 return r1*r1*t1 + r2*r2*t2 - d*r1*sin(t1);
65 }
66
67 int main() {
68 int T; Point c1, c2;
69 double ans, r, R, x1, y1, x2, y2;
70 scanf("%d", &T);
71 for(int cas = 1; cas <= T; ++cas) {
72 scanf("%lf%lf%lf%lf%lf%lf", &r, &R, &x1, &y1, &x2, &y2);
73 c1.x = x1; c1.y = y1;
74 c2.x = x2; c2.y = y2;
75 ans = Ac(c1, R, c2, R) - Ac(c1, R, c2, r) - Ac(c1, r, c2, R)
76 + Ac(c1, r, c2, r);
77 printf("Case #%d: %.6lf\n", cas, ans);
78 }
79 return 0;
80 }
