POJ 2986 A Triangle and a Circle 圆与三角形的公共面积

计算几何模板

 #include<stdio.h>
 #include<string.h>
 #include<stdlib.h>
 #include<math.h>
 #include<algorithm>

 const double eps = 1e-;
 const double pi = acos(-1.0);

 int dcmp(double x)
 {
     if(x > eps) return ;
     return x < -eps ? - : ;
 }

 struct Point
 {
     double x, y;
     Point()
     {
         x = y = ;
     }
     Point(double a, double b)
     {
         x = a, y = b;
     }
     inline void read()
     {
         scanf("%lf%lf", &x, &y);
     }
     inline Point operator-(const Point &b)const
     {
         return Point(x - b.x, y - b.y);
     }
     inline Point operator+(const Point &b)const
     {
         return Point(x + b.x, y + b.y);
     }
     inline Point operator*(const double &b)const
     {
         return Point(x * b, y * b);
     }
     inline double dot(const Point &b)const
     {
         return x * b.x + y * b.y;
     }
     inline double cross(const Point &b, const Point &c)const
     {
         return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);
     }
     inline double Dis(const Point &b)const
     {
         return sqrt((*this - b).dot(*this - b));
     }
     inline bool InLine(const Point &b, const Point &c)const//三点共线
     {
         return !dcmp(cross(b, c));
     }
     inline bool OnSeg(const Point &b, const Point &c)const//点在线段上，包括端点
     {
         return InLine(b, c) && (*this - c).dot(*this - b) < eps;
     }
 };

 inline double min(double a, double b)
 {
     return a < b ? a : b;
 }
 inline double max(double a, double b)
 {
     return a > b ? a : b;
 }
 inline double Sqr(double x)
 {
     return x * x;
 }
 inline double Sqr(const Point &p)
 {
     return p.dot(p);
 }

 Point LineCross(const Point &a, const Point &b, const Point &c, const Point &d)
 {
     double u = a.cross(b, c), v = b.cross(a, d);
     return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));
 }

 double LineCrossCircle(const Point &a, const Point &b, const Point &r,
                        double R, Point &p1, Point &p2)
 {
     Point fp = LineCross(r, Point(r.x + a.y - b.y, r.y + b.x - a.x), a, b);
     double rtol = r.Dis(fp);
     double rtos = fp.OnSeg(a, b) ? rtol : min(r.Dis(a), r.Dis(b));
     double atob = a.Dis(b);
     double fptoe = sqrt(R * R - rtol * rtol) / atob;
     if(rtos > R - eps) return rtos;
     p1 = fp + (a - b) * fptoe;
     p2 = fp + (b - a) * fptoe;
     return rtos;
 }

 double SectorArea(const Point &r, const Point &a, const Point &b, double R)
 //不大于180度扇形面积，r->a->b逆时针
 {
     double A2 = Sqr(r - a), B2 = Sqr(r - b), C2 = Sqr(a - b);
     return R * R * acos((A2 + B2 - C2) * 0.5 / sqrt(A2) / sqrt(B2)) * 0.5;
 }

 double TACIA(const Point &r, const Point &a, const Point &b, double R)
 //TriangleAndCircleIntersectArea，逆时针，r为圆心
 {
     double adis = r.Dis(a), bdis = r.Dis(b);
     if(adis < R + eps && bdis < R + eps) return r.cross(a, b) * 0.5;
     Point ta, tb;
     if(r.InLine(a, b)) return 0.0;
     double rtos = LineCrossCircle(a, b, r, R, ta, tb);
     if(rtos > R - eps) return SectorArea(r, a, b, R);
     if(adis < R + eps) return r.cross(a, tb) * 0.5 + SectorArea(r, tb, b, R);
     if(bdis < R + eps) return r.cross(ta, b) * 0.5 + SectorArea(r, a, ta, R);
     return r.cross(ta, tb) * 0.5 +
            SectorArea(r, a, ta, R) + SectorArea(r, tb, b, R);
 }

 const int N = ;

 Point p[N];

 double SPICA(int n, Point r, double R)//SimplePolygonIntersectCircleArea
 {
     int i;
     double res = , if_clock_t;
     for(i = ; i < n; ++ i)
     {
         if_clock_t = dcmp(r.cross(p[i], p[(i + ) % n]));
         if(if_clock_t < ) res -= TACIA(r, p[(i + ) % n], p[i], R);
         else res += TACIA(r, p[i], p[(i + ) % n], R);
     }
     return fabs(res);
 }

 double r;

 int main()
 {
     while (~scanf("%lf%lf", &p[].x, &p[].y))
     {
         for (int i = ; i < ; i++)
             p[i].read();
         scanf("%lf", &r);
         printf("%.2f\n", SPICA(, p[], r));
     }
     return ;
 }