HDU2892 area 简单多边形与圆面积交

以圆心为中心将简单多边形划分为n个矢量三角形，对每个三角形与圆求交，根据有向边判断相交面积正负，最后相加取绝对值。

一个顶点在圆心的三角形与圆的交需要讨论的情况比较少，容易计算。

  1 #include<stdio.h>

  2 #include<string.h>

  3 #include<stdlib.h>

  4 #include<math.h>

  5 #include<algorithm>

  6 const int maxn = 111111;

  7 const int maxisn = 21;

  8 const double eps = 1e-8;

  9 const double pi = acos(-1.0);

 10 int dcmp(double x)

 11 {

 12     if(x > eps) return 1;

 13     return x < -eps ? -1 : 0;

 14 }

 15 struct Point

 16 {

 17     double x, y;

 18     Point(){x = y = 0;}

 19     Point(double a, double b)

 20     {x = a, y = b;}

 21     inline Point operator-(const Point &b)const

 22     {return Point(x - b.x, y - b.y);}

 23     inline Point operator+(const Point &b)const

 24     {return Point(x + b.x, y + b.y);}

 25     inline Point operator*(const double &b)const

 26     {return Point(x * b, y * b);}

 27     inline double dot(const Point &b)const

 28     {return x * b.x + y * b.y;}

 29     inline double cross(const Point &b, const Point &c)const

 30     {return (b.x - x) * (c.y - y) - (c.x - x) * (b.y - y);}

 31     inline double Dis(const Point &b)const

 32     {return sqrt((*this - b).dot(*this - b));}

 33     inline bool InLine(const Point &b, const Point &c)const//三点共线

 34     {return !dcmp(cross(b, c));}

 35     inline bool OnSeg(const Point &b, const Point &c)const//点在线段上，包括端点

 36     {return InLine(b, c) && (*this - c).dot(*this - b) < eps;}

 37 };

 38 inline double min(double a, double b)

 39 {return a < b ? a : b;}

 40 inline double max(double a, double b)

 41 {return a > b ? a : b;}

 42 inline double Sqr(double x)

 43 {return x * x;}

 44 inline double Sqr(const Point &p)

 45 {return p.dot(p);}

 46 Point LineCross(const Point &a, const Point &b, const Point &c, const Point &d)

 47 {

 48     double u = a.cross(b, c), v = b.cross(a, d);

 49     return Point((c.x * v + d.x * u) / (u + v), (c.y * v + d.y * u) / (u + v));

 50 }

 51 double LineCrossCircle(const Point &a, const Point &b, const Point &r, 

 52             double R, Point &p1, Point &p2)

 53 {

 54     Point fp = LineCross(r, Point(r.x + a.y - b.y, r.y + b.x - a.x), a, b);

 55     double rtol = r.Dis(fp);

 56     double rtos = fp.OnSeg(a, b) ? rtol : min(r.Dis(a), r.Dis(b));

 57     double atob = a.Dis(b);

 58     double fptoe = sqrt(R * R - rtol * rtol) / atob;

 59     if(rtos > R - eps) return rtos;

 60     p1 = fp + (a - b) * fptoe;

 61     p2 = fp + (b - a) * fptoe;

 62     return rtos;

 63 }

 64 double SectorArea(const Point &r, const Point &a, const Point &b, double R)

 65 //不大于180度扇形面积，r->a->b逆时针

 66 {

 67     double A2 = Sqr(r - a), B2 = Sqr(r - b), C2 = Sqr(a - b);

 68     return R * R * acos((A2 + B2 - C2) * 0.5 / sqrt(A2) / sqrt(B2)) * 0.5;

 69 }

 70 double TACIA(const Point &r, const Point &a, const Point &b, double R)

 71 //TriangleAndCircleIntersectArea，逆时针，r为圆心

 72 {

 73     double adis = r.Dis(a), bdis = r.Dis(b);

 74     if(adis < R + eps && bdis < R + eps) return r.cross(a, b) * 0.5;

 75     Point ta, tb;

 76     if(r.InLine(a, b)) return 0.0;

 77     double rtos = LineCrossCircle(a, b, r, R, ta, tb);

 78     if(rtos > R - eps) return SectorArea(r, a, b, R);

 79     if(adis < R + eps) return r.cross(a, tb) * 0.5 + SectorArea(r, tb, b, R);

 80     if(bdis < R + eps) return r.cross(ta, b) * 0.5 + SectorArea(r, a, ta, R);

 81     return r.cross(ta, tb) * 0.5 + 

 82         SectorArea(r, a, ta, R) + SectorArea(r, tb, b, R);

 83 }

 84 double SPICA(int n, Point r, double R)//SimplePolygonIntersectCircleArea

 85 {

 86     int i;

 87     Point ori, p[2];

 88     scanf("%lf%lf", &ori.x, &ori.y);

 89     p[0] = ori;

 90     double res = 0, if_clock_t;

 91     for(i = 1; i <= n; ++ i)

 92     {

 93         if(i == n) p[i & 1] = ori;

 94         else scanf("%lf%lf", &p[i & 1].x, &p[i & 1].y);

 95         if_clock_t = dcmp(r.cross(p[~i & 1], p[i & 1]));

 96         if(if_clock_t < 0) res -= TACIA(r, p[i & 1], p[~i & 1], R);

 97         else res += TACIA(r, p[~i & 1], p[i & 1], R);

 98     }

 99     return fabs(res);

100 }

101 Point boom;

102 int n;

103 double R;

104 int main()

105 {

106     double sx, sy, h, vx, vy;

107     while(scanf("%lf%lf%lf", &sx, &sy, &h) != EOF)

108     {

109         scanf("%lf%lf%lf", &vx, &vy, &R);

110         h = sqrt(2 * h / 10);

111         boom = Point(h * vx + sx, h * vy + sy);

112         scanf("%d", &n);

113         printf("%.2f\n", SPICA(n, boom, R));

114     }

115     return 0;

116 }