hdu 2892 Area

http://acm.hdu.edu.cn/showproblem.php?pid=2892

解题思路：

求多边形与圆的相交的面积是多少。

以圆心为顶点，将多边形划分为n个三角形。

接下来就求出每个三角形与圆相交的面积。

因为三角形的一个点是圆心，所以三角形的另外两个点与圆的情况有以下几种：

（1）两点都在圆里，三角形与圆相交的面积=三角形的面积。

（2）一个点在圆外，一个点在圆里，三角形与圆相交的面积=小三角形的面积+扇形面积

（3）两点都在圆外，又分为几种情况：

　　1、两点构成的线段与圆相交的点数0或1个时，三角形与圆相交的面积=扇形的面积

　　2.两点构成的线段与圆相交的点数2个时，三角形与圆相交的面积=大扇形面积+小三角形面积-小扇形的面积

 #include<cmath>
 #include<cstdio>
 #include<vector>
 #include<algorithm>
 using namespace std;

 #define MAXN 100000+10
 #define PI acos(-1.0)
 #define EPS 0.00000001

 int dcmp(double x){
     if(fabs(x) < EPS)
         return ;
     return x <  ? - : ;
 }

 struct Point{
     double x, y;
     Point(double x = , double y = ): x(x), y(y) {}
 };

 struct Circle{
     Point c;
     double r;
     Circle(Point c = Point(, ), double r = ): c(c), r(r) {}
 };

 typedef Point Vector;

 Vector operator + (Vector A, Vector B){
     return Vector(A.x + B.x, A.y + B.y);
 }
 Vector operator - (Point A, Point B){
     return Vector(A.x - B.x, A.y - B.y);
 }
 Vector operator * (Vector A, double p){
     return Vector(A.x * p, A.y * p);
 }
 Vector operator / (Vector A, double p){
     return Vector(A.x / p, A.y / p);
 }

 double dot(Vector A, Vector B){
     return A.x * B.x + A.y * B.y;
 }

 double length(Vector A){
     return sqrt(dot(A, A));
 }

 double angle(Vector A, Vector B){
     return acos(dot(A, B) / length(A) / length(B));
 }

 double cross(Vector A, Vector B){
     return A.x * B.y - A.y * B.x;
 }

 Circle bomb;//炸弹爆炸的坐标及半径
 Point p[MAXN];//岛屿的点
 int n;//岛屿点数

 double point_line_distance(Point P, Point A, Point B){//点到直线的距离
     Vector AP = P - A, AB = B - A;
     return fabs(cross(AP, AB) / length(AB));
 }

 Point point_line_projection(Point P, Point A, Point B){//点在直线上的映射
     Vector v = B - A;
     return A + v * (dot(v, P - A) / dot(v, v));
 }

 int circle_line_intersect(Circle C, Point A, Point B, vector<Point> &v){
     double dist = point_line_distance(C.c, A, B);
     int d = dcmp(dist - C.r);
     if(d > ){
         return ;
     }
     Point pro = point_line_projection(C.c, A, B);
     if(d == ){
         v.push_back(pro);
         return ;
     }
     double len = sqrt(C.r * C.r - dist * dist);//勾股定理
     Vector AB = B - A;
     Vector l = AB / length(AB) * len;
     v.push_back(pro + l);
     v.push_back(pro - l);
     return ;
 }

 bool point_on_segment(Point P, Point A, Point B){//判断点在线段上
     Vector PA = A - P, PB = B - P;
     return dcmp(cross(PA, PB)) ==  && dcmp(dot(PA, PB)) <= ;
 }

 double circle_delta_intersect_area(Circle C, Point A, Point B){
     Vector CA = A - C.c, CB = B - C.c;
     double da = length(CA), db = length(CB);

     da = dcmp(da - C.r), db = dcmp(db - C.r);

     if(da <=  && db <= ){//三角形在圆里面
         return fabs(cross(CA, CB)) * 0.5;
     }

     vector<Point> v;
     int num = circle_line_intersect(C, A, B, v);//圆和直线的关系
     double carea = C.r * C.r * PI;
     Point t;
     if(da <=  && db > ){//左边的点在圆里 右边的点在圆外
         t = point_on_segment(v[], A, B) ? v[] : v[];

         double area = fabs(cross(CA, t - C.c)) * 0.5, an = angle(CB, t - C.c);
         return area + carea * an / PI / ;
     }
     if(da >  && db <= ){//左边点在圆外 右边点在圆里
         t = point_on_segment(v[], A, B) ? v[] : v[];

         double area = fabs(cross(CB, t - C.c)) * 0.5, an = angle(CA, t - C.c);
         return area + carea * an / PI / ;
     }
     //两个点都在圆外
     if(num == ){
         double bigarea = carea * angle(CA, CB) / PI / ,
             smallarea = carea * angle(v[] - C.c, v[] - C.c) / PI / ,
             deltaarea = fabs(cross(v[] - C.c, v[] - C.c)) * 0.5;
         return bigarea + deltaarea - smallarea;
     }
     return carea * angle(CA, CB) / PI / ;//两点都在圆外 直线AB与圆交点1个或两个
 }

 double circle_polygon_intersect_area(){//源于多边形相交面积
     p[n] = p[];
     double ans = ;
     for(int i = ; i < n; i++ ){
         double area = circle_delta_intersect_area( bomb, p[i], p[i + ] );
         if(cross(p[i] - bomb.c, p[i + ] - bomb.c) < ){
             area = -area;
         }
         ans += area;
     }
     return ans >  ? ans : -ans;
 }

 void solve(){
     scanf("%d", &n );
     for(int i = ; i < n; i++ ){
         scanf("%lf%lf", &p[i].x, &p[i].y );
     }
     printf("%.2lf\n", circle_polygon_intersect_area() );
 }

 int main(){
     //freopen("data.in", "r", stdin );
     double x, y, h, x1, y1, r;
     while(~scanf("%lf%lf%lf", &x, &y, &h )){
         scanf("%lf%lf%lf", &x1, &y1, &r  );

         double t = sqrt(0.2 * h);//h = 0.5 * G * t^2 重力加速度公式

         bomb = Circle( Point(x1 * t + x, y1 * t + y), r );

         solve();
     }
     return ;
 }