Hdu-2892 area 计算几何 圆与凸多边形面积交

题面

题意:有一个凸多边形岛屿,然后告诉你从高空(x,y,h)投下炸弹,爆炸半径r,飞机水平速度和重力加速度,问岛屿被炸了多少

题解:算出来岛屿落地位置,再利用圆与凸多边形面积交

 #include<bits/stdc++.h>
 #define inf 1000000000000
 #define M 100009
 #define eps 1e-12
 #define PI acos(-1.0)
 using namespace std;
 struct Point
 {
     double x,y;
     Point(){}
     Point(double xx,double yy){x=xx;y=yy;}
     Point operator -(Point s){return Point(x-s.x,y-s.y);}
     Point operator +(Point s){return Point(x+s.x,y+s.y);}
     double operator *(Point s){return x*s.x+y*s.y;}
     double operator ^(Point s){return x*s.y-y*s.x;}
 }p[M];
 double max(double a,double b){return a>b?a:b;}
 double min(double a,double b){return a<b?a:b;}
 double len(Point a){return sqrt(a*a);}
 double dis(Point a,Point b){return len(b-a);}//两点之间的距离
 double cross(Point a,Point b,Point c)//叉乘
 {
     return (b-a)^(c-a);
 }
 double dot(Point a,Point b,Point c)//点乘
 {
     return (b-a)*(c-a);
 }
 int judge(Point a,Point b,Point c)//判断c是否在ab线段上（前提是c在直线ab上）
 {
     if (c.x>=min(a.x,b.x)
        &&c.x<=max(a.x,b.x)
        &&c.y>=min(a.y,b.y)
        &&c.y<=max(a.y,b.y)) return ;
     return ;
 }
 double area(Point b,Point c,double r)
 {
     Point a(0.0,0.0);
     if(dis(b,c)<eps) return 0.0;
     double h=fabs(cross(a,b,c))/dis(b,c);
     if(dis(a,b)>r-eps&&dis(a,c)>r-eps)//两个端点都在圆的外面则分为两种情况
     {
         double angle=acos(dot(a,b,c)/dis(a,b)/dis(a,c));
         if(h>r-eps) return 0.5*r*r*angle;else
         if(dot(b,a,c)>&&dot(c,a,b)>)
         {
             double angle1=*acos(h/r);
             return 0.5*r*r*fabs(angle-angle1)+0.5*r*r*sin(angle1);
         }else return 0.5*r*r*angle;
     }else
         if(dis(a,b)<r+eps&&dis(a,c)<r+eps) return 0.5*fabs(cross(a,b,c));//两个端点都在圆内的情况
         else//一个端点在圆上一个端点在圆内的情况
         {
             if(dis(a,b)>dis(a,c)) swap(b,c);//默认b在圆内
             if(fabs(dis(a,b))<eps) return 0.0;//ab距离为0直接返回0
             if(dot(b,a,c)<eps)
             {
                 double angle1=acos(h/dis(a,b));
                 double angle2=acos(h/r)-angle1;
                 double angle3=acos(h/dis(a,c))-acos(h/r);
                 return 0.5*dis(a,b)*r*sin(angle2)+0.5*r*r*angle3;
             }else
             {
                 double angle1=acos(h/dis(a,b));
                 double angle2=acos(h/r);
                 double angle3=acos(h/dis(a,c))-angle2;
                 return 0.5*r*dis(a,b)*sin(angle1+angle2)+0.5*r*r*angle3;
             }
         }
 }
 int main()
 {
     double x,y,h,x1,y1,R;
     while(scanf("%lf%lf%lf",&x,&y,&h)!=-)
     {
         scanf("%lf%lf%lf",&x1,&y1,&R);
         int n;
         scanf("%d",&n);
         for(int i=;i<=n;i++) scanf("%lf%lf",&p[i].x,&p[i].y);
         p[n+]=p[];
         double V=sqrt(**h);
         double t0=V/;
         double x0=x+x1*t0;
         double y0=y+y1*t0;
         Point O(x0,y0);
         for(int i=;i<=n+;i++) p[i]=p[i]-O;
         O=Point(,);
         double sum=;
         for(int i=;i<=n;i++)
         {
             int j=i+;
             double s=area(p[i],p[j],R);
             if(cross(O,p[i],p[j])>) sum+=s; else sum-=s;
         }
         printf("%.2lf\n",fabs(sum));
     }
     return ;
 }