Gym-101158J Cover the Polygon with Your Disk 计算几何 求动圆与多边形最大面积交

题面

题意:给出小于10个点形成的凸多边形 和一个半径为r 可以移动的圆 求圆心在何处的面积交最大,面积为多少

题解:三分套三分求出圆心位置,再用圆与多边形面积求交

 #include<bits/stdc++.h>
 #define inf 1000000000000
 #define M 100009
 #define eps 1e-12
 #define PI acos(-1.0)
 using namespace std;
 struct node
 {
     double x,y;
     node(){}
     node(double xx,double yy)
     {
         x=xx;
         y=yy;
     }
     node operator -(node s)
     {
         return node(x-s.x,y-s.y);
     }
     node operator +(node s)
     {
         return node(x+s.x,y+s.y);
     }
     double operator *(node s)
     {
         return x*s.x+y*s.y;
     }
     double operator ^(node s)
     {
         return x*s.y-y*s.x;
     }
 }p[M],a[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(node a)
 {
     return sqrt(a*a);
 }
 double dis(node a,node b)//两点之间的距离
 {
     return len(b-a);
 }
 double cross(node a,node b,node c)//叉乘
 {
     return (b-a)^(c-a);
 }
 double dot(node a,node b,node c)//点乘
 {
     return (b-a)*(c-a);
 }
 int judge(node a,node b,node 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(node b,node c,double r)
 {
     node 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)//两个端点都在圆内的情况
     {
         return 0.5*fabs(cross(a,b,c));
     }
     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))//默认b在圆内
         {
             swap(b,c);
         }
         if(fabs(dis(a,b))<eps)//ab距离为0直接返回0
         {
             return 0.0;
         }
         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 n;
 double x,y,h,x1,yy,R;
 double gets(node O)//求圆与多边形面积并
 {
     for (int i=;i<=n+;i++) p[i]=a[i];
       for(int i=;i<=n+;i++) p[i]=p[i]-O;
     O=node(,);
     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;
     }
     return fabs(sum);
 }
 int dcmp(double x)
 {
     if(x > eps) return ;
     return x < -eps ? - : ;
 }
 double calc(double x)
 {
     double l=,r=-,m1,m2,f1=,f2=;
     for (int i=;i<=n;i++)
     {
         if (dcmp((a[i].x-x) * (a[i+].x-x))<=)
         {
             node tmp;
             tmp.x=a[i].x+(a[i+].x-a[i].x)/(a[i+].x-a[i].x)*(x-a[i].x);
             tmp.y=a[i].y+(a[i+].y-a[i].y)/(a[i+].x-a[i].x)*(x-a[i].x);
             l=min(l,tmp.y);
             r=max(r,tmp.y);
         }
     }
     while (l+eps<r)
     {
         m1=(l+l+r)/3.0;
         node bom=node(x,m1);
         f1=gets(bom);
         m2=(l+r+r)/3.0;
         bom=node(x,m2);
         f2=gets(bom);
         if (f1>f2) r=m2;else l=m1;
     }
     return f1;
 }
 int main()
 {
     scanf("%d%lf",&n,&R);
     double l=,r=-,m1,m2,f1,f2;
     for(int i=;i<=n;i++)
     {
         scanf("%lf%lf",&a[i].x,&a[i].y);
         l=min(l,a[i].x);
         r=max(r,a[i].x);
     }
     a[n+]=a[];
     while (l+eps<r)
     {
         m1=(l+l+r)/3.0;f1=calc(m1);
         m2=(l+r+r)/3.0;f2=calc(m2);
         if (f1>f2) r=m2;else l=m1;
     }
     printf("%.6lf\n",f1);
     return ;
 }