版权声明:本文为博主原创文章,未经博主允许不得转载。 https://blog.csdn.net/liufengwei1/article/details/86577101
在网上找到了一个板子,直接运用了点积知道某两条向量的方向呈钝角,就可以得出是某个端点最近,否则就是直接运用叉积的方法,求垂线的高度。
其实还可以直接求垂足,然后坐标距离运算
#include<bits/stdc++.h>
#define maxl 100010
using namespace std;
const double PI=acos(-1.0);
struct point
{
double x,y;
point(double a=0,double b=0)
{
x=a;y=b;
}
point operator - (const point &b)const
{
return point(x-b.x,y-b.y);
}
double operator * (const point &b)const
{
return x*b.x+y*b.y;
}
double operator ^ (const point &b)const
{
return x*b.y-y*b.x;
}
};
struct line
{
point s,e;
line(point a=point(),point b=point())
{
s=a;e=b;
}
};
int n;
double r,R;
point P;
point a[maxl];
inline void prework()
{
scanf("%d",&n);
scanf("%lf%lf",&P.x,&P.y);
for(int i=1;i<=n;i++)
scanf("%lf%lf",&a[i].x,&a[i].y);
a[n+1]=a[1];
}
inline double getlen(point a)
{
return sqrt(a*a);
}
inline double PointToSegment(point a,point b,point c)
{
point x=a-b;
point y=c-b;
point z=c-a;
if((x*y)<0) return getlen(x);
if((y*z)<0) return getlen(z);
//return fabs((x^y)/getlen(y));
point v=c-b;
double t=((a-b)*v)/(v*v);
point fot=point(b.x+t*v.x,b.y+t*v.y);
return sqrt((fot.x-a.x)*(fot.x-a.x)+(fot.y-a.y)*(fot.y-a.y));
}
inline void mainwork()
{
R=0;r=1e18;
for(int i=1;i<=n;i++)
{
R=max(R,getlen(a[i]-P));
r=min(r,PointToSegment(P,a[i],a[i+1]));
}
}
inline void print()
{
double ans=PI*(R*R-r*r);
printf("%.8f",ans);
}
int main()
{
prework();
mainwork();
print();
return 0;
}