4
射线法判断是否在多边形内
#include <iostream>
#include <cmath>
#include <cstdio>
using namespace std;
const double eps=1e-8;
const int maxn =1000;
int sgn(double x)
{
if(fabs(x)<eps)
return 0;
if(x<0)
return -1;
else
return 1;
}
struct Point
{
double x,y;
Point(){}
Point(double _x,double _y)
{
x=_x;
y=_y;
}
Point operator -(const Point &b)const
{
return Point(x-b.x,y-b.y);
}
double operator ^(const Point &b)const
{
return x*b.y-y*b.x;
}
double operator *(const Point &b)const
{
return x*b.x+y*b.y;
}
};
struct Line
{
Point s,e;
Line(){}
Line(Point _s,Point _e)
{
s=_s;
e=_e;
}
};
Point p[maxn];
Line line[maxn];
bool OnSeg(Point p,Line l)
{
return
sgn((l.s-p)^(l.e-p)) ==0&&
sgn((p.x-l.s.x)*(p.x-l.e.x))<=0&&
sgn((p.y-l.s.y)*(p.y-l.e.y))<=0;
}
bool inter(Line l1,Line l2)
{
return
max(l1.s.x,l1.e.x)>=min(l2.s.x,l2.e.x)&&
max(l2.s.x,l2.e.x)>=min(l1.s.x,l1.e.x)&&
max(l1.s.y,l1.e.y)>=min(l2.s.y,l2.e.y)&&
max(l2.s.y,l2.e.y)>=min(l1.s.y,l1.e.y)&&
sgn((l1.s-l2.s)^(l1.e-l2.s))*sgn((l1.s-l2.e)^(l1.e-l2.e))<=0&&
sgn((l2.s-l1.s)^(l2.e-l1.s))*sgn((l2.s-l1.e)^(l2.e-l1.e))<=0;
}
int inPoly(Point p1,Point p[],int n)
{
int cnt;
Line ray,side;
cnt=0;
ray.s=p1;
ray.e.y=p1.y;
ray.e.x= -100000000000.0;
for(int i=0;i<n;i++)
{
side=Line(p[i],p[(i+1)%n]);
if(OnSeg(p1,side))
return 1;
if(sgn(side.s.y-side.e.y)==0)
continue;
if(OnSeg(side.s,ray))
{
if(sgn(side.s.y-side.e.y)>0)
cnt++;
}
else if(OnSeg(side.e,ray))
{
if(sgn(side.e.y-side.s.y)>0)
cnt++;
}
else if(inter(ray,side))
{
cnt++;
}
}
if(cnt%2==1)
return 1;
else
return -1;
}
int main()
{
int n;
int sum=1;
while(1)
{
int m;
cin>>n;
if(n==0)
break;
cin>>m;
for(int i=0;i<n;i++)
{
double x1,y1;
cin>>x1>>y1;
p[i]=Point(x1,y1);
}
if(sum!=1)
cout<<endl;
printf("Problem %d:\n",sum);
sum++;
for(int i=0;i<m;i++)
{
Point p1;
double x1,y1;
cin>>x1>>y1;
p1=Point(x1,y1);
if(inPoly(p1,p,n)==1)
cout<<"Within"<<endl;
else
cout<<"Outside"<<endl;
}
}
return 0;
}