ZOJ1081 Points Within，判断点是否在多边形 内

/*******************************************************************************
# Author : Neo Fung
# Email : neosfung@gmail.com
# Last modified: 2011-11-15 21:31
# Filename: ZOJ1081 Points Within.cpp
# Description :
******************************************************************************/
// #include "stdafx.h"
// #define DEBUG

#include <fstream>
#include <stdio.h>
#include <iostream>
#include <string.h>
#include <string>
#include <memory.h>
#include <limits.h>
#include <algorithm>
#include <math.h>
#include <float.h>

#define MAX 110
#define EPS 1e-10
using namespace std;

struct POINT
{
double x,y;
}point[MAX];

struct LINE{
POINT a,b;
};

double inline Distance(const POINT &lhs,const POINT &rhs)
{	return sqrt((lhs.x-rhs.x)*(lhs.x-rhs.x)+(lhs.y-rhs.y)*(lhs.y-rhs.y));}

double inline crossProduct(const POINT &a,const POINT &b,const POINT &c)
//向量ac在ab的方向
{
double ans=(c.x - a.x)*(b.y - a.y) - (b.x - a.x)*(c.y - a.y);
return ans;
}

bool inline _less(const double &lhs,const double &rhs)
{
return lhs < rhs - EPS;
}
bool inline _less_or_equal(const double &lhs,const double &rhs)
{
return lhs < rhs + EPS;
}
bool inline _equal(const double &lhs,const double &rhs)
{
return fabs(lhs-rhs)< EPS;
}

/************************************************************************/
/* 点c是否在点a与点b的线段上（包括端点）                                */
/************************************************************************/
bool PointOnSegment(const POINT &a,const POINT &b,const POINT &c)
{
if(_equal(crossProduct(a,b,c),0.0) &&
_less_or_equal(min(a.x,b.x),c.x) &&
_less_or_equal(c.x,max(a.x,b.x)) &&
_less_or_equal(min(a.y,b.y),c.y) &&
_less_or_equal(c.y,max(a.y,b.y)))
return true;
else
return false;
}

/************************************************************************/
/* 确定两条线段是否相交                                                 */
/************************************************************************/
int   intersect(const LINE  &lhs,const LINE &rhs)
{
return((max(lhs.a.x,lhs.b.x)>=min(rhs.a.x,rhs.b.x))&&
(max(rhs.a.x,rhs.b.x)>=min(lhs.a.x,lhs.b.x))&&
(max(lhs.a.y,lhs.b.y)>=min(rhs.a.y,rhs.b.y))&&
(max(rhs.a.y,rhs.b.y)>=min(lhs.a.y,lhs.b.y))&&
(crossProduct(lhs.a,lhs.b,rhs.a)*crossProduct(lhs.a,rhs.b,lhs.b)>=0)&&
(crossProduct(rhs.a,rhs.b,lhs.a)*crossProduct(rhs.a,lhs.b,rhs.b)>=0));
}

bool inPolygon(const POINT &p,const POINT *pArray,const int &n)
{
if(n==1)
return(_equal(pArray[0].x,p.x)&&_equal(pArray[0].y,p.y));
if(n==2)
return PointOnSegment(pArray[0],pArray[1],p);

int sum=0;
LINE tline;
tline.a=p;
tline.b.x=DBL_MAX;
tline.b.y=p.y;

for(int i=0;i<n;++i)
{
const POINT p1=pArray[i];
const POINT p2=pArray[(i+1)%n];
LINE side;
side.a=p1;
side.b=p2;

if(PointOnSegment(p1,p2,p))
return true;
if(_equal(p1.y,p2.y))
continue;

if (intersect(side,tline))
{
++sum;
}

}
return sum%2;
}

int main(void)
{
#ifdef DEBUG
freopen("data.txt","r",stdin);
#endif
int n,m;
int ncases=1,flag=1;
POINT p;

while(scanf("%d",&n) && n)
{
if (flag)
flag=0;
else
printf("\n");

scanf("%d",&m);
printf("Problem %d:\n",ncases++);
for (int i=0;i<n;++i)
{
scanf("%lf%lf",&point[i].x,&point[i].y);
}

while(m--)
{
scanf("%lf%lf",&p.x,&p.y);
if (inPolygon(p,point,n))
{
printf("Within\n");
}
else
{
printf("Outside\n");
}
}
}

return 0;
}