POJ 1584 A Round Peg in a Ground Hole 判断凸多边形 点到线段距离 点在多边形内

POJ 1584 A Round Peg in a Ground Hole（判断凸多边形，点到线段距离，点在多边形内）

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;

const double eps=1e-8;
const double PI = acos(-1.0);

int sgn(double x)
{
if(fabs(x) < eps) return 0;
return x < 0 ? -1:1;
}

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);
}
//叉积
double operator ^(const Point &b)const
{
return x*b.y - y*b.x;
}
//点积
double operator *(const Point &b)const
{
return x*b.x + y*b.y;
}
void input()
{
scanf("%lf%lf",&x,&y);
}
};

struct Line
{
Point p,q;
Line() {};
Line(Point _p,Point _q)
{
p = _p,q = _q;
}
};

//*两点间距离
double dist(Point a,Point b)
{
return sqrt((a-b)*(a-b));
}

//*判断凸多边形
//允许共线边
//点可以是顺时针给出也可以是逆时针给出
//点的编号0~n-1
bool isconvex(Point poly[],int n)
{
bool s[3];
memset(s,false,sizeof(s));
for(int i = 0; i < n; i++)
{
s[sgn( (poly[(i+1)%n]-poly[i])^(poly[(i+2)%n]-poly[i]) )+1] = true;
if(s[0] && s[2])return false;
}
return true;
}

//*点到线段的距离
//返回点到线段最近的点
Point NearestPointToLineSeg(Point P,Line L)
{
Point result;
double t = ((P-L.p)*(L.q-L.p))/((L.q-L.p)*(L.q-L.p));
if(t >= 0 && t <= 1)
{
result.x = L.p.x + (L.q.x - L.p.x)*t;
result.y = L.p.y + (L.q.y - L.p.y)*t;
}
else
{
result = dist(P,L.p) < dist(P,L.q)? L.p:L.q;
}
return result;
}

//*判断点在线段上
bool OnSeg(Point P,Line L)
{
return
sgn((L.p-P)^(L.q-P)) == 0 &&
sgn((P.x - L.p.x) * (P.x - L.q.x)) <= 0 &&
sgn((P.y - L.p.y) * (P.y - L.q.y)) <= 0;
}

//*判断点在凸多边形内
//点形成一个凸包，而且按逆时针排序（如果是顺时针把里面的<0改为>0）
//点的编号:0~n-1
//返回值：
//-1:点在凸多边形外
//0:点在凸多边形边界上
//1:点在凸多边形内
int inConvexPoly(Point a,Point p[],int n)
{
for(int i = 0; i < n; i++)
{
if(sgn((p[i]-a)^(p[(i+1)%n]-a)) < 0)return -1;
else if(OnSeg(a,Line(p[i],p[(i+1)%n])))return 0;
}
return 1;
}

//*判断线段相交
bool inter(Line l1,Line l2)
{
return
max(l1.p.x,l1.q.x) >= min(l2.p.x,l2.q.x) &&
max(l2.p.x,l2.q.x) >= min(l1.p.x,l1.q.x) &&
max(l1.p.y,l1.q.y) >= min(l2.p.y,l2.q.y) &&
max(l2.p.y,l2.q.y) >= min(l1.p.y,l1.q.y) &&
sgn((l2.p-l1.q)^(l1.p-l1.q))*sgn((l2.q-l1.q)^(l1.p-l1.q)) <= 0 &&
sgn((l1.p-l2.q)^(l2.p-l2.q))*sgn((l1.q-l2.q)^(l2.p-l2.q)) <= 0;
}

//*判断点在任意多边形内
//射线法，poly[]的顶点数要大于等于3,点的编号0~n-1
//返回值
//-1:点在多边形外
//0:点在多边形边界上
//1:点在多边形内
int inPoly(Point p,Point poly[],int n)
{
int cnt;
Line ray,side;
cnt = 0;
ray.p = p;
ray.q.y = p.y;
ray.q.x = -100000000000.0;//-INF,注意取值防止越界
for(int i = 0; i < n; i++)
{
side.p = poly[i];
side.q = poly[(i+1)%n];
if(OnSeg(p,side))return 0;
//如果平行轴则不考虑
if(sgn(side.p.y - side.q.y) == 0)
continue;
if(OnSeg(side.p,ray))
{
if(sgn(side.p.y - side.q.y) > 0)cnt++;
}
else if(OnSeg(side.q,ray))
{
if(sgn(side.q.y - side.p.y) > 0)cnt++;
}
else if(inter(ray,side)) cnt++;
}
return cnt % 2 ? 1:-1;
}

Point pot[105],peg;
double rad;

int main()
{
//    freopen("in.txt","r",stdin);
int n;
while(~scanf("%d",&n))
{
if(n<3) break;
scanf("%lf",&rad);
peg.input();
for(int i=0;i<n;i++)
pot[i].input();
if(!isconvex(pot,n))
{
puts("HOLE IS ILL-FORMED");
continue;
}
if(inPoly(peg,pot,n)<0)
{
puts("PEG WILL NOT FIT");
continue;
}
bool flag=true;
for(int i=0;i<n-1;i++)
{
if( sgn(dist(peg,NearestPointToLineSeg(peg,Line(pot[i],pot[(i+1)%n])))-rad)<0 )
{
flag=false;
break;
}
}
puts(flag? "PEG WILL FIT":"PEG WILL NOT FIT");
}
return 0;
}