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

Posted 2020-09-29 Pacify

首先判断是不是凸多边形

然后判断圆是否在凸多边形内

不知道给出的点是顺时针还是逆时针，所以用判断是否在多边形内的模板，不用是否在凸多边形内的模板

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;
}