POJ 1584 A Round Peg in a Ground Hole（判斷凸多邊形，點到線段最短距離）

圓在多邊形內的條件是：圓心在多邊形內，且圓心到個線段最短距離小於半徑。

#include <iostream>
#include <stdio.h>
#include <string.h>
#include <algorithm>
#include <queue>
#include <map>
#include <vector>
#include <set>
#include <string>
#include <math.h>
#include <cstdio>
#include <cstring>

using namespace std;

const double eps = 1e-8;
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;
    }
    //向量
    Point operator -(const Point &b)const
    {
        return Point(x - b.x,y - b.y);
    }
    //叉積
    double operator ^(const Point &b)const
    {
        return x*b.y - y*b.x;
    }
    //點積
    double operator *(const Point &b)const
    {
        return x*b.x + y*b.y;
    }
    void input()
    {
        scanf("%lf%lf",&x,&y);
    }
};
struct Line
{
    Point s,e;
    Line(){}
    Line(Point _s,Point _e)
    {
        s = _s;e = _e;
    }
    //兩直線相交求交點
    //第一個值爲0表示直線重合，爲1表示平行，爲0表示相交,爲2是相交
    //只有第一個值爲2時，交點纔有意義
    pair<int,Point> operator &(const Line &b)const
    {
        Point res = s;
        if(sgn((s-e)^(b.s-b.e)) == 0)
        {
            if(sgn((s-b.e)^(b.s-b.e)) == 0)
                return make_pair(0,res);//重合
            else return make_pair(1,res);//平行
        }
        double t = ((s-b.s)^(b.s-b.e))/((s-e)^(b.s-b.e));
        res.x += (e.x-s.x)*t;
        res.y += (e.y-s.y)*t;
        return make_pair(2,res);
    }
};
double dist(Point a,Point b)
{
    return sqrt((a-b)*(a-b));
}
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;
}

bool inter(Line l1,Line l2)//判斷線段相交
{
    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((l2.s-l1.e)^(l1.s-l1.e))*sgn((l2.e-l1.e)^(l1.s-l1.e)) <= 0 &&
    sgn((l1.s-l2.e)^(l2.s-l2.e))*sgn((l1.e-l2.e)^(l2.s-l2.e)) <= 0;
}

//*判斷點在線段上
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;
}

int inPoly(Point p,Point poly[],int n)
{
    int cnt;
    Line ray,side;
    cnt = 0;
    ray.s = p;
    ray.e.y = p.y;
    ray.e.x = -100000000000.0;//-INF,注意取值防止越界

    for(int i = 0;i < n;i++)
    {
        side.s = poly[i];
        side.e = poly[(i+1)%n];

        if(OnSeg(p,side))return 0;

        //如果平行軸則不考慮
        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;
}

//點到線段的距離
//返回點到線段最近的點
double NearestPointToLineSeg(Point P,Line L)
{
    Point result;
    double t = ((P-L.s)*(L.e-L.s))/((L.e-L.s)*(L.e-L.s));
    if(t >= 0 && t <= 1)
    {
        result.x = L.s.x + (L.e.x - L.s.x)*t;
        result.y = L.s.y + (L.e.y - L.s.y)*t;
    }
    else
    {
        if(dist(P,L.s) < dist(P,L.e))
            result = L.s;
        else result = L.e;
    }
    return dist(result, P);
}

const int maxn = 1000;

Point poly[maxn];

int main()
{
    int n;
    Point peg;
    double rad;
    while (~scanf("%d", &n) && n >= 3) {
        scanf("%lf%lf%lf", &rad, &peg.x, &peg.y);
        for (int i = 0; i < n; i++)
            scanf("%lf%lf", &poly[i].x, &poly[i].y);
        if (!isconvex(poly, n)) {
            puts("HOLE IS ILL-FORMED");
            continue;
        }
        bool ok = (inPoly(peg, poly, n) == 1);
        for (int i = 0; ok && i < n; i++) {
            double d = NearestPointToLineSeg(peg, Line(poly[i], poly[(i+1) % n]));
            if (sgn(d - rad) < 0) {
                ok = false;
                break;
            }
        }
        puts(ok ? "PEG WILL FIT" : "PEG WILL NOT FIT");
    }

    return 0;
}