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
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; }
