http://poj.org/problem?id=1584
题意
按照顺时针或逆时针方向输入一个n边形的顶点坐标集，先判断这个n边形是否为凸包。
再给定一个圆形（圆心坐标和半径），判断这个圆是否完全在n边形内部。
分析
1.判断给出了多边形是不是凸多边形。
2.判断圆包含在凸多边形中：一定要保证圆心在凸多边形里面。然后判断圆心到每条线段的距离要大于等于半径。。
#include <iostream> #include <stdio.h> #include <string.h> #include <algorithm> #include <queue> #include <map> #include <vector> #include <set> #include <string> #include <math.h> using namespace std; const double eps = 1e-8; const double PI = acos(-1.0); 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; } 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 s,e; Line(){} Line(Point _s,Point _e) { s = _s;e = _e; } }; //*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1~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.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 result; } //*判断点在线段上 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; } //*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.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:点在凸多边形外 //0:点在凸多边形边界上 //1:点在凸多边形内 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; //如果平行轴则不考虑 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; } Point p[110]; int main() { //freopen("in.txt","r",stdin); //freopen("out.txt","w",stdout); int n; double R,x,y; while(scanf("%d",&n) == 1) { if(n < 3)break; scanf("%lf%lf%lf",&R,&x,&y); for(int i = 0 ;i < n;i++) p[i].input(); if(!isconvex(p,n)) { printf("HOLE IS ILL-FORMED\n"); continue; } Point P = Point(x,y); if(inPoly(P,p,n) < 0) { printf("PEG WILL NOT FIT\n"); continue; } bool flag = true; for(int i = 0;i < n;i++) { if(sgn(dist(P,NearestPointToLineSeg(P,Line(p[i],p[(i+1)%n]))) - R) < 0 ) { flag = false; break; } } if(flag)printf("PEG WILL FIT\n"); else printf("PEG WILL NOT FIT\n"); } return 0; }