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
#include#include #include #include #include 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-1bool 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