Poj 3335 rotating scoreboard semi-plane intersection polygon Kernel

Question: How to calculate the kernel template with polygon

Idea: I use the semi-plane intersection of O (nlogn), but one problem is that when the polygon kernel is a vertex, the answer to the semi-plane intersection is a null set, but the output should be yes. There is no good solution. In the end, we can only move all the straight lines to the right and then find the kernel. However, in this case, different values of the EPS can sometimes be a or not. Is there any good solution !!! Please answer !!!

Code:

#include <cmath>#include <cstdio>#include <cstring>#include <iostream>#include <algorithm>#define MAX 110#define EPS 1e-12#define DCMP(a)(fabs(a) < EPS ? true:false)using namespace std;struct Point{double x,y;Point(double _ = 0.0,double __ = 0.0):x(_),y(__) {}Point operator -(const Point &a)const {return Point(x - a.x,y - a.y);}Point operator +(const Point &a)const {return Point(x + a.x,y + a.y);}Point operator *(double a)const {return Point(x * a,y * a);}void operator += (const Point &a) {x += a.x, y += a.y;}void Read() {scanf("%lf%lf",&x,&y);}}point[MAX],p[MAX],polygon[MAX];struct Line{Point p,v;double alpha;bool operator <(const Line &a)const {return alpha < a.alpha;}Line(Point _,Point __):p(_),v(__) {alpha = atan2(v.y,v.x);}Line() {}}line[MAX],q[MAX];int cases;int points,lines;inline void Initialize();inline void MakeLine(const Point &a,const Point &b);inline double Cross(const Point &a,const Point &b);inline bool OnLeft(const Line &l,const Point &p);inline bool HalfPlaneIntersection();inline Point GetIntersection(const Line &a,const Line &b);int main(){for(cin >> cases;cases; --cases) {scanf("%d",&points);Initialize();for(int i = 1;i <= points; ++i)point[i].Read();for(int i = points;i > 1; --i)MakeLine(point[i],point[i - 1]);MakeLine(point[1],point[points]);sort(line + 1,line + lines + 1);bool ans = HalfPlaneIntersection();if(ans)puts("YES");elseputs("NO");}return 0;}inline void Initialize(){lines = 0;}inline void MakeLine(const Point &a,const Point &b){Point p = a;Point v = b - a;p += Point(v.y, -v.x) * (EPS * 0.5);line[++lines] = Line(p, v);}inline double Cross(const Point &a,const Point &b){return a.x * b.y - a.y * b.x;}inline bool OnLeft(const Line &l,const Point &p){return Cross(l.v,p - l.p) > 0;}inline Point GetIntersection(const Line &a,const Line &b){Point u = a.p - b.p;double temp = Cross(b.v,u) / Cross(a.v,b.v);return a.p + a.v * temp;}inline bool HalfPlaneIntersection(){int front = 1,tail = 1;q[1] = line[1];for(int i = 2;i <= lines; ++i) {while(front < tail && !OnLeft(line[i],p[tail - 1]))--tail;while(front < tail && !OnLeft(line[i],p[front]))++front;if(DCMP(Cross(line[i].v,q[tail].v)))q[tail] = OnLeft(q[tail],line[i].p) ? line[i]:q[tail];elseq[++tail] = line[i];if(front < tail)p[tail - 1] = GetIntersection(q[tail],q[tail - 1]);}while(front < tail && !OnLeft(q[front],p[tail - 1]))--tail;return front < tail;}

Poj 3335 rotating scoreboard semi-plane intersection polygon Kernel