poj-1584 判断凸包算法+极角排序+判断点在几何内外 模板

#include<cstdio>
#include<cmath>
#include<stack>
#include<algorithm>
using namespace std;
struct point{
double x,y;
}p[20000],tubao[20000];
int n,mi;
double r,x,y,minx,miny;
bool cmp(point a,point b)
{
if(fabs((a.x-minx)*(b.y-miny)-(a.y-miny)*(b.x-minx))<=1e-8)return fabs(a.x-minx)<fabs(b.x-minx);
else return (a.x-minx)*(b.y-miny)-(a.y-miny)*(b.x-minx)>0;
}//极角排序所用cmp函数
bool toJudgeLeftOrRight(int p1,int p2,int p3)
{
point P1,P2;
P1.x = p[p3].x-p[p1].x;
P1.y = p[p3].y-p[p1].y;
P2.x = p[p2].x-p[p1].x;
P2.y = p[p2].y-p[p1].y;
if(fabs(P2.x*P1.y-P2.y*P1.x)<=1e-8||P2.x*P1.y-P2.y*P1.x>0)
return true;
else return false;
}//判断点是否往左歪 判断凸包
bool  grahamScan()
{
mi = 0;
minx = p[mi].x;
miny = p[mi].y;
for(int i=0;i<n;i++)
if(p[i].y<p[mi].y){
mi = i;
minx = p[i].x;
miny = p[i].y;
}
else if(fabs(p[i].y-p[mi].y)<=1e-11&&p[i].x<p[mi].x)
{
mi = i;
minx = p[i].x;
miny = p[i].y;
}
sort(p,p+n,cmp);//极角排序
stack<int>st;
st.push(0);
st.push(1);
for(int i=2;i<n;i++)
{
while(st.size())
{
int p1,p2,p3 = i;
p2 = st.top();
st.pop();
p1 = st.top();
st.pop();
if(toJudgeLeftOrRight(p1,p2,p3))
{
st.push(p1);
st.push(p2);
st.push(i);
break;
}
else{
st.push(p1);
}
}
}
if(st.size()==n)return true;
else return false;
}//判断凸包
bool toJudgePointOutOrIn()
{
int sum = 0;
for(int i=0;i<n;i++)
{
if(!(fabs((p[(i+1)%n].x - p[i].x))<=1e-11))
{
double k = (p[(i+1)%n].y - p[i].y)/(p[(i+1)%n].x - p[i].x),
b = p[i].y - k*p[i].x;
double X = (y-b)/k;
if(fabs(x-X)<=1e-11)return false;
else if(x-X<0)
{
double y1 = min(p[(i+1)%n].y,p[i].y);
double y2 = max(p[(i+1)%n].y,p[i].y);
if(y>y1&&(y<y2||fabs(y-y2)<=1e-11))sum++;
}
}
else{
if(fabs(x-p[i].x)<=1e-11)return false;
else if(x-p[i].x<0)
{
double y1 = min(p[(i+1)%n].y,p[i].y);
double y2 = max(p[(i+1)%n].y,p[i].y);
if(y>y1&&(y<y2||fabs(y-y2)<=1e-11))sum++;
}
}
}
if(sum%2)return true;
else return false;
}//判断点是否在闭合几何内
bool toJudgeCircal()
{
for(int i=0;i<n;i++)
{
if(!(fabs((p[(i+1)%n].x - p[i].x))<=1e-11))
{
double k = (p[(i+1)%n].y - p[i].y)/(p[(i+1)%n].x - p[i].x),
b = p[i].y - k*p[i].x;
double R = fabs(y-k*x-b)/sqrt(1+k*k);
if(fabs(R-r)<=1e-11||R>r);
else return false;
}
else{
double R = fabs(p[i].x-x);
if(fabs(R-r)<=1e-11||R>r);
else return false;
}
}

return true;
}//在前几步的基础上判断圆是否与凸包有交点
int main()
{
while(scanf("%d",&n))
{
if(n<3)break;
scanf("%lf%lf%lf",&r,&x,&y);
for(int i=0;i<n;i++)
scanf("%lf%lf",&p[i].x,&p[i].y);
if(grahamScan())
{
if(toJudgePointOutOrIn()){
if(toJudgeCircal())printf("PEG WILL FIT\n");
else printf("PEG WILL NOT FIT\n");
}
else printf("PEG WILL NOT FIT\n");
}
else printf("HOLE IS ILL-FORMED\n");
}
return 0;
}