#include <stdlib.h>
#include <math.h>
#define MAXN 1000
#define offset 10000
#define eps 1e-8
#define zero(x) (((x)>0?(x):-(x))<eps)
#define _sign(x) ((x)>eps?1:((x)<-eps?2:0))
struct point{double x,y;};
struct line{point a,b;};
double xmult(point p1,point p2,point p0){
return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}
//判定凸多边形,顶点按顺时针或逆时针给出,允许相邻边共线
int is_convex(int n,point* p){
int i,s[3]={1,1,1};
for (i=0;i<n&&s[1]|s[2];i++)
s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;
return s[1]|s[2];
}
//判定凸多边形,顶点按顺时针或逆时针给出,不允许相邻边共线
int is_convex_v2(int n,point* p){
int i,s[3]={1,1,1};
for (i=0;i<n&&s[0]&&s[1]|s[2];i++)
s[_sign(xmult(p[(i+1)%n],p[(i+2)%n],p[i]))]=0;
return s[0]&&s[1]|s[2];
}
//判点在凸多边形内或多边形边上,顶点按顺时针或逆时针给出
int inside_convex(point q,int n,point* p){
int i,s[3]={1,1,1};
for (i=0;i<n&&s[1]|s[2];i++)
s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;
return s[1]|s[2];
}
//判点在凸多边形内,顶点按顺时针或逆时针给出,在多边形边上返回0
int inside_convex_v2(point q,int n,point* p){
int i,s[3]={1,1,1};
for (i=0;i<n&&s[0]&&s[1]|s[2];i++)
s[_sign(xmult(p[(i+1)%n],q,p[i]))]=0;
return s[0]&&s[1]|s[2];
}
//判点在任意多边形内,顶点按顺时针或逆时针给出
//on_edge表示点在多边形边上时的返回值,offset为多边形坐标上限
int inside_polygon(point q,int n,point* p,int on_edge=1){
point q2;
int i=0,count;
while (i<n)
for (count=i=0,q2.x=rand()+offset,q2.y=rand()+offset;i<n;i++)
if (zero(xmult(q,p[i],p[(i+1)%n]))&&(p[i].x-q.x)*(p[(i+1)%n].x-q.x)<eps&&(p[i].y-q.y)*(p[(i+1)%n].y-q.y)<eps)
return on_edge;
else if (zero(xmult(q,q2,p[i])))
break;
else if (xmult(q,p[i],q2)*xmult(q,p[(i+1)%n],q2)<-eps&&xmult(p[i],q,p[(i+1)%n])*xmult(p[i],q2,p[(i+1)%n])<-eps)
count++;
return count&1;
}
inline int opposite_side(point p1,point p2,point l1,point l2){
return xmult(l1,p1,l2)*xmult(l1,p2,l2)<-eps;
}
inline int dot_online_in(point p,point l1,point l2){
return zero(xmult(p,l1,l2))&&(l1.x-p.x)*(l2.x-p.x)<eps&&(l1.y-p.y)*(l2.y-p.y)<eps;
}
//判线段在任意多边形内,顶点按顺时针或逆时针给出,与边界相交返回1
int inside_polygon(point l1,point l2,int n,point* p){
point t[MAXN],tt;
int i,j,k=0;
if (!inside_polygon(l1,n,p)||!inside_polygon(l2,n,p))
return 0;
for (i=0;i<n;i++)
if (opposite_side(l1,l2,p[i],p[(i+1)%n])&&opposite_side(p[i],p[(i+1)%n],l1,l2))
return 0;
else if (dot_online_in(l1,p[i],p[(i+1)%n]))
t[k++]=l1;
else if (dot_online_in(l2,p[i],p[(i+1)%n]))
t[k++]=l2;
else if (dot_online_in(p[i],l1,l2))
t[k++]=p[i];
for (i=0;i<k;i++)
for (j=i+1;j<k;j++){
tt.x=(t[i].x+t[j].x)/2;
tt.y=(t[i].y+t[j].y)/2;
if (!inside_polygon(tt,n,p))
return 0;
}
return 1;
}
point intersection(line u,line v){
point ret=u.a;
double t=((u.a.x-v.a.x)*(v.a.y-v.b.y)-(u.a.y-v.a.y)*(v.a.x-v.b.x))
/((u.a.x-u.b.x)*(v.a.y-v.b.y)-(u.a.y-u.b.y)*(v.a.x-v.b.x));
ret.x+=(u.b.x-u.a.x)*t;
ret.y+=(u.b.y-u.a.y)*t;
return ret;
}
point barycenter(point a,point b,point c){
line u,v;
u.a.x=(a.x+b.x)/2;
u.a.y=(a.y+b.y)/2;
u.b=c;
v.a.x=(a.x+c.x)/2;
v.a.y=(a.y+c.y)/2;
v.b=b;
return intersection(u,v);
}
//多边形重心
point barycenter(int n,point* p){
point ret,t;
double t1=0,t2;
int i;
ret.x=ret.y=0;
for (i=1;i<n-1;i++)
if (fabs(t2=xmult(p[0],p[i],p[i+1]))>eps){
t=barycenter(p[0],p[i],p[i+1]);
ret.x+=t.x*t2;
ret.y+=t.y*t2;
t1+=t2;
}
if (fabs(t1)>eps)
ret.x/=t1,ret.y/=t1;
return ret;
}
//多边形面积
double area_polygon(int n,point* p)
{
double s1=0,s2=0;
int i;
for (i=0; i<n; i++)
s1+=p[(i+1)%n].y*p[i].x,s2+=p[(i+1)%n].y*p[(i+2)%n].x;
return fabs(s1-s2)/2;
}
//多边形费马点，点集pt，大小n，传入ptres作为费马点这一点，返回值是所有点到费马点的距离
double fermat_point(point pt [], int n, point & ptres)
{
point u, v;
double step = 0.0, curlen, explen, minlen;
int i, j, k, idx;
bool flag;
u.x = u.y = v.x = v.y = 0.0;
for (i = 0; i < n; ++i)
{
step += fabs(pt[i].x) + fabs(pt[i].y);
u.x += pt[i].x;
u.y += pt[i].y;
}
u.x /= n;
u.y /= n;
flag = 0;
while (step > 1e-10)
{
for (k = 0; k < 10; step /= 2, ++k)
for (i = -1; i <= 1; ++i)
for (j = -1; j <= 1; ++j)
{
v.x = u.x + step*i;
v.y = u.y + step*j;
curlen = explen = 0.0;
for (idx = 0; idx < n; ++idx)
{
curlen += distance(u, pt[idx]);
explen += distance(v, pt[idx]);
}
if (curlen > explen)
{
u = v;
minlen = explen;
flag = 1;
}
}
}
ptres = u;
return flag ? minlen : curlen;
}
