250 lines
5.8 KiB
C++
250 lines
5.8 KiB
C++
#include<stdio.h>
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#include<algorithm>
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#include<string.h>
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#include<math.h>
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#include<stdlib.h>
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using namespace std;
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const int MAXN=550;
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const double eps=1e-8;
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struct Point
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{
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double x,y,z;
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Point(){}
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Point(double xx,double yy,double zz):x(xx),y(yy),z(zz){}
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Point operator -(const Point p1)
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{
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return Point(x-p1.x,y-p1.y,z-p1.z);
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}
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Point operator +(const Point p1)
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{
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return Point(x+p1.x,y+p1.y,z+p1.z);
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}
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Point operator *(const Point p)
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{
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return Point(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);
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}
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Point operator *(double d)
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{
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return Point(x*d,y*d,z*d);
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}
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Point operator / (double d)
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{
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return Point(x/d,y/d,z/d);
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}
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double operator ^(Point p)
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{
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return (x*p.x+y*p.y+z*p.z);
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}
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};
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struct CH3D
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{
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struct face
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{
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int a,b,c;
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bool ok;
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};
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int n;
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Point P[MAXN];
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int num;
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face F[8*MAXN];
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int g[MAXN][MAXN];
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double vlen(Point a)
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{
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return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);
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}
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Point cross(const Point &a,const Point &b,const Point &c)
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{
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return Point((b.y-a.y)*(c.z-a.z)-(b.z-a.z)*(c.y-a.y),
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(b.z-a.z)*(c.x-a.x)-(b.x-a.x)*(c.z-a.z),
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(b.x-a.x)*(c.y-a.y)-(b.y-a.y)*(c.x-a.x)
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);
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}
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double area(Point a,Point b,Point c)
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{
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return vlen((b-a)*(c-a));
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}
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double volume(Point a,Point b,Point c,Point d)
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{
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return (b-a)*(c-a)^(d-a);
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}
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double dblcmp(Point &p,face &f)
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{
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Point m=P[f.b]-P[f.a];
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Point n=P[f.c]-P[f.a];
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Point t=p-P[f.a];
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return (m*n)^t;
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}
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void deal(int p,int a,int b)
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{
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int f=g[a][b];
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face add;
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if(F[f].ok)
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{
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if(dblcmp(P[p],F[f])>eps)
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dfs(p,f);
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else
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{
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add.a=b;
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add.b=a;
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add.c=p;
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add.ok=true;
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g[p][b]=g[a][p]=g[b][a]=num;
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F[num++]=add;
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}
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}
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}
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void dfs(int p,int now)
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{
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F[now].ok=0;
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deal(p,F[now].b,F[now].a);
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deal(p,F[now].c,F[now].b);
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deal(p,F[now].a,F[now].c);
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}
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bool same(int s,int t)
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{
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Point &a=P[F[s].a];
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Point &b=P[F[s].b];
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Point &c=P[F[s].c];
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return fabs(volume(a,b,c,P[F[t].a]))<eps &&
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fabs(volume(a,b,c,P[F[t].b]))<eps &&
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fabs(volume(a,b,c,P[F[t].c]))<eps;
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}
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void create()
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{
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int i,j,tmp;
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face add;
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num=0;
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if(n<4)return;
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bool flag=true;
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for(i=1;i<n;i++)
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{
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if(vlen(P[0]-P[i])>eps)
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{
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swap(P[1],P[i]);
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flag=false;
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break;
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}
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}
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if(flag)return;
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flag=true;
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for(i=2;i<n;i++)
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{
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if(vlen((P[0]-P[1])*(P[1]-P[i]))>eps)
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{
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swap(P[2],P[i]);
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flag=false;
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break;
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}
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}
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if(flag)return;
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flag=true;
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for(int i=3;i<n;i++)
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{
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if(fabs((P[0]-P[1])*(P[1]-P[2])^(P[0]-P[i]))>eps)
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{
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swap(P[3],P[i]);
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flag=false;
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break;
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}
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}
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if(flag)return;
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for(i=0;i<4;i++)
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{
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add.a=(i+1)%4;
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add.b=(i+2)%4;
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add.c=(i+3)%4;
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add.ok=true;
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if(dblcmp(P[i],add)>0)swap(add.b,add.c);
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g[add.a][add.b]=g[add.b][add.c]=g[add.c][add.a]=num;
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F[num++]=add;
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}
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for(i=4;i<n;i++)
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{
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for(j=0;j<num;j++)
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{
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if(F[j].ok&&dblcmp(P[i],F[j])>eps)
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{
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dfs(i,j);
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break;
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}
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}
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}
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tmp=num;
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for(i=num=0;i<tmp;i++)
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if(F[i].ok)
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F[num++]=F[i];
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}
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double area()
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{
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double res=0;
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if(n==3)
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{
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Point p=cross(P[0],P[1],P[2]);
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res=vlen(p)/2.0;
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return res;
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}
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for(int i=0;i<num;i++)
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res+=area(P[F[i].a],P[F[i].b],P[F[i].c]);
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return res/2.0;
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}
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double volume()
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{
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double res=0;
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Point tmp(0,0,0);
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for(int i=0;i<num;i++)
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res+=volume(tmp,P[F[i].a],P[F[i].b],P[F[i].c]);
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return fabs(res/6.0);
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}
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int triangle()
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{
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return num;
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}
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int polygon()
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{
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int i,j,res,flag;
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for(i=res=0;i<num;i++)
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{
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flag=1;
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for(j=0;j<i;j++)
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if(same(i,j))
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{
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flag=0;
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break;
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}
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res+=flag;
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}
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return res;
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}
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Point barycenter()
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{
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Point ans(0,0,0),o(0,0,0);
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double all=0;
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for(int i=0;i<num;i++)
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{
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double vol=volume(o,P[F[i].a],P[F[i].b],P[F[i].c]);
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ans=ans+(o+P[F[i].a]+P[F[i].b]+P[F[i].c])/4.0*vol;
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all+=vol;
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}
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ans=ans/all;
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return ans;
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}
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double ptoface(Point p,int i)
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{
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return fabs(volume(P[F[i].a],P[F[i].b],P[F[i].c],p)/vlen((P[F[i].b]-P[F[i].a])*(P[F[i].c]-P[F[i].a])));
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}
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};
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CH3D hull;
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int main()
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{
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while(scanf("%d",&hull.n)==1)
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{
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for(int i=0;i<hull.n;i++)
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{
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scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);
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}
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hull.create();
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printf("%d\n",hull.polygon());
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}
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return 0;
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}
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