324 lines
8.2 KiB
C++
324 lines
8.2 KiB
C++
#include<cstdio>
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#include<cstdlib>
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#include<cstring>
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#include<cmath>
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#include <algorithm>
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using namespace std;
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#define INF (1<<30)
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#define PI acos(-1)
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#define SET(a,b) memset(a,b,sizeof(a))
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#define M 10010
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#define N 505
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#define EPS 1e-8
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struct pt
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{
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double x,y,z;
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pt() {}
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pt(double _x,double _y,double _z): x(_x),y(_y),z(_z) {}
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pt operator - (const pt p1)
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{
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return pt(x-p1.x,y-p1.y,z-p1.z);
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}
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pt operator * (pt p)
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{
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return pt(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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double operator ^ (pt 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 _3DCH
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{
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struct fac
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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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pt P[N];
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int cnt;
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fac F[N*8];
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int to[N][N];
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double vlen(pt 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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double area(pt a,pt b,pt 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(pt a,pt b,pt c,pt 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 ptof(pt &p,fac &f)
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{
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pt m=P[f.b]-P[f.a],n=P[f.c]-P[f.a],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=to[a][b];
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fac add;
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if(F[f].ok)
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if(ptof(P[p],F[f])>EPS) dfs(p,f);
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else
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{
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add.a=b; add.b=a; add.c=p; add.ok=1;
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to[p][b]=to[a][p]=to[b][a]=cnt;
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F[cnt++]=add;
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}
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}
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void dfs(int p,int cur)
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{
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F[cur].ok=0;
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deal(p,F[cur].b,F[cur].a);
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deal(p,F[cur].c,F[cur].b);
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deal(p,F[cur].a,F[cur].c);
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}
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bool same(int s,int t)
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{
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pt &a=P[F[s].a],&b=P[F[s].b],&c=P[F[s].c];
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return fabs(volume(a,b,c,P[F[t].a]))<EPS && fabs(volume(a,b,c,P[F[t].b]))<EPS && fabs(volume(a,b,c,P[F[t].c]))<EPS;
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}
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void construct()
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{
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cnt=0;
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if(n<4) return;
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bool sb=1;
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for(int i=1;i<n;i++)
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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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sb=0;
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break;
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}
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if(sb) return; sb=1;
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for(int i=2;i<n;i++)
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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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sb=0;
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break;
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}
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if(sb) return; sb=1;
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for(int i=3;i<n;i++)
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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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sb=0;
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break;
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}
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if(sb) return;
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fac add;
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for(int 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=1;
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if(ptof(P[i],add)>0) swap(add.b,add.c);
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to[add.a][add.b]=to[add.b][add.c]=to[add.c][add.a]=cnt;
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F[cnt++]=add;
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}
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for(int i=4;i<n;i++)
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for(int j=0;j<cnt;j++)
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if(F[j].ok && ptof(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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int tmp=cnt;
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cnt=0;
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for(int i=0;i<tmp;i++)
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if(F[i].ok) F[cnt++]=F[i];
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}
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double ptoface(pt 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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void get_panel(double &a,double &b,double &c,double &d,pt p1,pt p2,pt p3)
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{
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a=(p2.y-p1.y)*(p3.z-p1.z)-(p2.z-p1.z)*(p3.y-p1.y);
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b=(p2.z-p1.z)*(p3.x-p1.x)-(p2.x-p1.x)*(p3.z-p1.z);
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c=(p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x);
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d=-(a*p1.x+b*p1.y+c*p1.z);
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}
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inline double dist(pt p1, pt p2)
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{
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return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y)+(p1.z-p2.z)*(p1.z-p2.z));
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}
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}hull;
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inline int sign(double d)
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{
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if(d>EPS) return 1;
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if(d<-EPS) return -1;
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return 0;
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}
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struct point
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{
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double x,y,z;
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point(double x=0,double y=0,double z=0): x(x),y(y),z(z) {}
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point operator - (point p)
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{
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return point(x-p.x,y-p.y,z-p.z);
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}
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point operator + (point p)
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{
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return point(x+p.x,y+p.y,z+p.z);
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}
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point operator / (double len)
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{
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return point(x/len,y/len,z/len);
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}
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point operator * (double len)
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{
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return point(x*len,y*len,z*len);
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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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point operator * (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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double getlen()
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{
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return sqrt(x*x+y*y+z*z);
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}
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}con[N],ps[N],org;
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double a,b,c,d;
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int n;
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inline point get_point(point u,point v,point p)
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{
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double a,b,t;
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a=(v.x-u.x)*(v.x-u.x)+(v.y-u.y)*(v.y-u.y)+(v.z-u.z)*(v.z-u.z);
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b=(p.x-u.x)*(v.x-u.x)+(p.y-u.y)*(v.y-u.y)+(p.z-u.z)*(v.z-u.z);
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t=b/a;
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point ans;
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ans.x=v.x*t+(1-t)*u.x;
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ans.y=v.y*t+(1-t)*u.y;
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ans.z=v.z*t+(1-t)*u.z;
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return ans;
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}
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inline double dist(point a,point b)
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{
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return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)+(a.z-b.z)*(a.z-b.z));
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}
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point rotate(point u,point v,point p,double ang)
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{
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point root=get_point(u,v,p),e,r;
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point ans;
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e=(v-u)/dist(u,v);
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r=p-root;
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e=e*r;
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ans=r*cos(ang)+e*sin(ang)+root;
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return ans;
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}
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double inter_pro(point u1,point v1,point u2,point v2)
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{
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return (v1.x-u1.x)*(v2.y-u2.y)-(v1.y-u1.y)*(v2.x-u2.x);
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}
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bool cmp(point a,point b)
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{
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return a.y<b.y || a.y==b.y && a.x<b.x;
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}
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void Graham(point* pol, int n, point* con, int& len){
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sort(pol, pol+ n, cmp);
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con[0] = pol[0];
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con[1] = pol[1];
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int top = 1;
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for(int i = 2; i < n; i++){
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while(top > 0 && inter_pro(con[top - 1], con[top], con[top - 1], pol[i]) <= 0) top--;
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con[++top] = pol[i];
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}
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int tmp = top;
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for(int i = n - 2; i >= 0; i--){
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while(top > tmp && inter_pro(con[top - 1], con[top], con[top - 1], pol[i]) <= 0) top--;
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con[++top] = pol[i];
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}
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len = top;
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}
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double polyArea(point* ps, int n){
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ps[n] = ps[0];
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int i;
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double ans=0;
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for(i = 0; i < n; i++){
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ans += (ps[i].x*ps[i+1].y-ps[i].y*ps[i+1].x);
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}
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return fabs(ans/2.0);
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}
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double solve()
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{
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point tp(0,0,0),end(0,0,1),vec;
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double ang;
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int i,cn;
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if(sign(a)) tp.x=d/a;
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else if(sign(b)) tp.y=d/b;
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else if(sign(c)) tp.z=d/c;
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ps[n+1]=tp;
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vec=(point(a,b,c))*(end);
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if(sign(vec.x)==0) vec.x=0;
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if(sign(vec.y)==0) vec.y=0;
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if(sign(vec.z)==0) vec.z=0;
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ang=(a*end.x+b*end.y+c*end.z)/(point(a,b,c).getlen());
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ang=acos(ang);
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if(sign(ang)!=-0 && sign(ang-PI)!=0)
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for(i=0;i<n;i++)
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ps[i]=rotate(org,vec,ps[i],ang);
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for(int i=0;i<n;i++) ps[i].z=0;
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Graham(ps,n,con,cn);
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double ans=fabs(polyArea(con,cn));
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return ans;
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}
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int main()
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{
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while (scanf("%d",&hull.n) && hull.n)
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{
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for(int i=0;i<hull.n;i++)
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scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);
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if(n==1)
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{
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printf("0.000 0.000\n");
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continue;
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}
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if(n==2)
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{
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printf("%.3lf 0.000\n",hull.dist(hull.P[0],hull.P[1]));
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continue;
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}
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hull.construct();
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n=hull.n;
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double ans1=0,ans2=1e100;
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if(hull.cnt==0)
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{
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double max0=0;
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for(int i=0;i<hull.n;i++)
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for(int j=0;j<hull.n;j++)
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max0=max(max0,hull.dist(hull.P[i],hull.P[j]));
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printf("%.3lf 0.000\n",max0);
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continue;
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}
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n=hull.n;
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for(int i=0;i<hull.cnt;i++)
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{
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for(int j=0;j<hull.n;j++)
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ps[j].x=hull.P[j].x,
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ps[j].y=hull.P[j].y,
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ps[j].z=hull.P[j].z;
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hull.get_panel(a,b,c,d,hull.P[hull.F[i].a],hull.P[hull.F[i].b],hull.P[hull.F[i].c]);
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d=-d;
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double dist=0;
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for(int j=0;j<hull.n;j++)
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dist=max(dist,hull.ptoface(hull.P[j],i));
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double ans=solve();
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if(dist>ans1) ans1=dist,ans2=ans;
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else if(fabs(dist-ans1)<EPS) if(ans2>ans) ans1=dist,ans2=ans;
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}
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printf("%.3f %.3f\n",ans1,ans2);
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}
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return 0;
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}
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