hdu4273Rescue三维凸包的重心

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题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4273
题意：求一个三维凸包的重心到凸包各个面的的最小距离。
模板如下：
/** File:   main.cpp* Author: ssslpk** Created on 2012年9月8日, 下午3:39*/#include<stdio.h>#include<string.h>#include<math.h>#include<algorithm>using namespace std;#define PR 1e-8#define N 1000struct TPoint{    double x,y,z;    TPoint(){}    TPoint(double _x,double _y,double _z):x(_x),y(_y),z(_z){}    TPoint operator-(const TPoint p) {return TPoint(x-p.x,y-p.y,z-p.z);}    TPoint operator*(const TPoint p) {return TPoint(y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x);}//叉积    double operator^(const TPoint p) {return x*p.x+y*p.y+z*p.z;}//点积}p[N];struct fac//{    int a,b,c;//凸包一个面上的三个点的编号    bool ok;//该面是否是最终凸包中的面};struct T3dhull{    int n;//初始点数    TPoint ply[N];//初始点    int trianglecnt;//凸包上三角形数    fac tri[N];//凸包三角形    int vis[N][N];//点i到点j是属于哪个面    double dist(TPoint a){return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);}//两点长度    double area(TPoint a,TPoint b,TPoint c){return dist((b-a)*(c-a));}//三角形面积*2    double volume(TPoint a,TPoint b,TPoint c,TPoint d){return (b-a)*(c-a)^(d-a);}//四面体有向体积*6    double ptoplane(TPoint &p,fac &f)//正：点在面同向    {        TPoint m=ply[f.b]-ply[f.a],n=ply[f.c]-ply[f.a],t=p-ply[f.a];        return (m*n)^t;    }    void deal(int p,int a,int b)    {        int f=vis[a][b];        fac add;        if(tri[f].ok)        {            if((ptoplane(ply[p],tri[f]))>PR) dfs(p,f);            else            {                add.a=b,add.b=a,add.c=p,add.ok=1;                vis[p][b]=vis[a][p]=vis[b][a]=trianglecnt;                tri[trianglecnt++]=add;            }        }    }    void dfs(int p,int cnt)//维护凸包，如果点p在凸包外更新凸包    {        tri[cnt].ok=0;        deal(p,tri[cnt].b,tri[cnt].a);        deal(p,tri[cnt].c,tri[cnt].b);        deal(p,tri[cnt].a,tri[cnt].c);    }    bool same(int s,int e)//判断两个面是否为同一面    {        TPoint a=ply[tri[s].a],b=ply[tri[s].b],c=ply[tri[s].c];        return fabs(volume(a,b,c,ply[tri[e].a]))<PR            &&fabs(volume(a,b,c,ply[tri[e].b]))<PR            &&fabs(volume(a,b,c,ply[tri[e].c]))<PR;    }    void construct()//构建凸包    {        int i,j;        trianglecnt=0;        if(n<4) return ;        bool tmp=true;        for(i=1;i<n;i++)//前两点不共点        {            if((dist(ply[0]-ply[i]))>PR)            {                swap(ply[1],ply[i]); tmp=false; break;            }        }        if(tmp) return;        tmp=true;        for(i=2;i<n;i++)//前三点不共线        {            if((dist((ply[0]-ply[1])*(ply[1]-ply[i])))>PR)            {                swap(ply[2],ply[i]); tmp=false; break;            }        }        if(tmp) return ;        tmp=true;        for(i=3;i<n;i++)//前四点不共面        {            if(fabs((ply[0]-ply[1])*(ply[1]-ply[2])^(ply[0]-ply[i]))>PR)            {                swap(ply[3],ply[i]); tmp=false; break;            }        }        if(tmp) return ;        fac add;        for(i=0;i<4;i++)//构建初始四面体        {            add.a=(i+1)%4,add.b=(i+2)%4,add.c=(i+3)%4,add.ok=1;            if((ptoplane(ply[i],add))>0) swap(add.b,add.c);            vis[add.a][add.b]=vis[add.b][add.c]=vis[add.c][add.a]=trianglecnt;            tri[trianglecnt++]=add;        }        for(i=4;i<n;i++)//构建更新凸包        {            for(j=0;j<trianglecnt;j++)            {                if(tri[j].ok&&(ptoplane(ply[i],tri[j]))>PR)                {                    dfs(i,j); break;                }            }        }        int cnt=trianglecnt;        trianglecnt=0;        for(i=0;i<cnt;i++)        {            if(tri[i].ok)                tri[trianglecnt++]=tri[i];        }    }    double area()//表面积    {        double ret=0;        for(int i=0;i<trianglecnt;i++)            ret+=area(ply[tri[i].a],ply[tri[i].b],ply[tri[i].c]);        return ret/2.0;    }    double volume()//体积    {        TPoint p(0,0,0);        double ret=0;        for(int i=0;i<trianglecnt;i++)            ret+=volume(p,ply[tri[i].a],ply[tri[i].b],ply[tri[i].c]);        return fabs(ret/6);    }    int facetri() {return trianglecnt;}//表面三角形数    int facepolygon()//表面多边形数    {        int ans=0,i,j,k;        for(i=0;i<trianglecnt;i++)        {            for(j=0,k=1;j<i;j++)            {                if(same(i,j)) {k=0;break;}            }            ans+=k;        }        return ans;    }TPoint gracen()//重心{TPoint res=TPoint(0,0,0);double sumv=0;TPoint po=TPoint(0,0,0);//原点for(int i=0;i<facetri();i++){double v=hull.volume(po,ply[tri[i].a],ply[hull.tri[i].b],ply[tri[i].c])/6.0;sumv+=v;res.x+=(ply[tri[i].a].x+ply[tri[i].b].x+ply[tri[i].c].x) * v;res.y+=(ply[tri[i].a].y+ply[tri[i].b].y+ply[tri[i].c].y) * v;res.z+=(ply[tri[i].a].z+ply[tri[i].b].z+ply[tri[i].c].z) * v;}res.x/=(4*sumv);res.y/=(4*sumv);res.z/=(4*sumv);return res;}}hull;double min(double a,double b){return a>b? b: a;}int main(){    int n,i;    while(scanf("%d",&hull.n)!=EOF)    {        for( i=0; i<hull.n; i++)scanf("%lf%lf%lf",&hull.ply[i].x,&hull.ply[i].y,&hull.ply[i].z);        hull.construct();        double ans=10000000.0;       TPoint cen=hull.gracen();        for( i=0;i<hull.facetri();i++)        {            double dis=fabs(hull.volume(cen,hull.ply[hull.tri[i].a],hull.ply[hull.tri[i].b],hull.ply[hull.tri[i].c]) )/hull.area(hull.ply[hull.tri[i].a],hull.ply[hull.tri[i].b],hull.ply[hull.tri[i].c]);//=dis2(i);            ans=min(ans,dis);        }        printf("%.3lf\n",ans);    }    return 0;}/*//三点转化为平面的系数void get_panel(TPoint p1,TPoint p2,TPoint p3,double &a,double &b,double &c,double &d){    a = ( (p2.y-p1.y)*(p3.z-p1.z)-(p2.z-p1.z)*(p3.y-p1.y) );    b = ( (p2.z-p1.z)*(p3.x-p1.x)-(p2.x-p1.x)*(p3.z-p1.z) );    c = ( (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x) );    d = ( 0-(a*p1.x+b*p1.y+c*p1.z) );}//点到平面的距离double dis_pt2panel(TPoint pt,double a,double b,double c,double d){return fabs(a*pt.x+b*pt.y+c*pt.z+d)/sqrt(a*a+b*b+c*c);}*/