三维凸包模版 求三维凸包的表面积和体积

#include <stdio.h>
#include <string.h>
#include <stdlib.h>
#include <math.h>
#include <iostream>
#include <queue>
#include <algorithm>
using namespace std;
#define PR 1e-8
#define N 510
struct 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);}
    double operator^(const TPoint p){return x*p.x+y*p.y+z*p.z;}
};
struct fac{
    int a, b, c;
    bool ok;
};
struct T3dhull{
    int n;
    TPoint ply[N];
    int trianglecnt;
    fac tri[N];
    int vis[N][N];
    double dist(TPoint a){return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);}
    double area(TPoint a, TPoint b, TPoint c)
    { return dist((b-a)*(c-a));}
    double volume(TPoint a, TPoint b, TPoint c, TPoint d)
    { return (b-a)*(c-a)^(d-a);}
    double ptoplane(TPoint &p, fac &f)
    {
        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) {
        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) {
        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()
    {
        int i, j;
        trianglecnt = 0;
        if(n<4) return ;
        bool tmp = true;
        for(i = 1; i < n; i++)
        {
            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++)
        {
            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++)
        {
            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++)
        {
            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++)
        {
            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()
    {
        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()
    {
        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);
    }
}hull;  

int main(){
    int Cas = 1;
    while(scanf("%d",&hull.n), hull.n){
        int i ;
        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();
        printf("Case %d: %.2lf\n", Cas++, hull.area());
    }
    return 0;
}