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
;
int trianglecnt;
fac tri
;
int vis

;
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;
}