三维凸包模板

#include <cstring>
#include <cstdio>
#include <cmath>
#include <algorithm>
using namespace std;
#define inf 0x7fffffff
#define max(a,b) (a>b?a:b)
#define min(a,b) (a<b?a:b)
#define eps 1e-7
#define MAXV 505

//三维点
struct pt
{
double x, y, z;
pt() {}
pt(double _x, double _y, double _z): x(_x), y(_y), z(_z) {}
pt operator - (const pt p1)
{
return pt(x - p1.x, y - p1.y, z - p1.z);
}
pt operator * (pt p)
{
return pt(y*p.z-z*p.y, z*p.x-x*p.z, x*p.y-y*p.x);    //叉乘
}
double operator ^ (pt p)
{
return x*p.x+y*p.y+z*p.z;    //点乘
}
};

struct _3DCH
{
struct fac
{
int a, b, c;    //表示凸包一个面上三个点的编号
bool ok;        //表示该面是否属于最终凸包中的面
};

int n;    //初始点数
pt P[MAXV];    //初始点

int cnt;    //凸包表面的三角形数
fac F[MAXV*8]; //凸包表面的三角形

int to[MAXV][MAXV];

double vlen(pt a)
{
return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);    //向量长度
}
double area(pt a, pt b, pt c)
{
return vlen((b-a)*(c-a));    //三角形面积*2
}
double volume(pt a, pt b, pt c, pt d)
{
return (b-a)*(c-a)^(d-a);    //四面体有向体积*6
}

//正：点在面同向
double ptof(pt &p, fac &f)
{
pt m = P[f.b]-P[f.a], n = P[f.c]-P[f.a], t = p-P[f.a];
return (m * n) ^ t;
}

void deal(int p, int a, int b)
{
int f = to[a][b];
fac add;
if (F[f].ok)
{
if (ptof(P[p], F[f]) > eps)
dfs(p, f);
else
{
add.a = b, add.b = a, add.c = p, add.ok = 1;
to[p][b] = to[a][p] = to[b][a] = cnt;
F[cnt++] = add;
}
}
}

void dfs(int p, int cur)
{
F[cur].ok = 0;
deal(p, F[cur].b, F[cur].a);
deal(p, F[cur].c, F[cur].b);
deal(p, F[cur].a, F[cur].c);
}

bool same(int s, int t)
{
pt &a = P[F[s].a], &b = P[F[s].b], &c = P[F[s].c];
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;
}

//构建三维凸包
void construct()
{
cnt = 0;
if (n < 4)
return;

bool sb = 1;
//使前两点不公点
for (int i = 1; i < n; i++)
{
if (vlen(P[0] - P[i]) > eps)
{
swap(P[1], P[i]);
sb = 0;
break;
}
}
if (sb)return;

sb = 1;
//使前三点不公线
for (int i = 2; i < n; i++)
{
if (vlen((P[0] - P[1]) * (P[1] - P[i])) > eps)
{
swap(P[2], P[i]);
sb = 0;
break;
}
}
if (sb)return;

sb = 1;
//使前四点不共面
for (int i = 3; i < n; i++)
{
if (fabs((P[0] - P[1]) * (P[1] - P[2]) ^ (P[0] - P[i])) > eps)
{
swap(P[3], P[i]);
sb = 0;
break;
}
}
if (sb)return;

fac add;
for (int i = 0; i < 4; i++)
{
add.a = (i+1)%4, add.b = (i+2)%4, add.c = (i+3)%4, add.ok = 1;
if (ptof(P[i], add) > 0)
swap(add.b, add.c);
to[add.a][add.b] = to[add.b][add.c] = to[add.c][add.a] = cnt;
F[cnt++] = add;
}

for (int i = 4; i < n; i++)
{
for (int j = 0; j < cnt; j++)
{
if (F[j].ok && ptof(P[i], F[j]) > eps)
{
dfs(i, j);
break;
}
}
}
int tmp = cnt;
cnt = 0;
for (int i = 0; i < tmp; i++)
{
if (F[i].ok)
{
F[cnt++] = F[i];
}
}
}

//表面积
double area()
{
double ret = 0.0;
for (int i = 0; i < cnt; i++)
{
ret += area(P[F[i].a], P[F[i].b], P[F[i].c]);
}
return ret / 2.0;
}

//体积
double volume()
{
pt O(0, 0, 0);
double ret = 0.0;
for (int i = 0; i < cnt; i++)
{
ret += volume(O, P[F[i].a], P[F[i].b], P[F[i].c]);
}
return fabs(ret / 6.0);
}

//表面三角形数
int facetCnt_tri()
{
return cnt;
}

//表面多边形数
int facetCnt()
{
int ans = 0;
for (int i = 0; i < cnt; i++)
{
bool nb = 1;
for (int j = 0; j < i; j++)
{
if (same(i, j))
{
nb = 0;
break;
}
}
ans += nb;
}
return ans;
}
}hull;

int main()
{
int i,n;
while(scanf("%d",&hull.n)!=EOF)
{
for(i = 0 ; i < hull.n ;i++)
scanf("%lf%lf%lf",&hull.P[i].x,&hull.P[i].y,&hull.P[i].z);
hull.construct();
printf("%.3f\n",hull.area());
}
return 0;
}