[模板]三维凸包(无讲解)

 1 // luogu-judger-enable-o2
 2 #include<bits/stdc++.h>
 3 using namespace std;
 4 typedef long double ld;
 5 const int maxn=2E3+5;
 6 const ld eps=1E-9;
 7 int n;
 8 bool vis[maxn][maxn];
 9 struct pt
10 {
11     ld x,y,z;
12     pt(ld a=0,ld b=0,ld c=0):x(a),y(b),z(c){}
13     pt operator+(const pt&A){return pt(x+A.x,y+A.y,z+A.z);}
14     pt operator-(const pt&A){return pt(x-A.x,y-A.y,z-A.z);}
15     pt operator*(const pt&A){return pt(y*A.z-z*A.y,z*A.x-x*A.z,x*A.y-y*A.x);}
16     ld operator&(const pt&A){return x*A.x+y*A.y+z*A.z;}
17     ld len(){return sqrt(x*x+y*y+z*z);}
18 }a[maxn];
19 struct face
20 {
21     int v[3];
22     pt normal(){return (a[v[1]]-a[v[0]])*(a[v[2]]-a[v[0]]);}
23     ld area(){return normal().len()/2;}
24 }f[maxn],wait[maxn];
25 int cnt;
26 inline int see(face A,pt B)
27 {
28     return ((B-a[A.v[0]])&A.normal())>0;
29 }
30 void solve()
31 {
32     f[++cnt]=(face){1,2,3};
33     f[++cnt]=(face){3,2,1};
34     for(int i=4;i<=n;++i)
35     {
36         int tot=0;
37         for(int j=1;j<=cnt;++j)
38         {
39             if(!see(f[j],a[i]))
40             {
41                 wait[++tot]=f[j];
42                 for(int k=0;k<3;++k)
43                     vis[f[j].v[k]][f[j].v[(k+1)%3]]=0;
44             }
45             else
46             {
47                 for(int k=0;k<3;++k)
48                     vis[f[j].v[k]][f[j].v[(k+1)%3]]=1;
49             }
50         }
51         for(int j=1;j<=cnt;++j)
52             for(int k=0;k<3;++k)
53             {
54                 int x=f[j].v[k],y=f[j].v[(k+1)%3];
55                 if(vis[x][y]&&(!vis[y][x]))
56                     wait[++tot]=(face){x,y,i};
57             }
58         for(int j=1;j<=tot;++j)
59             f[j]=wait[j];
60         cnt=tot;
61     }
62 }
63 int main()
64 {
65     ios::sync_with_stdio(false);
66     cin>>n;
67     for(int i=1;i<=n;++i)
68         cin>>a[i].x>>a[i].y>>a[i].z;
69     solve();
70     ld ans=0;
71     for(int i=1;i<=cnt;++i)
72         ans+=f[i].normal().len()/2;
73     cout<<fixed<<setprecision(3)<<ans<<endl;
74     return 0;
75 }