三维凸包板子-计算几何

三维凸包板子-计算几何

解析

先放个模板，待填坑

代码

#include<bits/stdc++.h>
using namespace std;
const int M=2009;
const double eps=1e-10;//注意精度
int n,cnt,vis[M][M],tot;
double ans;
double Rand(){return rand()/(double)RAND_MAX;}
double reps(){return (Rand()-0.5)*eps;}
struct point{
    double x,y,z;
    void shake(){x+=reps();y+=reps();z+=reps();}
    double len(){return sqrt(x*x+y*y+z*z);}
    point operator-(point p){return (point){x-p.x,y-p.y,z-p.z};}
    point operator*(point p){return (point){y*p.z-z*p.y,z*p.x-x*p.z,x*p.y-y*p.x};}
    double operator^(point p){return x*p.x+y*p.y+z*p.z;}
}p[M];
struct face{
    int v[3];
    point normal(){return (p[v[1]]-p[v[0]])*(p[v[2]]-p[v[0]]);}
    double area(){return normal().len()/2.0;}
}f[M],q[M];
int see(face a,point b) {return ((b-p[a.v[0]])^a.normal())>0;}
void Convex_3D(){
    f[++cnt]=(face){1,2,3};
    f[++cnt]=(face){3,2,1};
    for(int i=4,tot=0;i<=n;i++){
        for(int j=1,v;j<=cnt;j++){
            if(!(v=see(f[j],p[i]))) q[++tot]=f[j];
            for(int k=0;k<3;k++) vis[f[j].v[k]][f[j].v[(k+1)%3]]=v;
        }
        for(int j=1;j<=cnt;j++)
            for(int k=0;k<3;k++){
                int x=f[j].v[k],y=f[j].v[(k+1)%3];
                if(vis[x][y]&&!vis[y][x]) q[++tot]=(face){x,y,i};
            }for(int j=1;j<=tot;j++) f[j]=q[j];
        cnt=tot,tot=0;
    }
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;i++) scanf("%lf%lf%lf",&p[i].x,&p[i].y,&p[i].z),p[i].shake();
    Convex_3D();
    for(int i=1;i<=cnt;i++) ans+=f[i].area();
    printf("%.3lf\n",ans);
}