hdu4273Rescue(三维凸包重心)

链接

模板题已不叫题。。

三维凸包+凸包重心+点到平面距离（体积/点积）  体积-->混合积（先点乘再叉乘）

#include <iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<stdlib.h>
#include<vector>
#include<cmath>
#include<queue>
#include<set>
using namespace std;
#define N 510
#define INF 1e20
#define max(a,b) (a>b?a:b)
#define min(a,b) (a<b?a:b)
#define eps 1e-8
#define MAXV 505
const double pi = acos(-1.0);
const double inf = ~0u>>2;
//三维点
struct point3
{
    double x, y,z;
    point3() {}
    point3(double _x, double _y, double _z): x(_x), y(_y), z(_z) {}
    point3 operator +(const point3 p1)
    {
        return point3(x+p1.x,y+p1.y,z+p1.z);
    }
    point3 operator - (const point3 p1)
    {
        return point3(x - p1.x, y - p1.y, z - p1.z);
    }
    point3 operator * (point3 p)
    {
        return point3(y*p.z-z*p.y, z*p.x-x*p.z, x*p.y-y*p.x);    //叉乘
    }
    point3 operator *(double d)
    {
        return point3(x*d,y*d,z*d);
    }
    point3 operator /(double d)
    {
        return point3(x/d,y/d,z/d);
    }
    double operator ^ (point3 p)
    {
        return x*p.x+y*p.y+z*p.z;    //点乘
    }

} pp[N],rp[N];
struct point
{
    double x,y;
    point(double x=0,double y=0):x(x),y(y) {}
    point operator -(point b)
    {
        return point(x-b.x,y-b.y);
    }
} p[N],ch[N];
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
    point3 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(point3 a)
    {
        return sqrt(a.x*a.x+a.y*a.y+a.z*a.z);
    }  //向量长度
    double area(point3 a, point3 b, point3 c)
    {
        return vlen((b-a)*(c-a));
    }    //三角形面积*2
    double volume(point3 a, point3 b, point3 c, point3 d)
    {
        return (b-a)*(c-a)^(d-a);    //四面体有向体积*6
    }
    //正：点在面同向
    double point3of(point3 &p, fac &f)
    {
        point3 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 (point3of(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)
    {
        point3 &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 (point3of(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 && point3of(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;
    }
    double ptoface(point3 p,int i)
    {
        return fabs(volume(P[F[i].a],P[F[i].b],P[F[i].c],p)/vlen((P[F[i].b]-P[F[i].a])*(P[F[i].c]-P[F[i].a])));
    }
    //体积
    double volume()
    {
        point3 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;
    }
    //三维凸包重心
    point3 barycenter()
    {
        point3 ans(0,0,0),o(0,0,0);
        double all=0;
        for(int i=0;i<cnt;i++)
        {
            double vol=volume(o,P[F[i].a],P[F[i].b],P[F[i].c]);
            ans=ans+(o+P[F[i].a]+P[F[i].b]+P[F[i].c])/4.0*vol;
            all+=vol;
        }
        ans=ans/all;
        return ans;
    }

}hull;

void solve()
{
    double ans = INF;
    int i;
    int cnt = hull.cnt;
    point3 pp = hull.barycenter();
    for(i = 0 ; i < cnt ; i++)
    {
        ans = min(ans,hull.ptoface(pp,i));
    }
    printf("%.3f
",ans);
}
int main()
{
    int n,i;
    while(scanf("%d",&n)!=EOF)
    {
        hull.n = n;
        for(i = 0 ; i < n; i++)
        {
            scanf("%lf%lf%lf",&pp[i].x,&pp[i].y,&pp[i].z);
            hull.P[i] = pp[i];
        }
        hull.construct();
        solve();
    }
}