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>>;
 //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=,double y=):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*]; //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 = ;
                 to[p][b] = to[a][p] = to[b][a] = cnt;
                 F[cnt++] = add;
             }
         }
     }
     void dfs(int p, int cur)
     {
         F[cur].ok = ;
         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 = ;
         if (n < )
             return;
         bool sb = ;
         //使前两点不公点
         for (int i = ; i < n; i++)
         {
             if (vlen(P[] - P[i]) > eps)
             {
                 swap(P[], P[i]);
                 sb = ;
                 break;
             }
         }
         if (sb)return;
         sb = ;
         //使前三点不公线
         for (int i = ; i < n; i++)
         {
             if (vlen((P[] - P[]) * (P[] - P[i])) > eps)
             {
                 swap(P[], P[i]);
                 sb = ;
                 break;
             }
         }
         if (sb)return;
         sb = ;
         //使前四点不共面
         for (int i = ; i < n; i++)
         {
             if (fabs((P[] - P[]) * (P[] - P[]) ^ (P[] - P[i])) > eps)
             {
                 swap(P[], P[i]);
                 sb = ;
                 break;
             }
         }
         if (sb)return;
         fac add;
         for (int i = ; i < ; i++)
         {
             add.a = (i+)%, add.b = (i+)%, add.c = (i+)%, add.ok = ;
             if (point3of(P[i], add) > )
                 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 = ; i < n; i++)
         {
             for (int j = ; j < cnt; j++)
             {
                 if (F[j].ok && point3of(P[i], F[j]) > eps)
                 {
                     dfs(i, j);
                     break;
                 }
             }
         }
         int tmp = cnt;
         cnt = ;
         for (int i = ; i < tmp; i++)
         {
             if (F[i].ok)
             {
                 F[cnt++] = F[i];
             }
         }
     }
     //表面积
     double area()
     {
         double ret = 0.0;
         for (int i = ; 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(, , );
         double ret = 0.0;
         for (int i = ; 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 = ;
         for (int i = ; i < cnt; i++)
         {
             bool nb = ;
             for (int j = ; j < i; j++)
             {
                 if(same(i, j))
                 {
                     nb = ;
                     break;
                 }
             }
             ans += nb;
         }
         return ans;
     }
     //三维凸包重心
     point3 barycenter()
     {
         point3 ans(,,),o(,,);
         double all=;
         for(int i=;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 =  ; i < cnt ; i++)
     {
         ans = min(ans,hull.ptoface(pp,i));
     }
     printf("%.3f\n",ans);
 }
 int main()
 {
     int n,i;
     while(scanf("%d",&n)!=EOF)
     {
         hull.n = n;
         for(i =  ; i < n; i++)
         {
             scanf("%lf%lf%lf",&pp[i].x,&pp[i].y,&pp[i].z);
             hull.P[i] = pp[i];
         }
         hull.construct();
         solve();
     }
 }