hdu 4273 Rescue（三维凸包重心） - c++编程基础

裸的三维凸包重心到表面的最近距离。
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#include  
#define FF(i, a, b) for(int i=a; i=b; i--)  
#define REP(i, n) for(int i=0; i




& P) const {  
    return Cross(P[v[1]]-P[v[0]], P[v[2]]-P[v[0]]);  
  }  
  // f是否能看见P[i]  
  int CanSee(const vector& P, int i) const {  
    return Dot(P[i]-P[v[0]], Normal(P)) > 0;  
  }  
};  
  
// 增量法求三维凸包  
// 注意：没有考虑各种特殊情况（如四点共面）。实践中，请在调用前对输入点进行微小扰动  
vector CH3D(const vector& P) {  
  int n = P.size();  
  vector > vis(n);  
  for(int i = 0; i < n; i++) vis[i].resize(n);  
  
  vector cur;  
  cur.push_back(Face(0, 1, 2)); // 由于已经进行扰动，前三个点不共线  
  cur.push_back(Face(2, 1, 0));  
  for(int i = 3; i < n; i++) {  
    vector next;  
    // 计算每条边的“左面”的可见性  
    for(int j = 0; j < cur.size(); j++) {  
      Face& f = cur[j];  
      int res = f.CanSee(P, i);  
      if(!res) next.push_back(f);  
      for(int k = 0; k < 3; k++) vis[f.v[k]][f.v[(k+1)%3]] = res;  
    }  
    for(int j = 0; j < cur.size(); j++)  
      for(int k = 0; k < 3; k++) {  
        int a = cur[j].v[k], b = cur[j].v[(k+1)%3];  
        if(vis[a][b] != vis[b][a] && vis[a][b]) // (a,b)是分界线，左边对P[i]可见  
          next.push_back(Face(a, b, i));  
      }  
    cur = next;  
  }  
  return cur;  
}  
  
struct ConvexPolyhedron {  
  int n;  
  vector P, P2;  
  vector faces;  
  
  bool read() {  
    if(scanf("%d", &n) != 1) return false;  
    P.resize(n);  
    P2.resize(n);  
    for(int i = 0; i < n; i++) { P[i] = read_point3(); P2[i] = add_noise(P[i]); }  
    faces = CH3D(P2);  
    return true;  
  }  
  
  Point3 centroid() {  
    Point3 C = P[0];  
    double totv = 0;  
    Point3 tot(0,0,0);  
    for(int i = 0; i < faces.size(); i++) {  
      Point3 p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];  
      double v = -Volume6(p1, p2, p3, C);  
      totv += v;  
      tot = tot + Centroid(p1, p2, p3, C)*v;  
    }  
    return tot / totv;  
  }  
  
  double mindist(Point3 C) {  
    double ans = 1e30;  
    for(int i = 0; i < faces.size(); i++) {  
      Point3 p1 = P[faces[i].v[0]], p2 = P[faces[i].v[1]], p3 = P[faces[i].v[2]];  
      ans = min(ans, fabs(-Volume6(p1, p2, p3, C) / Area2(p1, p2, p3)));  
    }  
    return ans;  
  }  
}P1;  
  
int main()  
{  
  int n, m;  
  ConvexPolyhedron P1, P2;  
  while(P1.read()) {  
    Point3 C1 = P1.centroid();  
    double d1 = P1.mindist(C1);  
    printf("%.3f\n", d1);  
  }  
  return 0;  
}