hdu 4273 Rescue（三维凸包重心）
裸的三维凸包重心到表面的最近距离。
#include<algorithm>#include<iostream>#include<cstring>#include<fstream>#include<sstream>#include<vector>#include<string>#include<cstdio>#include<bitset>#include<queue>#include<stack>#include<cmath>#include<map>#include<set>#define FF(i, a, b) for(int i=a; i<b; i++)#define FD(i, a, b) for(int i=a; i>=b; i--)#define REP(i, n) for(int i=0; i<n; i++)#define CLR(a, b) memset(a, b, sizeof(a))#define debug puts("**debug**")#define LL long long#define PB push_back#define MP make_pair#define eps 1e-8using namespace std;int dcmp(double x) { if(fabs(x) < eps) return 0; else return x < 0 ? -1 : 1; }struct Point3 { double x, y, z; Point3(double x=0, double y=0, double z=0):x(x),y(y),z(z) { }};typedef Point3 Vector3;Vector3 operator + (const Vector3& A, const Vector3& B) { return Vector3(A.x+B.x, A.y+B.y, A.z+B.z); }Vector3 operator - (const Point3& A, const Point3& B) { return Vector3(A.x-B.x, A.y-B.y, A.z-B.z); }Vector3 operator * (const Vector3& A, double p) { return Vector3(A.x*p, A.y*p, A.z*p); }Vector3 operator / (const Vector3& A, double p) { return Vector3(A.x/p, A.y/p, A.z/p); }bool operator == (const Point3& a, const Point3& b) { return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0 && dcmp(a.z-b.z) == 0;}Point3 read_point3() { Point3 p; scanf("%lf%lf%lf", &p.x, &p.y, &p.z); return p;}double Dot(const Vector3& A, const Vector3& B) { return A.x*B.x + A.y*B.y + A.z*B.z; }double Length(const Vector3& A) { return sqrt(Dot(A, A)); }double Angle(const Vector3& A, const Vector3& B) { return acos(Dot(A, B) / Length(A) / Length(B)); }Vector3 Cross(const Vector3& A, const Vector3& B) { return Vector3(A.y*B.z - A.z*B.y, A.z*B.x - A.x*B.z, A.x*B.y - A.y*B.x); }double Area2(const Point3& A, const Point3& B, const Point3& C) { return Length(Cross(B-A, C-A)); }double Volume6(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return Dot(D-A, Cross(B-A, C-A)); }Point3 Centroid(const Point3& A, const Point3& B, const Point3& C, const Point3& D) { return (A + B + C + D)/4.0; }double rand01() { return rand() / (double)RAND_MAX; }double randeps() { return (rand01() - 0.5) * eps; }Point3 add_noise(const Point3& p) { return Point3(p.x + randeps(), p.y + randeps(), p.z + randeps());}struct Face { int v[3]; Face(int a, int b, int c) { v[0] = a; v[1] = b; v[2] = c; } Vector3 Normal(const vector<Point3>& 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<Point3>& 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<Face> CH3D(const vector<Point3>& P) { int n = P.size(); vector<vector<int> > vis(n); for(int i = 0; i < n; i++) vis[i].resize(n); vector<Face> 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<Face> 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<Point3> P, P2; vector<Face> 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;}