三维凸包模板_Hdu 4273 Rescue

typedef long long LL;
typedef unsigned long long ULL;
typedef vector <int> VI;
const int INF = 0x3f3f3f3f;
const double eps = 1e-10;
const int MOD = 100000007;
const int MAXN = 400;
const double PI = acos(-1.0);

inline int dcmp(double x)
{
if(fabs(x) < eps) return 0;
else return x < 0 ? -1 : 1;
}

struct Point
{
double x, y, z;
Point(double x=0, double y=0, double z=0):x(x),y(y),z(z) { }
inline void read() { scanf("%lf%lf%lf", &x, &y, &z); }
};

typedef Point Vector;

inline Vector operator + (Vector A, Vector B)
{
return Vector(A.x+B.x, A.y+B.y, A.z+B.z);
}
inline Vector operator - (Point A, Point B)
{
return Vector(A.x-B.x, A.y-B.y, A.z-B.z);
}
inline Vector operator * (Vector A, double p)
{
return Vector(A.x*p, A.y*p, A.z*p);
}
inline Vector operator / (Vector A, double p)
{
return Vector(A.x/p, A.y/p, A.z/p);
}

bool operator == (const Point& a, const Point& b)
{
return dcmp(a.x-b.x) == 0 && dcmp(a.y-b.y) == 0 && dcmp(a.z-b.z) == 0;
}

inline double Dot(Vector A, Vector B)
{
return A.x*B.x + A.y*B.y + A.z*B.z;
}
inline double Length(Vector A)
{
return sqrt(Dot(A, A));
}
inline double Angle(Vector A, Vector B)
{
return acos(Dot(A, B) / Length(A) / Length(B));
}
inline Vector Cross(Vector A, Vector B)
{
return Vector(A.y*B.z - A.z*B.y, A.z*B.x - A.x*B.z, A.x*B.y - A.y*B.x);
}
inline double Area2(Point A, Point B, Point C)
{
return Length(Cross(B-A, C-A));
}
inline double Volume6(Point A, Point B, Point C, Point D)
{
return Dot(D-A, Cross(B-A, C-A));
}
inline Point Centroid(Point A, Point B, Point C, Point D)
{
return (A + B + C + D)/4.0;
}

inline double rand01()
{
return rand() / (double)RAND_MAX;
}
inline double randeps()
{
return (rand01() - 0.5) * eps;
}

inline Point add_noise(Point p)
{
return Point(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;
}
inline Vector Normal(const vector<Point>& P) const
{
return Cross(P[v[1]]-P[v[0]], P[v[2]]-P[v[0]]);
}
// f是否能看见P[i]
inline int CanSee(const vector<Point>& 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<Point>& 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 < (int)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 < (int)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<Point> 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();
P2[i] = add_noise(P[i]);
}
faces = CH3D(P2);
return true;
}

Point centroid()
{
Point C = P[0];
double totv = 0;
Point tot(0,0,0);
for(int i = 0; i < (int)faces.size(); i++)
{
Point 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(Point C)
{
double ans = 1e30;
for(int i = 0; i < (int)faces.size(); i++)
{
Point 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()
{
ConvexPolyhedron P1, P2;
while(P1.read())
{
Point C1 = P1.centroid();
double d1 = P1.mindist(C1);
printf("%.3lf\n", d1);
}
return 0;
}