bzoj 1209

三维凸包裸题。

1、通过volume计算有向体积，判断点与面的位置关系。

2、噪声

 /**************************************************************
     Problem: 1209
     User: idy002
     Language: C++
     Result: Accepted
     Time:20 ms
     Memory:1864 kb
 ****************************************************************/

 #include <cstdio>
 #include <cstdlib>
 #include <cmath>
 #include <vector>
 #define eps 1e-10
 #define N 1000
 using namespace std;

 struct Vector {
     double x, y, z;
     void read() {
         scanf( "%lf%lf%lf", &x, &y, &z );
     }
     Vector(){}
     Vector( double x, double y, double z ):x(x),y(y),z(z){}
     Vector operator+( const Vector &b ) const { return Vector(x+b.x,y+b.y,z+b.z); }
     Vector operator-( const Vector &b ) const { return Vector(x-b.x,y-b.y,z-b.z); }
     Vector operator*( double b ) const { return Vector(x*b,y*b,z*b); }
     Vector operator/( double b ) const { return Vector(x/b,y/b,z/b); }
     double operator&( const Vector &b ) const { return x*b.x+y*b.y+z*b.z; }
     Vector operator^( const Vector &b ) const { return Vector(y*b.z-z*b.y,z*b.x-x*b.z,x*b.y-y*b.x); }
     double len() { return sqrt(x*x+y*y+z*z); }
 };
 typedef Vector Point;
 struct Face {
     int p[];
     Face(){}
     Face( int a, int b, int c ) {
         p[]=a, p[]=b, p[]=c;
     }
 };
 typedef vector<Face> Convex;

 int n;
 Point pts[N];
 bool vis[N][N];

 double rand01() {
     return (double) rand()/RAND_MAX;
 }
 double randeps() {
     return (rand01()-0.5)*eps;
 }
 void noise() {
     for( int i=; i<n; i++ ) {
         pts[i].x += randeps();
         pts[i].y += randeps();
         pts[i].z += randeps();
     }
 }
 double volume( int p, int a, int b, int c ) {
     return (pts[a]-pts[p])&((pts[b]-pts[a])^(pts[c]-pts[a]))/6.0;
 }
 bool cansee( Face &f, int p ) {
     return volume(p,f.p[],f.p[],f.p[]) < 0.0;
 }
 Convex convex() {
     static Point back[N];
     for( int i=; i<n; i++ )
         back[i] = pts[i];
     noise();

     int nt[] = { , ,  };
     if( n<= ) return Convex();

     Convex cur;
     cur.push_back( Face(,,) );
     cur.push_back( Face(,,) );
     for( int i=; i<n; i++ ) {
         Convex nxt;
         for( int t=; t<cur.size(); t++ ) {
             Face &f = cur[t];
             bool see = cansee( f, i );
             if( !see ) nxt.push_back(f);
             for( int j=; j<; j++ )
                 vis[f.p[j]][f.p[nt[j]]] = see;
         }
         for( int t=; t<cur.size(); t++ ) {
             Face &f = cur[t];
             for( int j=; j<; j++ ) {
                 int a=f.p[j], b=f.p[nt[j]];
                 if( (vis[a][b]^vis[b][a]) && vis[a][b] )
                     nxt.push_back( Face(a,b,i) );
             }
         }
         cur = nxt;
     }
     for( int i=; i<n; i++ )
         pts[i] = back[i];
     return cur;
 }
 void print( Convex &cvx ) {
     fprintf( stderr, "%d\n", cvx.size() );
     for( int t=; t<cvx.size(); t++ ) {
         printf( "(%.0lf,%.0lf,%.0lf) (%.0lf,%.0lf,%.0lf) (%.0lf,%.0lf,%.0lf)\n",
                 pts[cvx[t].p[]].x, pts[cvx[t].p[]].y, pts[cvx[t].p[]].z,
                 pts[cvx[t].p[]].x, pts[cvx[t].p[]].y, pts[cvx[t].p[]].z,
                 pts[cvx[t].p[]].x, pts[cvx[t].p[]].y, pts[cvx[t].p[]].z );
     }
 }
 double area( int a, int b, int c ) {
     return ((pts[a]-pts[b])^(pts[a]-pts[c])).len() / 2.0;
 }

 int main() {
     scanf( "%d", &n );
     for( int i=; i<n; i++ )
         pts[i].read();
     Convex cvx = convex();

 //  print( cvx );

     double ans = 0.0;
     for( int i=; i<cvx.size(); i++ )
         ans += area( cvx[i].p[], cvx[i].p[], cvx[i].p[] );
     printf( "%.6lf\n", ans );
 }