// file: examples/Polyhedron/polyhedron_prog_subdiv.C

#include <CGAL/Cartesian.h>
#include <CGAL/Polyhedron_3.h>
#include <CGAL/IO/Polyhedron_iostream.h>
#include <iostream>
#include <algorithm>
#include <vector>

typedef CGAL::Cartesian<double>                              Kernel;
typedef Kernel::Vector_3                                     Vector;
typedef Kernel::Point_3                                      Point;
typedef CGAL::Polyhedron_3<Kernel>                           Polyhedron;

typedef Polyhedron::Vertex                                   Vertex;
typedef Polyhedron::Vertex_iterator                          Vertex_iterator;
typedef Polyhedron::Halfedge_handle                          Halfedge_handle;
typedef Polyhedron::Edge_iterator                            Edge_iterator;
typedef Polyhedron::Facet_iterator                           Facet_iterator;
typedef Polyhedron::Halfedge_around_vertex_const_circulator  HV_circulator;
typedef Polyhedron::Halfedge_around_facet_circulator         HF_circulator;

void create_center_vertex( Polyhedron& P, Facet_iterator f) {
    Vector vec( 0.0, 0.0, 0.0);
    std::size_t order = 0;
    HF_circulator h = f->facet_begin();
    do {
        vec = vec + ( h->vertex()->point() - CGAL::ORIGIN);
        ++ order;
    } while ( ++h != f->facet_begin());
    CGAL_assertion( order >= 3); // guaranteed by definition of polyhedron
    Point center =  CGAL::ORIGIN + (vec / order);
    Halfedge_handle new_center = P.create_center_vertex( f->halfedge());
    new_center->vertex()->point() = center;
}

struct Smooth_old_vertex {
    Point operator()( const Vertex& v) const {
        CGAL_precondition((CGAL::circulator_size( v.vertex_begin()) & 1) == 0);
        std::size_t degree = CGAL::circulator_size( v.vertex_begin()) / 2;
        double alpha = ( 4.0 - 2.0 * cos( 2.0 * CGAL_PI / degree)) / 9.0;
        Vector vec = (v.point() - CGAL::ORIGIN) * ( 1.0 - alpha);
        HV_circulator h = v.vertex_begin();
        do {
            vec = vec + ( h->opposite()->vertex()->point() - CGAL::ORIGIN) 
                       * alpha / degree;
            ++ h;
            CGAL_assertion( h != v.vertex_begin()); // even degree guaranteed
            ++ h;
        } while ( h != v.vertex_begin());
        return (CGAL::ORIGIN + vec);
    }
};

void flip_edge( Polyhedron& P, Halfedge_handle e) {
    Halfedge_handle h = e->next();
    P.join_facet( e);
    P.split_facet( h, h->next()->next());
}

void subdiv( Polyhedron& P) {
    if ( P.size_of_facets() == 0)
        return;
    // We use that new vertices/halfedges/facets are appended at the end.
    std::size_t nv = P.size_of_vertices();
    Vertex_iterator last_v = P.vertices_end();
    -- last_v;  // the last of the old vertices
    Edge_iterator last_e = P.edges_end();
    -- last_e;  // the last of the old edges
    Facet_iterator last_f = P.facets_end();
    -- last_f;  // the last of the old facets

    Facet_iterator f = P.facets_begin();    // create new center vertices
    do {
        create_center_vertex( P, f);
    } while ( f++ != last_f);

    std::vector<Point> pts;                    // smooth the old vertices
    pts.reserve( nv);  // get intermediate space for the new points
    ++ last_v; // make it the past-the-end position again
    std::transform( P.vertices_begin(), last_v, std::back_inserter( pts), 
                    Smooth_old_vertex());
    std::copy( pts.begin(), pts.end(), P.points_begin());

    Edge_iterator e = P.edges_begin();              // flip the old edges
    ++ last_e; // make it the past-the-end position again
    while ( e != last_e) {
        Halfedge_handle h = e;
        ++e; // careful, incr. before flip since flip destroys current edge
        flip_edge( P, h);
    };
    CGAL_postcondition( P.is_valid());
}

int main() {
    Polyhedron P;
    std::cin >> P;
    P.normalize_border();
    if ( P.size_of_border_edges() != 0) {
        std::cerr << "The input object has border edges. Cannot subdivide." 
                  << std::endl;
        std::exit(1);
    }
    subdiv( P);
    std::cout << P;
    return 0;
}