CGAL 2D APOLLONIUS diagram for Weighted Voronoi - How to generate and get the faces and vertices?

Question

I'm trying to generate weighted voronoi based on apollonius diagram. I'm using CGAL library. I couldn't find good example of how to get faces and vertices from apollonius. I have following typedefs:

typedef double                                                                  NT;
typedef CGAL::Cartesian< NT>                                                    KernelCartes;
typedef CGAL::Ray_2<KernelCartes>                                               Cartes_Ray;
typedef CGAL::Line_2<KernelCartes>                                              Cartes_Line;
typedef CGAL::Segment_2<KernelCartes>                                           Cartes_Segment;
typedef std::list<Cartes_Ray>                                                   Cartes_RayList;
typedef std::list<Cartes_Line>                                                  Cartes_LineList;
typedef std::list<Cartes_Segment>                                               Cartes_SegmentList;
typedef CGAL::Point_2<KernelCartes>                                             Cartes_Point;
typedef CGAL::Apollonius_graph_traits_2<KernelCartes>                           ApoTraits;
typedef CGAL::Apollonius_graph_2<ApoTraits>                                     Apo_Graph;
typedef Apo_Graph::Site_2                                                       Apo_Site;

In the following, I'm trying to create Apollonius diagram. WVD is weighted voronoi diagram (Apo_Graph).

    WVD.clear();
    double Weight;
    foreach(QPointF point,List_Nodes)
    {
        Weight = NewRandomNumber(1,10);
        Apo_Site k(Cartes_Point(point.x(),point.y()),Weight);
        WVD.insert(k);
    }

Now, I need to know how can I get access to weighted voronoi and generated faces (and vertices afterwards for each face).

Answer 1

Finally I did it like this:

typedef CGAL::Apollonius_graph_traits_2<Kernel_Exact>             APT;
typedef CGAL::Apollonius_site_2<Kernel_Exact>                   Site_2_Apo;
typedef Site_2_Apo::Point_2                                     Site_2_Point_2;
typedef Site_2_Apo::Weight                                      Site_2_Weight;

typedef CGAL::Apollonius_graph_traits_2<Kernel_Exact>                              AGT2_K;
typedef CGAL::Apollonius_graph_2<AGT2_K>                                            AG2;
typedef CGAL::Apollonius_graph_adaptation_traits_2<AG2>                            AG2_Trait;
typedef CGAL::Apollonius_graph_caching_degeneracy_removal_policy_2<AG2>            AG2_Policy;
typedef CGAL::Voronoi_diagram_2<AG2,AG2_Trait,AG2_Policy>                          VD_AG2;

loading some points:

std::vector<Site_2_Apo> List_Nodes;
    for (int i = 0; i<= 100; i = i++)
    {
        for(int j = 0; j <= 100; j = j++)
        {
            List_Nodes.push_back(Site_2_Apo(Site_2_Point_2(i+NewRandomNumber(0,30),j+NewRandomNumber(0,30)),Site_2_Weight(NewRandomNumber(1,50))));
        }
    }

and the rest:

VD_AG2 VDA;      //Voronoi Apol 

    ///Voronoi Generation
    VDA.clear();
    VDA.insert(List_Nodes.begin(),List_Nodes.end());

and access to the faces and vertices:

  for(A_Bounded_faces_iterator f = VDA.bounded_faces_begin(); f != VDA.bounded_faces_end(); f++)
    {

        A_Ccb_halfedge_circulator ec_start = (f)->ccb();
        A_Ccb_halfedge_circulator ec = ec_start;
        poly.clear();
        do {
            x = ((A_Halfedge_handle)ec)->source()->point().x();
            y = ((A_Halfedge_handle)ec)->source()->point().y();
            poly.push_back(QPointF(x,y));
        } while ( ++ec != ec_start );        
        List_Poly.push_back(poly);
    }

and this is the result:

http://i.stack.imgur.com/Esv8c.png

Answer 2

The template class CGAL::Apollonius_graph_2 shares most of its API with CGAL 2D Delaunay triangulations. That API is sum up in the concept DelaunayGraph_2. CGAL::Apollonius_graph_2<ApoTraits> is a model of that concept.