// Copyright (c) 2017  GeometryFactory (France).  All rights reserved.
//
// This file is part of CGAL (www.cgal.org)
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/BGL/include/CGAL/boost/graph/Face_filtered_graph.h $
// $Id: include/CGAL/boost/graph/Face_filtered_graph.h b26b07a1242 $
// SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Maxime Gimeno

#ifndef CGAL_BOOST_GRAPH_FACE_FILTERED_GRAPH_H
#define CGAL_BOOST_GRAPH_FACE_FILTERED_GRAPH_H

#include <CGAL/assertions.h>
#include <CGAL/boost/graph/properties.h>
#include <CGAL/boost/graph/iterator.h>
#include <CGAL/Named_function_parameters.h>
#include <CGAL/boost/graph/named_params_helper.h>
#include <CGAL/boost/graph/helpers.h>
#include <CGAL/boost/iterator/transform_iterator.hpp>
#include <CGAL/Default.h>
#include <CGAL/Dynamic_property_map.h>

#include <boost/dynamic_bitset.hpp>
#include <boost/graph/graph_traits.hpp>
#include <boost/iterator/filter_iterator.hpp>
#include <boost/range/has_range_iterator.hpp>

#include <unordered_set>
#include <bitset>
#include <utility>
#include <vector>

namespace CGAL {

  /*!
   * \ingroup PkgBGLAdaptors
   *
   * The class `Face_filtered_graph` is an adaptor that creates a filtered view of a graph
   * by restricting it to a subset of faces. Contrary to
   * <a href="https://www.boost.org/doc/libs/release/libs/graph/doc/filtered_graph.html"><code>boost::filtered_graph</code></a>,
   * this class only requires a way to access the selected faces and will automatically select the
   * edges/halfedges and vertices present in the adapted graph. A vertex is selected if it is incident to at least one
   * selected face. An edge is selected if it is incident to at least a selected face. A halfedge is selected if its edge
   * is selected.
   *
   * Since this class is a model of the `FaceGraph` concept, there is a restriction on the set of selected faces:
   * the adapted graph must define a manifold mesh. In order to check that this condition is verified, you can
   * use the function `is_selection_valid()`.
   *
   * There are two different ways to initialize this class: you can directly provide a set of selected faces,
   * or provide a set of patch identifiers as well as a map between faces and patch identifiers.
   * The latter option is convenient if you want to access some connected components of a graph
   * after having called `CGAL::Polygon_mesh_processing::connected_components()`, or if you want
   * to select only faces of a given color, for example.
   *
   * The documented interface of this class is limited on purpose and free functions of the concept
   * this class is a model of must be used to manipulate it.
   *
   * A BGL-like named parameter mechanism is used in the constructors of this class. %Default values are available but if you need
   * to set them, you can pass for `np` `CGAL::parameters::face_index_map(fim).halfedge_index_map(him).vertex_index_map(vim)`
   * where `fim`, `him`, and `vim` are the respective index maps. The order of the arguments is not important and any of them can be
   * missing if the default is fine.
   *
   * \tparam Graph must be a model of a `FaceListGraph`, `HalfedgeListGraph`, and \bgllink{VertexListGraph}.
   * \tparam FIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%face_descriptor` as key and `graph_traits<Graph>::%faces_size_type` as value
   * \tparam VIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%vertex_descriptor` as key and `graph_traits<Graph>::%vertices_size_type` as value
   * \tparam HIMap a model of `ReadablePropertyMap` with `graph_traits<Graph>::%halfedge_descriptor` as key and `graph_traits<Graph>::%halfedges_size_type` as value
   *
   * \cgalModels{FaceListGraph,HalfedgeListGraph,\bgllink{VertexListGraph}}
   */
template<typename Graph,
         typename FIMap = Default,
         typename VIMap = Default,
         typename HIMap = Default>
struct Face_filtered_graph
{
  typedef boost::graph_traits<Graph>                  gt;
  /// Vertex descriptor type
  typedef typename boost::graph_traits<Graph>::vertex_descriptor              vertex_descriptor;
  /// Halfedge descriptor type
  typedef typename boost::graph_traits<Graph>::halfedge_descriptor            halfedge_descriptor;
  /// Edge descriptor type
  typedef typename boost::graph_traits<Graph>::edge_descriptor                edge_descriptor;
  /// Face descriptor type
  typedef typename boost::graph_traits<Graph>::face_descriptor                face_descriptor;
  /// Size type
  #ifndef DOXYGEN_RUNNING
  typedef boost::dynamic_bitset<>::size_type size_type;
  #else
  typedef unspecified_type size_type;
  #endif

  // non documented types
  typedef typename Default::Get<FIMap, typename CGAL::GetInitializedFaceIndexMap<Graph>::const_type>::type FIM;
  typedef typename Default::Get<VIMap, typename CGAL::GetInitializedVertexIndexMap<Graph>::const_type>::type VIM;
  typedef typename Default::Get<HIMap, typename CGAL::GetInitializedHalfedgeIndexMap<Graph>::const_type>::type HIM;

  typedef typename boost::property_traits<FIM>::value_type face_index_type;
  typedef typename boost::property_traits<VIM>::value_type vertex_index_type;
  typedef typename boost::property_traits<HIM>::value_type halfedge_index_type;

  typedef Face_filtered_graph<Graph, FIMap, VIMap, HIMap> Self;

  /*!
   * \brief constructs an empty face filtered graph (no face is selected)
   *
   * \tparam NamedParameters a sequence of named parameters
   *
   * \param graph the underlying graph.
   *
   * \param np optional sequence of named parameters among the ones listed below
   *
   * \cgalNamedParamsBegin
   *   \cgalParamNBegin{vertex_index_map}
   *     \cgalParamDescription{a property map associating to each vertex of `graph` a unique index between `0` and `num_vertices(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%vertex_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{halfedge_index_map}
   *     \cgalParamDescription{a property map associating to each halfedge of `graph` a unique index between `0` and `num_halfedges(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%halfedge_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{face_index_map}
   *     \cgalParamDescription{a property map associating to each face of `graph` a unique index between `0` and `num_faces(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%face_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   * \cgalNamedParamsEnd
   */
  template <class CGAL_NP_TEMPLATE_PARAMETERS>
  Face_filtered_graph(const Graph& graph,
                      const CGAL_NP_CLASS& np = parameters::default_values())
    : _graph(const_cast<Graph&>(graph))
    , fimap(CGAL::get_initialized_face_index_map(graph, np))
    , vimap(CGAL::get_initialized_vertex_index_map(graph, np))
    , himap(CGAL::get_initialized_halfedge_index_map(graph, np))
    , selected_faces(num_faces(graph), 0)
    , selected_vertices(num_vertices(graph), 0)
    , selected_halfedges(num_halfedges(graph), 0)
  {}

  /*!
   * \brief Constructor where the set of selected faces is specified as a range of patch ids.
   *
   * \tparam FacePatchIDMap a model of `ReadablePropertyMap` with `face_descriptor` as key type
   *                        and whose value type is a model of `Hashable`.
   * \tparam FacePatchIDRange a model of `ConstRange` with `boost::property_traits<FacePatchIDMap>::%value_type` as value type.
   * \tparam NamedParameters a sequence of named parameters
   *
   * \param graph the underlying graph
   * \param face_patch_id_map the property map that assigns a patch ID to each face
   * \param selected_face_patch_ids a range of the face patch identifiers to select
   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
   *
   * \cgalNamedParamsBegin
   *   \cgalParamNBegin{vertex_index_map}
   *     \cgalParamDescription{a property map associating to each vertex of `graph` a unique index between `0` and `num_vertices(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%vertex_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{halfedge_index_map}
   *     \cgalParamDescription{a property map associating to each halfedge of `graph` a unique index between `0` and `num_halfedges(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%halfedge_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{face_index_map}
   *     \cgalParamDescription{a property map associating to each face of `graph` a unique index between `0` and `num_faces(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%face_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   * \cgalNamedParamsEnd
   */
  template <typename FacePatchIDMap, class FacePatchIDRange, class CGAL_NP_TEMPLATE_PARAMETERS>
  Face_filtered_graph(const Graph& graph,
                      const FacePatchIDRange& selected_face_patch_ids,
                      FacePatchIDMap face_patch_id_map,
                      const CGAL_NP_CLASS& np
#ifndef DOXYGEN_RUNNING
                    , std::enable_if_t<
                        boost::has_range_const_iterator<FacePatchIDRange>::value
                      >* = 0
#endif
                      )
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph, np)),
      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
  {
    set_selected_faces(selected_face_patch_ids, face_patch_id_map);
  }

  template <typename FacePatchIDMap, class FacePatchIDRange>
  Face_filtered_graph(const Graph& graph,
                      const FacePatchIDRange& selected_face_patch_ids,
                      FacePatchIDMap face_patch_id_map
                      , std::enable_if_t<
                          boost::has_range_const_iterator<FacePatchIDRange>::value
                      >* = 0
                      )
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph)),
      vimap(CGAL::get_initialized_vertex_index_map(graph)),
      himap(CGAL::get_initialized_halfedge_index_map(graph))
  {
    set_selected_faces(selected_face_patch_ids, face_patch_id_map);
  }
  /*!
   * \brief Constructor where the set of selected faces is specified as a patch id.
   *
   * \tparam FacePatchIDMap a model of `ReadablePropertyMap` with `face_descriptor` as key type
   *                        and whose value type is a model of `Hashable`.
   * \tparam NamedParameters a sequence of named parameters
   *
   * \param graph the underlying graph.
   * \param face_patch_id_map the property map that assigns a patch ID to each face
   * \param selected_face_patch_id the identifier of the face patch selected
   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
   *
   * \cgalNamedParamsBegin
   *   \cgalParamNBegin{vertex_index_map}
   *     \cgalParamDescription{a property map associating to each vertex of `graph` a unique index between `0` and `num_vertices(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%vertex_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{halfedge_index_map}
   *     \cgalParamDescription{a property map associating to each halfedge of `graph` a unique index between `0` and `num_halfedges(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%halfedge_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{face_index_map}
   *     \cgalParamDescription{a property map associating to each face of `graph` a unique index between `0` and `num_faces(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%face_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   * \cgalNamedParamsEnd
   */
  template <typename FacePatchIDMap, class CGAL_NP_TEMPLATE_PARAMETERS>
  Face_filtered_graph(const Graph& graph,
                      typename boost::property_traits<FacePatchIDMap>::value_type selected_face_patch_id,
                      FacePatchIDMap face_patch_id_map,
                      const CGAL_NP_CLASS& np)
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph, np)),
      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
  {
    set_selected_faces(selected_face_patch_id, face_patch_id_map);
  }

  template <typename FacePatchIDMap>
  Face_filtered_graph(const Graph& graph,
                      typename boost::property_traits<FacePatchIDMap>::value_type pid,
                      FacePatchIDMap face_patch_id_map)
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph)),
      vimap(CGAL::get_initialized_vertex_index_map(graph)),
      himap(CGAL::get_initialized_halfedge_index_map(graph))
  {
    set_selected_faces(pid, face_patch_id_map);
  }

  /*!
   * \brief Constructor where the set of selected faces is specified as a range of face descriptors.
   *
   * \tparam FaceRange a model of `ConstRange` with `face_descriptor` as value type.
   * \tparam NamedParameters a sequence of named parameters
   *
   * \param graph the graph containing the wanted patch
   * \param selected_faces the set of selected faces
   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
   *
   * \cgalNamedParamsBegin
   *   \cgalParamNBegin{vertex_index_map}
   *     \cgalParamDescription{a property map associating to each vertex of `graph` a unique index between `0` and `num_vertices(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%vertex_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{halfedge_index_map}
   *     \cgalParamDescription{a property map associating to each halfedge of `graph` a unique index between `0` and `num_halfedges(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%halfedge_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   *
   *   \cgalParamNBegin{face_index_map}
   *     \cgalParamDescription{a property map associating to each face of `graph` a unique index between `0` and `num_faces(graph) - 1`}
   *     \cgalParamType{a class model of `ReadablePropertyMap` with `boost::graph_traits<Graph>::%face_descriptor`
   *                    as key type and `std::size_t` as value type}
   *     \cgalParamDefault{an automatically indexed internal map}
   *     \cgalParamExtra{If this parameter is not passed, internal machinery will create and initialize
   *                     a face index property map, either using the internal property map if it exists
   *                     or using an external map. The latter might result in  - slightly - worsened performance
   *                     in case of non-constant complexity for index access.}
   *   \cgalParamNEnd
   * \cgalNamedParamsEnd
   */
  template <typename FaceRange, class CGAL_NP_TEMPLATE_PARAMETERS>
  Face_filtered_graph(const Graph& graph,
                      const FaceRange& selected_faces,
                      const CGAL_NP_CLASS& np)
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph, np)),
      vimap(CGAL::get_initialized_vertex_index_map(graph, np)),
      himap(CGAL::get_initialized_halfedge_index_map(graph, np))
  {
    set_selected_faces(selected_faces);
  }

  template <typename FaceRange>
  Face_filtered_graph(const Graph& graph,
                      const FaceRange& selected_faces)
    : _graph(const_cast<Graph&>(graph)),
      fimap(CGAL::get_initialized_face_index_map(graph)),
      vimap(CGAL::get_initialized_vertex_index_map(graph)),
      himap(CGAL::get_initialized_halfedge_index_map(graph))
  {
    set_selected_faces(selected_faces);
  }

  ///returns a const reference to the underlying graph.
  const Graph& graph()const{ return _graph; }
  ///returns a reference to the underlying graph.
  Graph& graph(){ return _graph; }

  // Handling of internal correspondency for index maps.
  // The indices must be kept valid when the selection changes.
  void initialize_face_indices() const
  {
    if(face_indices.empty())
    {
      face_index_type index = 0;
      face_indices.resize(num_faces(_graph));
      for(std::size_t i=selected_faces.find_first(); i<selected_faces.npos; i=selected_faces.find_next(i))
        face_indices[i] = index++;
    }
  }

  void initialize_vertex_indices() const
  {
    if(vertex_indices.empty())
    {
      vertex_index_type index = 0;
      vertex_indices.resize(num_vertices(_graph));
      for(std::size_t i=selected_vertices.find_first(); i<selected_vertices.npos; i=selected_vertices.find_next(i))
        vertex_indices[i] = index++;
    }
  }

  void initialize_halfedge_indices() const
  {
    if(halfedge_indices.empty())
    {
      halfedge_index_type index = 0;
      halfedge_indices.resize(num_halfedges(_graph));
      for(std::size_t i=selected_halfedges.find_first(); i<selected_halfedges.npos; i=selected_halfedges.find_next(i))
        halfedge_indices[i] = index++;
    }
  }

  void reset_indices()
  {
    face_indices.clear();
    vertex_indices.clear();
    halfedge_indices.clear();

    if(is_imap_in_use.test(0))
      initialize_face_indices();
    if(is_imap_in_use.test(1))
      initialize_vertex_indices();
    if(is_imap_in_use.test(2))
      initialize_halfedge_indices();
  }

  /// changes the set of selected faces using a patch id.
  template<class FacePatchIDMap>
  void set_selected_faces(typename boost::property_traits<FacePatchIDMap>::value_type face_patch_id,
                          FacePatchIDMap face_patch_id_map)
  {
    selected_faces.resize(num_faces(_graph));
    selected_vertices.resize(num_vertices(_graph));
    selected_halfedges.resize(num_halfedges(_graph));

    selected_faces.reset();
    selected_vertices.reset();
    selected_halfedges.reset();

    for(face_descriptor fd : faces(_graph) )
    {
      if(get(face_patch_id_map, fd) == face_patch_id)
      {
        selected_faces.set(get(fimap, fd));
        for(halfedge_descriptor hd : halfedges_around_face(halfedge(fd, _graph), _graph))
        {
          selected_halfedges.set(get(himap, hd));
          selected_halfedges.set(get(himap, opposite(hd, _graph)));
          selected_vertices.set(get(vimap, target(hd, _graph)));
        }
      }
    }

    reset_indices();
  }
  /// changes the set of selected faces using a range of patch ids
  template<class FacePatchIDRange, class FacePatchIDMap>
  void set_selected_faces(const FacePatchIDRange& selected_face_patch_ids,
                          FacePatchIDMap face_patch_id_map
#ifndef DOXYGEN_RUNNING
                          , std::enable_if_t<
                              boost::has_range_const_iterator<FacePatchIDRange>::value
                            >* = 0
#endif
                          )
  {
    selected_faces.resize(num_faces(_graph));
    selected_vertices.resize(num_vertices(_graph));
    selected_halfedges.resize(num_halfedges(_graph));

    selected_faces.reset();
    selected_vertices.reset();
    selected_halfedges.reset();

    typedef typename boost::property_traits<FacePatchIDMap>::value_type Patch_ID;
    std::unordered_set<Patch_ID> pids(std::begin(selected_face_patch_ids),
                                      std::end(selected_face_patch_ids));

    for(face_descriptor fd : faces(_graph))
    {
      if(pids.count(get(face_patch_id_map, fd)) != 0)
      {
        selected_faces.set(get(fimap, fd));
        for(halfedge_descriptor hd : halfedges_around_face(halfedge(fd, _graph), _graph))
        {
          selected_halfedges.set(get(himap, hd));
          selected_halfedges.set(get(himap, opposite(hd, _graph)));
          selected_vertices.set(get(vimap, target(hd, _graph)));
        }
      }
    }

    reset_indices();
  }

  /// changes the set of selected faces using a range of face descriptors.
  template<class FaceRange>
  void set_selected_faces(const FaceRange& selection)
  {
    selected_faces.resize(num_faces(_graph));
    selected_vertices.resize(num_vertices(_graph));
    selected_halfedges.resize(num_halfedges(_graph));

    selected_faces.reset();
    selected_vertices.reset();
    selected_halfedges.reset();

    for(face_descriptor fd : selection)
    {
      selected_faces.set(get(fimap, fd));
      for(halfedge_descriptor hd : halfedges_around_face(halfedge(fd, _graph), _graph))
      {
        selected_halfedges.set(get(himap, hd));
        selected_halfedges.set(get(himap, opposite(hd, _graph)));
        selected_vertices.set(get(vimap, target(hd, _graph)));
      }
    }

    reset_indices();
  }

  struct Is_simplex_valid
  {
    Is_simplex_valid(const Self* graph)
      :adapter(graph)
    {}

    Is_simplex_valid()
      :adapter(nullptr)
    {}
    template<typename Simplex>
    bool operator()(Simplex s)
    {
      CGAL_assertion(adapter!=nullptr);
      return (adapter->is_in_cc(s));
    }
    const Self* adapter;
  };

  bool is_in_cc(face_descriptor f) const
  {
    return selected_faces[get(fimap, f)];
  }

  bool is_in_cc(vertex_descriptor v) const
  {
    return selected_vertices[get(vimap, v)];
  }

  bool is_in_cc(halfedge_descriptor h) const
  {
    return selected_halfedges[get(himap, h)];
  }

  bool is_in_cc(edge_descriptor e) const
  {
    return selected_halfedges[get(himap, halfedge(e,_graph))];
  }

  /// returns the number of selected faces.
  size_type number_of_faces() const
  {
    return selected_faces.count();
  }

  /// returns the number of selected vertices.
  size_type number_of_vertices() const
  {
    return selected_vertices.count();
  }

  /// returns the number of selected halfedges.
  size_type number_of_halfedges() const
  {
    return selected_halfedges.count();
  }

  Compose_property_map<FIM, typename Pointer_property_map<typename boost::property_traits<FIM>::value_type>::type>
  get_face_index_map() const
  {
    is_imap_in_use.set(0);
    initialize_face_indices();

    return make_compose_property_map(fimap, make_property_map(face_indices));
  }

  Compose_property_map<VIM, typename Pointer_property_map<typename boost::property_traits<VIM>::value_type>::type>
  get_vertex_index_map() const
  {
    is_imap_in_use.set(1);
    initialize_vertex_indices();

    return make_compose_property_map(vimap, make_property_map(vertex_indices) );
  }

  Compose_property_map<HIM, typename Pointer_property_map<typename boost::property_traits<HIM>::value_type >::type>
  get_halfedge_index_map() const
  {
    is_imap_in_use.set(2);
    initialize_halfedge_indices();

    return make_compose_property_map(himap, make_property_map(halfedge_indices) );
  }

  /// returns `true` if around any vertex of a selected face there is at most a single umbrella
  bool is_selection_valid() const
  {
    typedef typename boost::graph_traits<Graph>::vertex_descriptor      vertex_descriptor;
    typedef typename boost::graph_traits<Graph>::halfedge_descriptor    halfedge_descriptor;

    // Non-manifoldness can appear if there are multiple umbrellas around a vertex.
    // In that case, we will find a non-visited halfedge that has for target a vertex
    // that is already visited.

    std::unordered_set<vertex_descriptor> vertices_visited;
    std::unordered_set<halfedge_descriptor> halfedges_handled;

    for(halfedge_descriptor hd : halfedges(*this))
    {
      CGAL_assertion(is_in_cc(hd));

      if(!halfedges_handled.insert(hd).second) // already treated this halfedge
        continue;

      vertex_descriptor vd = target(hd, *this);
      CGAL_assertion(is_in_cc(vd));

      // Check if we have already met this vertex before (necessarily in a different umbrella
      // since we have never treated the halfedge 'hd')
      if(!vertices_visited.insert(vd).second)
        return false;

      // Can't call halfedges_around_target(vd, *this) because 'halfedge(vd)' is not necessarily 'hd'
      halfedge_descriptor ihd = hd;
      do
      {
        halfedges_handled.insert(ihd);

        do
        {
          ihd = prev(opposite(ihd, _graph), _graph);
        }
        while(!is_in_cc(ihd) && ihd != hd);
      }
      while(ihd != hd);
    }

    return true;
  }

  /// inverts the selected status of faces.
  void invert_selection()
  {
    selected_faces=~selected_faces;
    selected_halfedges.reset();
    selected_vertices.reset();

    for(face_descriptor fd : faces(_graph))
    {
      if (!selected_faces.test(get(fimap, fd))) continue;
      for(halfedge_descriptor hd : halfedges_around_face(halfedge(fd, _graph), _graph))
      {
        selected_halfedges.set(get(himap, hd));
        selected_halfedges.set(get(himap, opposite(hd, _graph)));
        selected_vertices.set(get(vimap, target(hd, _graph)));
      }
    }

    reset_indices();
  }

private:
  Graph& _graph;
  FIM fimap;
  VIM vimap;
  HIM himap;
  boost::dynamic_bitset<> selected_faces;
  boost::dynamic_bitset<> selected_vertices;
  boost::dynamic_bitset<> selected_halfedges;

  mutable std::vector<face_index_type> face_indices;
  mutable std::vector<vertex_index_type> vertex_indices;
  mutable std::vector<halfedge_index_type> halfedge_indices;
  mutable std::bitset<3> is_imap_in_use; // one per descriptor type (face, vertex, halfedge)
};

} // namespace CGAL

namespace boost
{

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
struct graph_traits< CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >
{
  typedef CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> G;
  typedef boost::graph_traits<Graph> BGTG;
  typedef typename BGTG::vertex_descriptor vertex_descriptor;
  typedef typename BGTG::halfedge_descriptor halfedge_descriptor;
  typedef typename BGTG::edge_descriptor edge_descriptor;
  typedef typename BGTG::face_descriptor face_descriptor;

  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::vertex_iterator>    vertex_iterator;
  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::halfedge_iterator>  halfedge_iterator;
  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::edge_iterator>      edge_iterator;
  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::face_iterator>      face_iterator;

  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::out_edge_iterator>  out_edge_iterator;
  typedef boost::filter_iterator<typename G::Is_simplex_valid, typename BGTG::in_edge_iterator>   in_edge_iterator;

  typedef typename BGTG::directed_category directed_category;
  typedef typename BGTG::edge_parallel_category edge_parallel_category;
  typedef typename BGTG::traversal_category traversal_category;
  typedef typename boost::dynamic_bitset<>::size_type vertices_size_type;
  typedef typename boost::dynamic_bitset<>::size_type edges_size_type;
  typedef typename boost::dynamic_bitset<>::size_type halfedges_size_type;
  typedef typename boost::dynamic_bitset<>::size_type faces_size_type;
  typedef typename BGTG::degree_size_type degree_size_type;

  static vertex_descriptor null_vertex()
  {
    return BGTG::null_vertex();
  }

  static halfedge_descriptor null_halfedge()
  {
    return BGTG::null_halfedge();
  }

  static edge_descriptor null_edge()
  {
    return edge_descriptor(BGTG::null_halfedge());
  }

  static face_descriptor null_face()
  {
    return BGTG::null_face();
  }
};

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
struct graph_traits< const CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >
    : public graph_traits< CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >
{};


} // namespace boost


namespace CGAL {

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::size_type
num_vertices(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.number_of_vertices();
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::size_type
num_edges(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.number_of_halfedges()/2;
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Graph>::degree_size_type
degree(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  CGAL_assertion(w.is_in_cc(v));
  typename boost::graph_traits<Graph>::degree_size_type v_deg = 0;
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h = halfedge(v, w);
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor hcirc = h;
  do
  {
    if(w.is_in_cc(hcirc))
      ++v_deg;
    hcirc = opposite(next(hcirc, w.graph()), w.graph());
  }while(hcirc != h);
  return v_deg;
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Graph>::degree_size_type
degree(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::face_descriptor f,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return degree(f, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Graph>::degree_size_type
out_degree(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
           const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  CGAL_assertion(w.is_in_cc(v));
  return static_cast<typename boost::graph_traits<Graph>::degree_size_type>(
    std::distance(out_edges(v, w).first ,out_edges(v, w).second) );
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Graph>::degree_size_type
in_degree(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
          const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  CGAL_assertion(w.is_in_cc(v));
  return static_cast<typename boost::graph_traits<Graph>::degree_size_type>(
    std::distance(in_edges(v, w).first ,in_edges(v, w).second) );
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor
source(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor e,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(e));
  return source(e, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor
target(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor e,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(e));
  return target(e, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
std::pair<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor, bool>
edge(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor u,
     typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
     const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(u) && w.is_in_cc(v));
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor e = edge(u, v, w.graph()).first;
  bool res = w.is_in_cc(e);
  return std::make_pair(e, res);
}


template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
CGAL::Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_iterator>
vertices(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_iterator vertex_iterator;
  typedef typename boost::graph_traits<Graph >::vertex_iterator g_vertex_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  g_vertex_iterator b,e;
  std::tie(b,e) = vertices(w.graph());
  return make_range(vertex_iterator(predicate, b, e),
                    vertex_iterator(predicate, e, e));
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
CGAL::Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_iterator>
edges(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_iterator edge_iterator;
  typedef typename boost::graph_traits<Graph >::edge_iterator g_edge_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  g_edge_iterator b,e;
  std::tie(b,e) = edges(w.graph());
  return make_range(edge_iterator(predicate, b, e),
                    edge_iterator(predicate, e, e));
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
CGAL::Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::out_edge_iterator>
out_edges(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
          const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{

  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::out_edge_iterator out_edge_iterator;
  typedef typename boost::graph_traits<Graph >::out_edge_iterator g_out_edge_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  g_out_edge_iterator b,e;
  std::tie(b,e) = out_edges(v, w.graph());
  return make_range(out_edge_iterator(predicate, b, e),
                    out_edge_iterator(predicate, e, e));
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
CGAL::Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::in_edge_iterator>
in_edges(typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{

  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::in_edge_iterator in_edge_iterator;
  typedef typename boost::graph_traits<Graph >::in_edge_iterator g_in_edge_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  g_in_edge_iterator b,e;
  std::tie(b,e) = in_edges(v, w.graph());
  return make_range(in_edge_iterator(predicate, b, e),
                    in_edge_iterator(predicate, e, e));
}

//
// HalfedgeGraph
//
template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor
edge(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
     const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(h));
  return edge(h, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
halfedge(typename boost::graph_traits<  Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::edge_descriptor e,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(e));
  return halfedge(e, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
halfedge(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(v));
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h = halfedge(v, w.graph());
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor hcirc = h;
  do
  {
    if(w.is_in_cc(hcirc))
      return hcirc;
    hcirc = opposite(next(hcirc, w.graph()), w.graph());
  }while(hcirc != h);
  return boost::graph_traits< CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::null_halfedge();
}


template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
std::pair<typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor, bool>
halfedge(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor u,
         typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor v,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(u) && w.is_in_cc(v));
  typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h = halfedge(u, v, w.graph()).first;
  return std::make_pair(h, w.is_in_cc(h));
}


template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
opposite(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(h) );
     return opposite(h, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor
source(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(h) );
  return source(h, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::vertex_descriptor
target(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
       const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(h) );
  return target(h, w.graph());
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
next(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
     const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_precondition(w.is_in_cc(h));

  if(w.is_in_cc(next(h, w.graph())))
    return next(h, w.graph());

  //h is on the border of the selection
  CGAL_assertion( is_border(h, w.graph()) || !w.is_in_cc(face(h, w.graph())) );
  typedef typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h_d;
  h_d candidate = next(h, w.graph());
  CGAL_assertion(!w.is_in_cc(candidate));
  do{
    candidate = next(opposite(candidate, w.graph()), w.graph());
    CGAL_assertion(candidate!=opposite(h,w.graph()));
  }while(!w.is_in_cc(candidate));
  return candidate;
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
prev(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
     const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_precondition(w.is_in_cc(h));

  if(w.is_in_cc(prev(h, w.graph())))
    return prev(h, w.graph());

  //h is on the border of the selection
  CGAL_assertion( is_border(h, w.graph()) || !w.is_in_cc(face(h, w.graph())) );
  typedef typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h_d;
  h_d candidate = prev(h, w.graph());
  CGAL_assertion(!w.is_in_cc(candidate));
  do{
    candidate = prev(opposite(candidate, w.graph()), w.graph());
    CGAL_assertion(candidate!=opposite(h,w.graph()));
  }while(!w.is_in_cc(candidate));
  return candidate;
}

//
// HalfedgeListGraph
//

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_iterator>
halfedges(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_iterator halfedge_iterator;
  typedef typename boost::graph_traits<Graph >::halfedge_iterator g_halfedge_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  std::pair<g_halfedge_iterator, g_halfedge_iterator> original_halfedges = halfedges(w.graph());

  return make_range(halfedge_iterator(predicate, original_halfedges.first, original_halfedges.second),
                    halfedge_iterator(predicate, original_halfedges.second, original_halfedges.second));
}


template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::size_type
num_halfedges(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  return w.number_of_halfedges();
}

// FaceGraph
template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::face_descriptor
face(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor h,
     const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(h));
  if(face(h, w.graph()) == boost::graph_traits<Graph>::null_face()) // h is a border hafedge
    return boost::graph_traits< CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::null_face();
  else if(w.is_in_cc(face(h,w.graph())))
    return face(h,w.graph());
  else
    return boost::graph_traits< CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::null_face();
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::halfedge_descriptor
halfedge(typename boost::graph_traits< Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::face_descriptor f,
         const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  CGAL_assertion(w.is_in_cc(f));
  return halfedge(f,w.graph());
}


template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
Iterator_range<typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::face_iterator>
faces(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  typedef typename boost::graph_traits<Face_filtered_graph<Graph, FIMap, VIMap, HIMap> >::face_iterator face_iterator;
  typedef typename boost::graph_traits<Graph >::face_iterator g_face_iterator;

  typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap> ::Is_simplex_valid predicate(&w);
  std::pair<g_face_iterator, g_face_iterator> original_faces = faces(w.graph());

  return make_range(face_iterator(predicate, original_faces.first, original_faces.second),
                    face_iterator(predicate, original_faces.second, original_faces.second));
}



template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap>
typename Face_filtered_graph<Graph, FIMap, VIMap, HIMap>::size_type
num_faces(const Face_filtered_graph<Graph, FIMap, VIMap, HIMap> & w)
{
  return w.number_of_faces();
}

template <class Graph,
          typename FIMap,
          typename VIMap,
          typename HIMap,
          class PropertyTag>
typename boost::property_map<Graph, PropertyTag >::const_type
get(PropertyTag ptag, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return get(ptag, w.graph());
}

template <class Graph,
          typename FIMap,
          typename VIMap,
          typename HIMap,
          class PropertyTag>
typename boost::property_map<Graph, PropertyTag >::type
get(PropertyTag ptag, Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return get(ptag, w.graph());
}

#define CGAL_FFG_DYNAMIC_PMAP_SPEC(TAG) \
template <class Graph, \
          typename FIMap, \
          typename VIMap, \
          typename HIMap, \
          class T> \
typename boost::property_map<Graph, TAG<T> >::const_type \
get(TAG<T> ptag, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w) \
{ \
  return get(ptag, w.graph()); \
} \
\
template <class Graph, \
          typename FIMap, \
          typename VIMap, \
          typename HIMap, \
          class T> \
typename boost::property_map<Graph, TAG<T> >::type \
get(TAG<T> ptag, Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w) \
{ \
  return get(ptag, w.graph()); \
}

CGAL_FFG_DYNAMIC_PMAP_SPEC(dynamic_vertex_property_t)
CGAL_FFG_DYNAMIC_PMAP_SPEC(dynamic_halfedge_property_t)
CGAL_FFG_DYNAMIC_PMAP_SPEC(dynamic_edge_property_t)
CGAL_FFG_DYNAMIC_PMAP_SPEC(dynamic_face_property_t)

#undef CGAL_FFG_DYNAMIC_PMAP_SPEC

template <class Graph,
          typename FIMap,
          typename VIMap,
          typename HIMap,
          class PropertyTag>
typename boost::property_traits<typename boost::property_map<Graph,PropertyTag>::type>::value_type
get(PropertyTag ptag,
    const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w,
    const typename boost::property_traits<typename boost::property_map<Graph,PropertyTag>::type>::key_type& k)
{
  return get(ptag, w.graph(), k);
}


template <class Graph,
          typename FIMap,
          typename VIMap,
          typename HIMap,
          class PropertyTag>
void
put(PropertyTag ptag, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w,
    const typename boost::property_traits<typename boost::property_map<Graph,PropertyTag>::type>::key_type& k,
    typename boost::property_traits<typename boost::property_map<Graph,PropertyTag>::type>::value_type& v)
{
  put(ptag, w.graph(), k, v);
}

template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap,
         typename PropertyTag>
struct graph_has_property<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, PropertyTag>
    : graph_has_property<Graph, PropertyTag> {};
}//end namespace CGAL

namespace boost {
template<typename Graph,
         typename FIMap,
         typename VIMap,
         typename HIMap,
         typename PropertyTag>
struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>,PropertyTag> {
  typedef typename boost::property_map<Graph, PropertyTag >::type type;
  typedef typename boost::property_map<Graph, PropertyTag >::const_type const_type;
};

#define CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(DYNAMIC_TAG) \
template<typename Graph, \
         typename FIMap, \
         typename VIMap, \
         typename HIMap, \
         typename T> \
struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, CGAL::DYNAMIC_TAG<T> > { \
  typedef typename boost::property_map<Graph, CGAL::DYNAMIC_TAG<T> >::type type; \
  typedef typename boost::property_map<Graph, CGAL::DYNAMIC_TAG<T> >::const_type const_type; \
};

CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(dynamic_vertex_property_t)
CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(dynamic_edge_property_t)
CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(dynamic_halfedge_property_t)
CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION(dynamic_face_property_t)

#undef CGAL_FILTERED_FACE_GRAPH_DYNAMIC_PMAP_SPECIALIZATION

//specializations for indices
template<typename Graph, typename FIMap, typename VIMap, typename HIMap>
struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::face_index_t>
{
  typedef CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>                       FFG;
  typedef typename FFG::FIM                                                           FIM;

  typedef typename CGAL::Compose_property_map<FIM,
                     typename CGAL::Pointer_property_map<
                       typename boost::property_traits<FIM>::value_type>::type>       type;
  typedef type                                                                        const_type;
};

template<typename Graph, typename FIMap, typename VIMap, typename HIMap>
struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::vertex_index_t>
{
  typedef CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>                       FFG;
  typedef typename FFG::VIM                                                           VIM;

  typedef typename CGAL::Compose_property_map<VIM,
                     typename CGAL::Pointer_property_map<
                       typename boost::property_traits<VIM>::value_type>::type>       type;
  typedef type                                                                        const_type;
};

template<typename Graph, typename FIMap, typename VIMap, typename HIMap>
struct property_map<CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::halfedge_index_t>
{
  typedef CGAL::Face_filtered_graph<Graph, FIMap, VIMap, HIMap>                       FFG;
  typedef typename FFG::HIM                                                           HIM;

  typedef typename CGAL::Compose_property_map<HIM,
                     typename CGAL::Pointer_property_map<
                       typename boost::property_traits<HIM>::value_type>::type>       type;
  typedef type                                                                        const_type;
};

} // namespace boost

namespace CGAL {

//specializations for indices
template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::face_index_t >::const_type
get(boost::face_index_t, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_face_index_map();
}

template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::vertex_index_t >::const_type
get(boost::vertex_index_t, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_vertex_index_map();
}

template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::halfedge_index_t >::const_type
get(boost::halfedge_index_t, const Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_halfedge_index_map();
}

// non-const
template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::face_index_t >::type
get(boost::face_index_t, Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_face_index_map();
}

template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::vertex_index_t >::type
get(boost::vertex_index_t, Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_vertex_index_map();
}

template <class Graph, typename FIMap, typename VIMap, typename HIMap>
typename boost::property_map<Face_filtered_graph<Graph, FIMap, VIMap, HIMap>, boost::halfedge_index_t >::type
get(boost::halfedge_index_t, Face_filtered_graph<Graph, FIMap, VIMap, HIMap>& w)
{
  return w.get_halfedge_index_map();
}

} // namespace CGAL

#endif // CGAL_BOOST_GRAPH_FACE_FILTERED_GRAPH_H

