cgal/Combinatorial_map/include/CGAL/Combinatorial_map.h

// Copyright (c) 2010-2011 CNRS and LIRIS' Establishments (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; either version 3 of the License,
// or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
// Author(s)     : Guillaume Damiand <guillaume.damiand@liris.cnrs.fr>
//
#ifndef CGAL_COMBINATORIAL_MAP_H
#define CGAL_COMBINATORIAL_MAP_H 1

#include <CGAL/Compact_container.h>
#include <CGAL/internal/Combinatorial_map_utility.h>
#include <CGAL/internal/Combinatorial_map_internal_functors.h>
#include <CGAL/internal/Combinatorial_map_group_functors.h>
#include <CGAL/internal/Combinatorial_map_sewable.h>
#include <CGAL/Combinatorial_map_functors.h>
#include <CGAL/Combinatorial_map_min_items.h>
#include <CGAL/Dart_const_iterators.h>
#include <CGAL/Cell_const_iterators.h>
#include <CGAL/Combinatorial_map_basic_operations.h>
#include <bitset>
#include <vector>
#include <deque>

#include <boost/type_traits/is_same.hpp>

// suppress bogus warning when compiling with gcc 4.3 or 4.4
#if (__GNUC__ == 4 && (__GNUC_MINOR__ == 3 || __GNUC_MINOR__ == 4))
#pragma GCC diagnostic ignored "-Warray-bounds"
#endif

namespace CGAL {

  /** @file Combinatorial_map.h
   * Definition of generic dD Combinatorial map.
   */

  /** Generic definition of combinatorial map in dD.
   * The Combinatorial_map class describes an dD combinatorial map. It allows
   * mainly to create darts, to use marks onto these darts, to get and set
   * the beta links, and to manage enabled attributes.
   */
  template < unsigned int d_, class Refs,
             class Items_=Combinatorial_map_min_items<d_>,
             class Alloc_=CGAL_ALLOCATOR(int) >
  class Combinatorial_map_base
  {
  public:
    /// Types definition
    typedef Combinatorial_map_base<d_, Refs, Items_,Alloc_>  Self;

    typedef Items_ Items;
    typedef Alloc_ Alloc;

    typedef typename Items::template Dart_wrapper<Refs> Dart_wrapper;
    typedef typename Dart_wrapper::Dart                 Dart;

    typedef typename Alloc::template rebind<Dart>::other Dart_allocator;
    typedef Compact_container<Dart,Dart_allocator>       Dart_container;

    typedef typename Dart_container::iterator       Dart_handle;
    typedef typename Dart_container::const_iterator Dart_const_handle;
    typedef typename Dart_container::size_type      size_type;

    /// The dimension of the combinatorial map.
    static const unsigned int dimension = d_;

    /// Number of marks
    static const size_type NB_MARKS = 32;

    typedef internal::Combinatorial_map_helper<Self> Helper;

    /// Typedef for Dart_range, a range through all the darts of the map.
    typedef Dart_container       Dart_range;
    typedef const Dart_container Dart_const_range;

    typedef typename Dart_wrapper::Attributes Attributes;

    /// Typedef for attributes
    template<int i>
    struct Attribute_type: public Helper::template Attribute_type<i>
    {};
    template<int i>
    struct Attribute_handle: public Helper::template Attribute_handle<i>
    {};
    template<int i>
    struct Attribute_const_handle:
      public Helper::template Attribute_const_handle<i>
    {};
    template<int i>
    struct Attribute_range: public Helper::template Attribute_range<i>
    {};
    template<int i>
    struct Attribute_const_range:
      public Helper::template Attribute_const_range<i>
    {};

  public:
    /** Default Combinatorial_map constructor.
     * The map is empty.
     */
    Combinatorial_map_base()
    {
      CGAL_static_assertion_msg(Dart::dimension==dimension,
                  "Dimension of dart different from dimension of map");

      CGAL_static_assertion_msg(Helper::nb_attribs<=dimension+1,
                  "Too many attributes in the tuple Attributes_enabled");

      this->mnb_used_marks = 0;
      this->mmask_marks.reset();

      for ( size_type i = 0; i < NB_MARKS; ++i)
      {
        this->mfree_marks_stack[i]        = (int)i;
        this->mindex_marks[i]             = i;
        this->mnb_marked_darts[i]         = 0;
        this->mnb_times_reserved_marks[i] = 0;
      }

      // We must do this ony once, but problem because null_dart_handle
      // is static !
      if ( mnull_dart_container.empty() )
      {
        null_dart_handle =
          mnull_dart_container.emplace( std::bitset<NB_MARKS>() );

        for ( unsigned int i=0; i<=dimension; ++i)
        {
          null_dart_handle->unlink_beta(i);
        }
      }

      CGAL_assertion(number_of_darts()==0);
    }

    /** Clear the combinatorial map. Remove all darts and all attributes.
     *  Note that reserved marks are not free.
     */
    void clear()
    {
      mdarts.clear();
      for ( unsigned int i = 0; i < NB_MARKS; ++i)
        this->mnb_marked_darts[i]  = 0;

      internal::Clear_all::run(mattribute_containers);
    }

    /** Test if the map is empty.
     *  @return true iff the map is empty.
     */
    bool is_empty() const
    { return mdarts.empty(); }

    /** Create a new dart and add it to the map.
     * The marks of the darts are initialised with mmask_marks, i.e. the dart
     * is unmarked for all the marks.
     * @return a Dart_handle on the new dart.
     */
#ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
    template < typename... Args >
    Dart_handle create_dart(const Args&... args)
    { return mdarts.emplace(mmask_marks, args...); }
#else
    Dart_handle create_dart()
    { return mdarts.emplace(mmask_marks); }
    template < typename T1 >
    Dart_handle create_dart(const T1 &t1)
    { return mdarts.emplace(mmask_marks, t1); }
    template < typename T1, typename T2 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2)
    { return mdarts.emplace(mmask_marks, t1, t2); }
    template < typename T1, typename T2, typename T3 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3)
    { return mdarts.emplace(mmask_marks, t1, t2, t3); }
    template < typename T1, typename T2, typename T3, typename T4 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4); }
    template < typename T1, typename T2, typename T3, typename T4, typename T5 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4, const T5 &t5)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4, t5); }
    template < typename T1, typename T2, typename T3, typename T4, typename T5,
               typename T6 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4, const T5 &t5, const T6 &t6)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4, t5, t6); }
    template < typename T1, typename T2, typename T3, typename T4, typename T5,
               typename T6, typename T7 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4, const T5 &t5, const T6 &t6,
                            const T7 &t7)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4, t5, t6, t7); }
    template < typename T1, typename T2, typename T3, typename T4, typename T5,
               typename T6, typename T7, typename T8 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4, const T5 &t5, const T6 &t6,
                            const T7 &t7, const T8 &t8)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4, t5, t6, t7, t8); }
    template < typename T1, typename T2, typename T3, typename T4, typename T5,
               typename T6, typename T7, typename T8, typename T9 >
    Dart_handle create_dart(const T1 &t1, const T2 &t2, const T3 &t3,
                            const T4 &t4, const T5 &t5, const T6 &t6,
                            const T7 &t7, const T8 &t8, const T9 &t9)
    { return mdarts.emplace(mmask_marks, t1, t2, t3, t4, t5, t6, t7, t8, t9); }
#endif

    /** Erase a dart from the list of darts.
     * @param adart the dart to erase.
     */
    void erase_dart(Dart_handle adart)
    {
      // 1) We update the number of marked darts.
      for ( unsigned int i = 0; i < mnb_used_marks; ++i)
      {
        if (is_marked(adart, mused_marks_stack[i]))
          --mnb_marked_darts[mused_marks_stack[i]];
      }

      // 2) We update the attribute_ref_counting.
      Helper::template Foreach_enabled_attributes
        <internal::Decrease_attribute_functor<Self> >::run(this,adart);

      // 3) We erase the dart.
      mdarts.erase(adart);
    }

    /// @return a Dart_range (range through all the darts of the map).
    Dart_range& darts()             { return mdarts;}
    Dart_const_range& darts() const { return mdarts; }

    /** Get the first dart of this map.
     * @return the first dart.
     */
    Dart_handle first_dart()
    {
      if (darts().begin() == darts().end()) return null_dart_handle;
      return mdarts.begin();
    }
    Dart_const_handle first_dart() const
    {
      if (darts().begin() == darts().end()) return null_dart_handle;
      return mdarts.begin();
    }

    /// @return the Dart_handle corresponding to the given dart.
    Dart_handle dart_handle(Dart& adart)
    { return mdarts.iterator_to(adart); }
    Dart_const_handle dart_handle(const Dart& adart) const
    { return mdarts.iterator_to(adart); }

    /// @return the betas of ADart (beta are used in the same order than
    ///         they are given as parameters)
#ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
    template<typename ...Betas>
    Dart_handle beta(Dart_handle ADart, Betas... betas) const
    { return CGAL::internal::Beta_functor<Dart_handle, Betas...>::
        run(ADart, betas...); }
    template<typename ...Betas>
    Dart_const_handle beta(Dart_const_handle ADart, Betas... betas) const
    { return CGAL::internal::Beta_functor<Dart_const_handle, Betas...>::
        run(ADart, betas...); }
    template<int... Betas>
    Dart_handle beta(Dart_handle ADart) const
    { return CGAL::internal::Beta_functor_static<Dart_handle, Betas...>::
        run(ADart); }
    template<int... Betas>
    Dart_const_handle beta(Dart_const_handle ADart) const
    { return CGAL::internal::Beta_functor_static<Dart_const_handle, Betas...>::
        run(ADart); }
#else
    Dart_handle beta(Dart_handle ADart, int B1)
    { return CGAL::internal::Beta_functor<Dart_handle>::run(ADart, B1); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2)
    { return CGAL::internal::Beta_functor<Dart_handle>::run(ADart, B1, B2); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4, int B5)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4, B5); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4, int B5,
                     int B6)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4, B5, B6); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4, int B5,
                     int B6, int B7)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4, B5, B6, B7); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4, int B5,
                     int B6, int B7, int B8)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4, B5, B6, B7, B8); }
    Dart_handle beta(Dart_handle ADart, int B1, int B2, int B3, int B4, int B5,
                     int B6, int B7, int B8, int B9)
    { return CGAL::internal::Beta_functor<Dart_handle>::
          run(ADart, B1, B2, B3, B4, B5, B6, B7, B8, B9); }
#endif

    /** Count the number of used marks.
     * @return the number of used marks.
     */
    size_type number_of_used_marks() const
    { return mnb_used_marks; }

    /** Test if a given mark is reserved.
     *  @return true iff the mark is reserved (ie in used).
     */
    bool is_reserved(int amark) const
    {
      CGAL_assertion(amark>=0 && (size_type)amark<NB_MARKS);
      return (mnb_times_reserved_marks[(size_type)amark]!=0);
    }

    /**  Count the number of marked darts for a given mark.
     * @param amark the mark index.
     * @return the number of marked darts for amark.
     */
    size_type number_of_marked_darts(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );
      return mnb_marked_darts[(size_type)amark];
    }

    /**  Count the number of unmarked darts for a given mark.
     * @param amark the mark index.
     * @return the number of unmarked darts for amark.
     */
    size_type number_of_unmarked_darts(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );
      return number_of_darts() - number_of_marked_darts(amark);
    }

    /** Test if all the darts are unmarked for a given mark.
     * @param amark the mark index.
     * @return true iff all the darts are unmarked for amark.
     */
    bool is_whole_map_unmarked(int amark) const
    { return number_of_marked_darts(amark) == 0; }

    /** Test if all the darts are marked for a given mark.
     * @param amark the mark index.
     * @return true iff all the darts are marked for amark.
     */
    bool is_whole_map_marked(int amark) const
    {  return number_of_marked_darts(amark) == number_of_darts(); }

    /** Reserve a new mark.
     * Get a new free mark and return its index.
     * All the darts are unmarked for this mark.
     * @return the index of the new mark.
     * @pre mnb_used_marks < NB_MARKS
     */
    int get_new_mark() const
    {
      if (mnb_used_marks == NB_MARKS)
      {
        std::cerr << "Not enough Boolean marks: "
          "increase NB_MARKS in item class." << std::endl;
        return -1;
      }

      int m = mfree_marks_stack[mnb_used_marks];
      mused_marks_stack[mnb_used_marks] = m;

      mindex_marks[m] = mnb_used_marks;
      mnb_times_reserved_marks[m]=1;

      ++mnb_used_marks;
      CGAL_assertion(is_whole_map_unmarked(m));

      return m;
    }

    /** Increase the number of times a mark is reserved.
     *  @param amark the mark to share.
     */
    void share_a_mark(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );
      ++mnb_times_reserved_marks[amark];
    }

    /** @return the number of times a mark is reserved.
     *  @param amark the mark to share.
     */
    size_type get_number_of_times_mark_reserved(int amark) const
    { return mnb_times_reserved_marks[amark]; }

    /** Negate the mark of all the darts for a given mark.
     * After this call, all the marked darts become unmarked and all the
     * unmarked darts become marked (in constant time operation).
     * @param amark the mark index
     */
    void negate_mark(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );

      mnb_marked_darts[amark] =
        number_of_darts() - mnb_marked_darts[amark];

      mmask_marks.flip((size_type)amark);
    }

    /** Test if a given dart is marked for a given mark.
     * @param adart the dart to test.
     * @param amark the given mark.
     * @return true iff adart is marked for the mark amark.
     */
    bool is_marked(Dart_const_handle adart, int amark) const
    {
      // CGAL_assertion( adart != null_dart_handle );
      CGAL_assertion( is_reserved(amark) );

      return adart->get_mark(amark)!=mmask_marks[(size_type)amark];
    }

    /** Set the mark of a given dart to a state (on or off).
     * @param adart the dart.
     * @param amark the given mark.
     * @param astate the state of the mark (on or off).
     */
    void set_mark_to(Dart_const_handle adart, int amark,
                     bool astate) const
    {
      CGAL_assertion( adart != null_dart_handle );
      CGAL_assertion( is_reserved(amark) );

      if (is_marked(adart, amark) != astate)
      {
        if (astate) ++mnb_marked_darts[(size_type)amark];
        else --mnb_marked_darts[(size_type)amark];

        adart->set_mark(amark, astate ^ mmask_marks[(size_type)amark]);
      }
    }

    /** Mark the given dart.
     * @param adart the dart.
     * @param amark the given mark.
     */
    void mark(Dart_const_handle adart, int amark) const
    {
      CGAL_assertion( adart != null_dart_handle );
      CGAL_assertion( is_reserved(amark) );

      if (is_marked(adart, amark)) return;

      ++mnb_marked_darts[(size_type)amark];
      adart->set_mark(amark, !mmask_marks[(size_type)amark]);
    }

    /** Unmark the given dart.
     * @param adart the dart.
     * @param amark the given mark.
     */
    void unmark(Dart_const_handle adart, int amark) const
    {
      CGAL_assertion( adart != null_dart_handle );
      CGAL_assertion( is_reserved(amark) );

      if (!is_marked(adart, amark)) return;

      --mnb_marked_darts[(size_type)amark];
      adart->set_mark(amark, mmask_marks[(size_type)amark]);
    }

    /** Mark null_dart (used as a sentinel in iterators).
     * As null dart does not belong to the set of darts, it is not counted
     * as number of marked darts.
     * @param amark the given mark.
     */
    void mark_null_dart(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );

      null_dart_handle->set_mark(amark, !mmask_marks[(size_type)amark]);
    }

    /** Unmark null_dart.
     * @param amark the given mark.
     */
    void unmark_null_dart(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );

      null_dart_handle->set_mark(amark, mmask_marks[(size_type)amark]);
    }

    /** Unmark all the darts of the map for a given mark.
     * If all the darts are marked or unmarked, this operation takes O(1)
     * operations, otherwise it traverses all the darts of the map.
     * @param amark the given mark.
     */
    void unmark_all(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );

      if ( is_whole_map_marked(amark) )
      {
        negate_mark(amark);
      }
      else if ( !is_whole_map_unmarked(amark) )
      {
        for ( typename Dart_range::const_iterator it(darts().begin()),
               itend(darts().end()); it!=itend; ++it)
          unmark(it, amark);
      }
      CGAL_assertion(is_whole_map_unmarked(amark));
      unmark_null_dart(amark);
    }

    /** Free a given mark, previously calling unmark_all_darts.
     * @param amark the given mark.
     */
    void free_mark(int amark) const
    {
      CGAL_assertion( is_reserved(amark) );

      if ( mnb_times_reserved_marks[amark]>1 )
      {
        --mnb_times_reserved_marks[amark];
        return;
      }

      unmark_all(amark);

      // 1) We remove amark from the array mused_marks_stack by
      //    replacing it with the last mark in this array.
      mused_marks_stack[mindex_marks[(size_type)amark]] =
        mused_marks_stack[--mnb_used_marks];
      mindex_marks[mused_marks_stack[mnb_used_marks]] =
        mindex_marks[(size_type)amark];

      // 2) We add amark in the array mfree_marks_stack and update its index.
      mfree_marks_stack[ mnb_used_marks ] = amark;
      mindex_marks[(size_type)amark] = mnb_used_marks;

      mnb_times_reserved_marks[amark]=0;
    }

    /** Test if this map is without boundary for a given dimension.
     * @param i the dimension.
     * @return true iff all the darts are not i-free.
     * @pre 1<=i<=n
     */
    bool is_without_boundary(unsigned int i) const
    {
      CGAL_assertion(1<=i && i<=dimension);
      for ( typename Dart_const_range::const_iterator it(darts().begin()),
             itend(darts().end()); it!=itend; ++it)
        if (it->is_free(i)) return false;
      return true;
    }

    /** Test if this map is without boundary for all the dimensions.
     * @return true iff all the darts are non free.
     */
    bool is_without_boundary() const
    {
      for ( typename Dart_const_range::const_iterator it(darts().begin()),
             itend(darts().end()); it!=itend; ++it)
        for ( unsigned int i = 1; i<=dimension; ++i)
          if (it->is_free(i)) return false;
      return true;
    }

    /** Close the combinatorial map for a given dimension.
     *  @param i the dimension to close
     *  @return the number of new darts.
     *  @pre 2<=i<=n (TODO case i==1)
     *  @TODO move into Combinatorial_map_operations ?
     */
    unsigned int close(unsigned int i)
    {
      CGAL_assertion( 2<=i && i<=dimension );
      unsigned int res = 0;
      Dart_handle d, d2;

      for ( typename Dart_range::iterator it(darts().begin());
           it!=darts().end(); ++it)
      {
        if ( it->is_free(i) )
        {
          d = create_dart();
          ++res;

          // Here we cannot use link_beta as i is not a constant
          // TODO something to solve this problem ?
          basic_link_beta_for_involution(it, d, i);
          // we copy all the non void attribute
          Helper::template Foreach_enabled_attributes_except
              <CGAL::internal::Group_attribute_functor_of_dart
              <Self, dimension+1>, dimension+1>:: run(this,it,d);
          // we need to remove i-attrib, how to do that ?

          // Special cases for 0 and 1
          if ( !it->template is_free<1>() &&
               !it->template beta<1>()->is_free(i) )
            link_beta<1>(it->beta(1)->beta(i),d);
          if ( !it->template is_free<0>() &&
               !it->template beta<0>()->is_free(i) )
            link_beta<0>(it->template beta<0>()->beta(i),d);
          // General case for 2...dimension
          for ( unsigned int j=2; j<=dimension; ++j)
          {
            if ( j+1!=i && j!=i && j!=i+1 &&
                 !it->is_free(j) && !it->beta(j)->is_free(i) )
            {
              basic_link_beta_for_involution(it->beta(j)->beta(i), d, j);
            }
          }

          d2 = it;
          while (d2 != null_dart_handle && !d2->is_free(i-1))
          { d2 = d2->beta(i-1)->beta(i); }
          if (d2 != null_dart_handle)
          {
            if (i==2) basic_link_beta<1>(d2, d);
            else basic_link_beta_for_involution(d2, d, i-1);
          }
        }
      }
      return res;
    }

    /** Test if the map is valid.
     * @return true iff the map is valid.
     */
    bool is_valid() const
    {
      bool valid = true;
      unsigned int i = 0, j = 0;
      std::vector<int> marks(dimension+1);
      for ( i=0; i<=dimension; ++i)
        marks[i] = -1;

      Helper::template
        Foreach_enabled_attributes<Reserve_mark_functor<Self> >::
          run(this,&marks);

      for ( typename Dart_range::const_iterator it(darts().begin()),
             itend(darts().end()); it!=itend; ++it)
      {
        if ( !valid )
        { // We continue the traversal to mark all the darts.
          for ( i=0; i<=dimension; ++i)
            if (marks[i]!=-1) mark(it,marks[i]);
        }
        else
        {
          // beta0 must be the inverse of beta1
          if ((!it->is_free(0) && it->beta(0)->beta(1)!=it) ||
              (!it->is_free(1) && it->beta(1)->beta(0)!=it ))
          {
            std::cerr << "Map not valid: beta(0) "
              "is not the inverse of beta(1) for "
                      <<&(*it) << std::endl;
            valid = false;
          }

          // Each beta(i>=2) must be an involution
          for ( i = 2; i <= dimension; ++i)
            if (!it->is_free(i) && it->beta(i)->beta(i)!=it)
            {
              std::cerr << "Map not valid: beta(" << i
                        << ") is not an involution for "
                        <<&(*it) << std::endl;
              valid = false;
            }

          // beta1 o betai and beta0 o betai (i>=3) must be involutions
          if (!it->is_free(0))
          {
            for ( i = 3; i <= dimension; ++i)
              if ((it->is_free(i) != it->beta(0)->is_free(i)) ||
                  (!it->is_free(i) &&
                   it->beta(0)->beta(i)!=it->beta(i)->beta(1)))
              {
                std::cerr << "Map not valid: beta(0) o beta(" << i
                          << ") is not an involution for "
                          <<&(*it) << std::endl;
                valid = false;
              }
          }
          if (!it->is_free(1))
          {
            for ( i = 3; i <= dimension; ++i)
              if ((it->is_free(i) != it->beta(1)->is_free(i)) ||
                  (!it->is_free(i) &&
                   it->beta(1)->beta(i)!=it->beta(i)->beta(0)))
              {
                std::cerr << "Map not valid: beta(1) o beta(" << i
                          << ") is not an involution for "
                          <<&(*it)<< std::endl;
                valid = false;
              }
          }

          // beta(i>=2) o beta(j>=i+2) must be an involution
          for ( i = 2; i <= dimension; ++i)
          {
            if (!it->is_free(i))
            {
              for ( j = i + 2; j <= dimension; ++j)
                if ((it->is_free(j)!=it->beta(i)->is_free(j)) ||
                    (!it->is_free(j) &&
                     it->beta(i)->beta(j)!=it->beta(j)->beta(i)))
                {
                  std::cerr << "Map not valid: beta(" << i
                            << ") o beta(" << j
                            << ") is not an involution for "
                            << &(*it)<< std::endl;
                  valid = false;
                }
            }
          }
          Helper::template Foreach_enabled_attributes
            <internal::Test_is_valid_attribute_functor<Self> >::
            run(this,it,&marks,&valid);
        }
      }
      for ( i=0; i<=dimension; ++i)
        if ( marks[i]!=-1 )
        {
          CGAL_assertion( is_whole_map_marked(marks[i]) );
          free_mark(marks[i]);
        }

      return valid;
    }

    /// @return the number of darts.
    size_type number_of_darts() const
    { return mdarts.size(); }

    /// @return an estimation of the bytes used by the combinatorial map.
    size_type bytes() const
    {
      return mdarts.capacity() * sizeof(Dart) +
        internal::Count_bytes_all_attributes_functor<Self>::run(*this);
    }

    /** Write the content of the map: each dart and each beta links.
     * @param os the ostream.
     * @return the ostream.
     */
    std::ostream& display_darts(std::ostream & os, bool attribs=false) const
    {
      unsigned int nb = 0;
      for ( typename Dart_range::const_iterator it=darts().begin();
           it!=darts().end(); ++it)
      {
        os << " dart " << &(*it) << "; beta[i]=";
        for ( unsigned int i=0; i<=dimension; ++i)
        {
          os << &(*it->beta(i)) << ",\t";
          if (it->is_free(i)) os << "\t";
        }
        if ( attribs )
        {
          Helper::template Foreach_enabled_attributes
              <Display_attribute_functor<Self> >::run(this, it);
        }
        os << std::endl;
        ++nb;
      }
      os << "Number of darts: " << nb <<"(sizeofdarts="
         <<number_of_darts()<<")" << std::endl;
      return os;
    }

    /** Write the content of each given orbit of the map.
     * @param aos the ostream.
     * @return the ostream.
     */
    template < class Ite >
    std::ostream& display_orbits(std::ostream & aos) const
    {
      CGAL_static_assertion( (boost::is_same<typename Ite::Basic_iterator,
                              Tag_true>::value) );
      unsigned int nb = 0;
      int amark = get_new_mark();
      for ( typename Dart_range::const_iterator it1(darts().begin()),
             itend(darts().end()); it1!=itend; ++it1)
      {
        if ( !is_marked(it1, amark) )
        {
          ++nb;
          for ( Ite it2(*this, it1, amark); it2.cont(); ++it2 )
          {
            aos << &(**it2) << " - " << std::flush;
            mark(*it2, amark);
          }
          aos << std::endl;
        }
      }
      CGAL_assertion( is_whole_map_marked(amark) );
      free_mark(amark);
      aos << "Number of orbits: " << nb << std::endl;
      return aos;
    }

    /** Write the content of each i-cell of the map.
     * @param aos the ostream.
     * @return the ostream.
     */
    template < unsigned int i >
    std::ostream& display_cells(std::ostream & aos) const
    {
      return display_orbits<CMap_dart_const_iterator_basic_of_cell<Self,i> >
        (aos);
    }

    /** Write the number of darts and cells of the map into a given ostream.
     * @param os the ostream.
     * @return the ostream.
     */
    std::ostream& display_characteristics(std::ostream & os) const
    {
      std::vector<unsigned int> cells(dimension+2);
      for ( unsigned int i=0; i<=dimension+1; ++i)
      { cells[i]=i; }

      std::vector<unsigned int> res = count_cells(cells);

      os << "#Darts=" << number_of_darts();
      for ( unsigned int i=0; i<=dimension; ++i)
        os<<", #"<<i<<"-cells="<<res[i];
      os<<", #ccs="<<res[dimension+1];

      return os;
    }

    /// Create a new attribute.
    /// @return a handle on the new attribute.
#ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
    template<unsigned int i, typename ...Args>
    typename Attribute_handle<i>::type create_attribute(const Args&... args)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(args...);
    }
#else
    template<unsigned int i>
    typename Attribute_handle<i>::type
    create_attribute()
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace();
    }
    template<unsigned int i, typename T1>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1);
    }
    template<unsigned int i, typename T1, typename T2>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2);
    }
    template<unsigned int i, typename T1, typename T2, typename T3>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4,
             typename T5>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4,
                     const T5 &t5)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4, t5);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4,
             typename T5, typename T6>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4,
                     const T5 &t5, const T6 &t6)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4, t5, t6);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4,
             typename T5, typename T6, typename T7>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4,
                     const T5 &t5, const T6 &t6, const T7 &t7)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4, t5, t6, t7);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4,
             typename T5, typename T6, typename T7, typename T8>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4,
                     const T5 &t5, const T6 &t6, const T7 &t7, const T8 &t8)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4, t5, t6, t7, t8);
    }
    template<unsigned int i, typename T1, typename T2, typename T3, typename T4,
             typename T5, typename T6, typename T7, typename T8, typename T9>
    typename Attribute_handle<i>::type
    create_attribute(const T1 &t1, const T2 &t2, const T3 &t3, const T4 &t4,
                     const T5 &t5, const T6 &t6, const T7 &t7, const T8 &t8,
                     const T9 &t9)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "create_attribute<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).emplace(t1, t2, t3, t4, t5, t6, t7, t8, t9);
    }
#endif

    /// Erase an attribute.
    /// @param h a handle to the attribute to erase.
    template<unsigned int i>
    void erase_attribute(typename Attribute_handle<i>::type h)
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "erase_attribute<i> but i-attributes are disabled");
      CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).erase(h);
    }

    /// @return the number of attributes.
    template <unsigned int i>
    size_type number_of_attributes() const
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                  "number_of_attributes<i> but i-attributes are disabled");
      return  CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers).size();
    }

    /// @return a Attributes_range<i> (range through all the
    /// attributes<i> of the map).
    template<unsigned int i>
    typename Attribute_range<i>::type & attributes()
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                                "attributes<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers);
    }

    template<unsigned int i>
    typename Attribute_const_range<i>::type & attributes() const
    {
      CGAL_static_assertion_msg(Helper::template Dimension_index<i>::value>=0,
                                "attributes<i> but i-attributes are disabled");
      return CGAL::cpp11::get<Helper::template Dimension_index<i>::value>
        (mattribute_containers);
    }

    /** Double link a dart with beta 0 to a second dart.
     * \em adart1 is 0-linked to \em adart2 and \em adart2 is 1-linked
     * with \em adart1. Attributes are not updated, thus we can obtain
     * a non-valid map with darts belonging to a same orbit and having
     * different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    void basic_link_beta_0(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion(adart1 != NULL && adart2 != NULL);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      adart1->template basic_link_beta<0>(adart2);
      adart2->template basic_link_beta<1>(adart1);
    }

    /** Double link a dart with beta 0 to a second dart.
     * \em adart1 is 0-linked to \em adart2 and \em adart2 is 1-linked
     * with \em adart1. Attributes are not updated, thus we can obtain
     * a non-valid map with darts belonging to a same orbit and having
     * different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    void basic_link_beta_1(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion(adart1 != NULL && adart2 != NULL);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      adart1->template basic_link_beta<1>(adart2);
      adart2->template basic_link_beta<0>(adart1);
    }

    /** Double link a dart with beta i to a second dart, when i>=2.
     * \em adart1 is i-linked to \em adart2 and \em adart2 is i-linked
     * with \em adart1. Attributes are not updated, thus we can obtain
     * a non-valid map with darts belonging to a same orbit and having
     * different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     * @param i the dimension of the beta.
     */
    template<unsigned int i>
    void basic_link_beta_for_involution(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( i>=2 && i<=dimension );
      CGAL_assertion(adart1 != NULL && adart2 != NULL && adart1!=adart2);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      adart1->template basic_link_beta<i>(adart2);
      adart2->template basic_link_beta<i>(adart1);
    }
    void basic_link_beta_for_involution(Dart_handle adart1, Dart_handle adart2,
                                        unsigned int i)
    {
      CGAL_assertion( i>=2 && i<=dimension );
      CGAL_assertion(adart1 != NULL && adart2 != NULL && adart1!=adart2);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      adart1->basic_link_beta(adart2, i);
      adart2->basic_link_beta(adart1, i);
    }

    /** Double link a dart with betai to a second dart.
     * \em adart1 is i-linked to \em adart2 and \em adart2 is i^-1-linked
     * with \em adart1. Attributes are not updated, thus we can obtain
     * a non-valid map with darts belonging to a same orbit and having
     * different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    template<unsigned int i>
    void basic_link_beta(Dart_handle adart1, Dart_handle adart2)
    {
      if ( i==0 ) basic_link_beta_0(adart1, adart2);
      else if ( i==1 ) basic_link_beta_1(adart1, adart2);
      else basic_link_beta_for_involution<i>(adart1, adart2);
    }
    void basic_link_beta(Dart_handle adart1, Dart_handle adart2,
                         unsigned int i)
    {
      if ( i==0 ) basic_link_beta_0(adart1, adart2);
      else if ( i==1 ) basic_link_beta_1(adart1, adart2);
      else basic_link_beta_for_involution(adart1, adart2, i);
    }

    /** Double link two darts, and update the NULL attributes.
     * \em adart1 is 0-linked to \em adart2 and \em adart2 is 1-linked
     * with \em adart1. The NULL attributes of \em adart1 are updated to
     * non NULL attributes associated to \em adart2, and vice-versa.
     * If both darts have an attribute, the attribute of adart1 is
     * associated to adart2.
     * We can obtain a non-valid map with darts belonging to a same cell
     * and having different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    void link_beta_0(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion(adart1 != NULL && adart2 != NULL);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      Helper::template Foreach_enabled_attributes_except
        <internal::Group_attribute_functor_of_dart<Self, 0>, 1>::
        run(this,adart1,adart2);
      adart1->basic_link_beta<0>(adart2);
      adart2->basic_link_beta<1>(adart1);
    }

    /** Double link two darts, and update the NULL attributes.
     * \em adart1 is 1-linked to \em adart2 and \em adart2 is 0-linked
     * with \em adart1. The NULL attributes of \em adart1 are updated to
     * non NULL attributes associated to \em adart2, and vice-versa.
     * If both darts have an attribute, the attribute of adart1 is
     * associated to adart2.
     * We can obtain a non-valid map with darts belonging to a same cell
     * and having different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    void link_beta_1(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion(adart1 != NULL && adart2 != NULL);
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      Helper::template Foreach_enabled_attributes_except
        <internal::Group_attribute_functor_of_dart<Self, 1>, 1>::
        run(this,adart1,adart2);
      adart1->basic_link_beta<1>(adart2);
      adart2->basic_link_beta<0>(adart1);
    }

    /** Double link two darts, and update the NULL attributes.
     * \em adart1 is i-linked to \em adart2 and \em adart2 is i^-1-linked
     * with \em adart1. The NULL attributes of \em adart1 are updated to
     * non NULL attributes associated to \em adart2, and vice-versa.
     * If both darts have an attribute, the attribute of adart1 is
     * associated to adart2.
     * We can obtain a non-valid map with darts belonging to a same cell
     * and having different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     * @param i the dimension of the beta.
     * @pre 2<=i<=dimension.
     */
    template<unsigned int i>
    void link_beta_for_involution(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion(adart1 != NULL && adart2 != NULL && adart1!=adart2 );
      CGAL_assertion(adart1 != null_dart_handle && adart2 != null_dart_handle);
      CGAL_assertion( 2<=i && i<=dimension );
      Helper::template Foreach_enabled_attributes_except
        <internal::Group_attribute_functor_of_dart<Self, i>, i>::
        run(this,adart1,adart2);
      adart1->template basic_link_beta<i>(adart2);
      adart2->template basic_link_beta<i>(adart1);
    }

    /** Double link two darts, and update the NULL attributes.
     * \em adart1 is i-linked to \em adart2 and \em adart2 is i^-1-linked
     * with \em adart1. The NULL attributes of \em adart1 are updated to
     * non NULL attributes associated to \em adart2, and vice-versa.
     * If both darts have an attribute, the attribute of adart1 is
     * associated to adart2.
     * We can obtain a non-valid map with darts belonging to a same cell
     * and having different attributes.
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     */
    template<unsigned int i>
    void link_beta(Dart_handle adart1, Dart_handle adart2)
    {
      if ( i==0 ) link_beta_0(adart1, adart2);
      else if ( i==1 ) link_beta_1(adart1, adart2);
      else link_beta_for_involution<i>(adart1, adart2);
    }

    /** Double link a dart with betai to a second dart.
     * \em adart1 is i-linked to \em adart2 and \em adart2 is i^-1-linked
     * with \em adart1. The NULL attributes of \em adart1 are updated to
     * non NULL attributes associated to \em adart2, and vice-versa,
     * if both darts have an attribute, the attribute of adart1 is
     * associated to adart2 (only if update_attributes==true).
     * @param adart1 a first dart.
     * @param adart2 a second dart.
     * @param update_attributes a boolean to update the enabled attributes.
     */
    template<unsigned int i>
    void link_beta(Dart_handle adart1, Dart_handle adart2,
                   bool update_attributes)
    {
      if ( update_attributes ) link_beta<i>(adart1, adart2);
      else basic_link_beta<i>(adart1, adart2);
    }

    /** Double unlink a dart with beta 0.
     * beta0(\em adart) is 1-unlinked and \em adart is 0-unlinked.
     * The attributes are not updated, thus we can obtain a non-valid map
     * with darts belonging to different orbits and having the same
     * attributes.
     * @param adart a dart.
     */
    void unlink_beta_0(Dart_handle adart)
    {
      CGAL_assertion(adart!=NULL && !adart->template is_free<0>());
      adart->template beta<0>()->template unlink_beta<1>();
      adart->template unlink_beta<0>();
    }

    /** Double unlink a dart with beta 1.
     * beta1(\em adart) is 0-unlinked and \em adart is 1-unlinked.
     * The attributes are not updated, thus we can obtain a non-valid map
     * with darts belonging to different orbits and having the same
     * attributes.
     * @param adart a dart.
     */
    void unlink_beta_1(Dart_handle adart)
    {
      CGAL_assertion(adart!=NULL && !adart->template is_free<1>());
      adart->template beta<1>()->template unlink_beta<0>();
      adart->template unlink_beta<1>();
    }

    /** Double unlink a dart with beta i, for i>=2.
     * betai(\em adart) is i-unlinked and \em adart is i-unlinked.
     * The attributes are not updated, thus we can obtain a non-valid map
     * with darts belonging to different orbits and having the same
     * attributes.
     * @param adart a dart.
     * @param i the dimension of the beta.
     */
    template<unsigned int i>
    void unlink_beta_for_involution(Dart_handle adart)
    {
      CGAL_assertion(adart!=NULL && adart!=null_dart_handle &&
                     !adart->template is_free<i>());
      CGAL_assertion(2<=i && i<=dimension);
      adart->template beta<i>()->template unlink_beta<i>();
      adart->template unlink_beta<i>();
    }
    void unlink_beta_for_involution(Dart_handle adart, unsigned int i)
    {
      CGAL_assertion(adart!=NULL && adart!=null_dart_handle &&
                     !adart->is_free(i));
      CGAL_assertion(2<=i && i<=dimension);
      adart->beta(i)->unlink_beta(i);
      adart->unlink_beta(i);
    }

    /** Double unlink a dart with beta i.
     * betai(\em adart) is i-1-unlinked and \em adart is i-unlinked.
     * The attributes are not updated, thus we can obtain a non-valid map
     * with darts belonging to different orbits and having the same
     * attributes.
     * @param adart a dart.
     * @param i the dimension of the beta.
     */
    template<unsigned int i>
    void unlink_beta(Dart_handle adart)
    {
      if ( i==0 ) unlink_beta_0(adart);
      else if ( i==1 ) unlink_beta_1(adart);
      else unlink_beta_for_involution<i>(adart);
    }
    void unlink_beta(Dart_handle adart, unsigned int i)
    {
      if ( i==0 ) unlink_beta_0(adart);
      else if ( i==1 ) unlink_beta_1(adart);
      else unlink_beta_for_involution(adart, i);
    }

    /** Test if it is possible to sew by betai the two given darts
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @return true iff \em adart1 can be i-sewn with \em adart2.
     */
    template<unsigned int i>
    bool is_sewable(Dart_const_handle adart1, Dart_const_handle adart2) const
    {
      return CGAL::internal::
          Is_sewable_functor<Self, i>::run(this, adart1, adart2);
    }

    /** Topological sew by beta1 the two given darts plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<1>(adart1, adart2).
     */
    void topo_sew_1(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( (is_sewable<1>(adart1,adart2)) );

      if ( adart1==adart2 )
      {
        for ( CGAL::CMap_dart_iterator_of_involution<Self,1> it(*this, adart1);
              it.cont(); ++it )
        {
          basic_link_beta_1(it, it);
        }
      }
      else
      {
        int m = get_new_mark();
        std::deque<Dart_handle> dartv;
        for ( CGAL::CMap_dart_iterator_basic_of_cell<Self,0>
              it(*this, adart1, m); it.cont(); ++it )
        {
          mark(it,m);
          dartv.push_back(it);
        }

        CGAL::CMap_dart_iterator_of_involution<Self,1>     I1(*this, adart1);
        CGAL::CMap_dart_iterator_of_involution_inv<Self,1> I2(*this, adart2);
        for ( ; I1.cont(); ++I1, ++I2 )
        {
          if ( is_marked(I1,m) ) basic_link_beta_1(I1, I2);
          else                   basic_link_beta_0(I1, I2);
        }

        for ( typename std::deque<Dart_handle>::iterator it=dartv.begin();
              it!=dartv.end(); ++it)
        { unmark(*it,m); }
        CGAL_assertion( is_whole_map_unmarked(m) );
        free_mark(m);
      }
    }

    /** Topological sew by beta0 two given darts plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<0>(adart1, adart2).
     */
    void topo_sew_0(Dart_handle adart1, Dart_handle adart2)
    { topo_sew_1(adart2, adart1); }

    /** Topological sew by betai two given darts plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre 2<=i<=dimension.
     * @pre is_sewable<i>(adart1, adart2).
     */
    template<unsigned int i>
    void topo_sew_for_involution(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( 2<=i && i<=Self::dimension );
      CGAL_assertion( (is_sewable<i>(adart1,adart2)) );

      CGAL::CMap_dart_iterator_of_involution<Self,i>     I1(*this, adart1);
      CGAL::CMap_dart_iterator_of_involution_inv<Self,i> I2(*this, adart2);
      for ( ; I1.cont();  ++I1, ++I2 )
      {
        basic_link_beta_for_involution<i>(I1, I2);
      }
    }

    /** Topological sew by betai two given darts plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<i>(adart1, adart2).
     */
    template<unsigned int i>
    void topo_sew(Dart_handle adart1, Dart_handle adart2)
    {
      if ( i==0 ) topo_sew_1(adart2, adart1);
      else if ( i==1 ) topo_sew_1(adart1, adart2);
      else topo_sew_for_involution<i>(adart1, adart2);
    }

    /** Sew by beta0 the two given darts plus all the required darts
     * to satisfy the combinatorial map validity, and updates enabled
     * attributes when necessary so that the final map is valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<0>(adart1, adart2).
     * @post is_valid()
     */
    void sew_0(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( (is_sewable<0>(adart1,adart2)) );

      if ( adart1==adart2 )
      {
        for ( CGAL::CMap_dart_iterator_of_involution<Self,1> it(*this, adart1);
              it.cont(); ++it )
        {
          basic_link_beta_1(it, it);
        }
        return;
      }

      int m = get_new_mark();
      std::deque<Dart_handle> dartv;
      for ( CGAL::CMap_dart_iterator_basic_of_cell<Self, 0>
            it(*this, adart1, m); it.cont(); ++it )
      {
        mark(it,m);
        dartv.push_back(it);
      }

      int mark = get_new_mark();
      CGAL_assertion( mark!=-1 );

      CGAL::CMap_dart_iterator_basic_of_involution<Self, 1>
          I1(*this, adart1, mark);
      CGAL::CMap_dart_iterator_basic_of_involution_inv<Self, 1>
          I2(*this, adart2, mark);

      // This first loop do not modify the map, but only the attributes
      // (by calling when required the onmerge functors).
      for ( ; I1.cont(); ++I1, ++I2 )
      {
        if ( is_marked(I1,m) )
          Helper::template Foreach_enabled_attributes_except
              <CGAL::internal::Group_attribute_functor<Self, 0>, 1>::
              run(this, I1, I2);
        else
          Helper::template Foreach_enabled_attributes_except
              <CGAL::internal::Group_attribute_functor<Self, 1>, 1>::
              run(this, I1, I2);
      }

      // Now we update the beta links.
      negate_mark( mark );
      for ( I1.rewind(), I2.rewind(); I1.cont(); ++I1, ++I2 )
      {
        if ( is_marked(I1,m) ) basic_link_beta_0(I1, I2);
        else                   basic_link_beta_1(I1, I2);
      }

      for ( typename std::deque<Dart_handle>::iterator it=dartv.begin();
            it!=dartv.end(); ++it )
      { unmark(*it,m); }
      CGAL_assertion( is_whole_map_unmarked(m) );
      free_mark(m);

      negate_mark( mark );
      CGAL_assertion( is_whole_map_unmarked(mark) );
      free_mark(mark);
    }

    /** Sew by beta1 the two given darts plus all the required darts
     * to satisfy the combinatorial map validity, and updates enabled
     * attributes when necessary so that the final map is valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<1>(adart1, adart2).
     * @post is_valid()
     */
    void sew_1(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( (is_sewable<1>(adart1,adart2)) );

      if ( adart1==adart2 )
      {
        for ( CGAL::CMap_dart_iterator_of_involution<Self, 1>
              it(*this, adart1); it.cont(); ++it )
        {
          basic_link_beta_1(it, it);
        }
        return;
      }

      int m = get_new_mark();
      std::deque<Dart_handle> dartv;
      for ( CGAL::CMap_dart_iterator_basic_of_cell<Self, 0>
            it(*this, adart1, m); it.cont(); ++it )
      {
        mark(it,m);
        dartv.push_back(it);
      }

      int mark = get_new_mark();
      CGAL_assertion( mark!=-1 );

      CGAL::CMap_dart_iterator_basic_of_involution<Self, 1>
          I1(*this, adart1, mark);
      CGAL::CMap_dart_iterator_basic_of_involution_inv<Self, 1>
          I2(*this, adart2, mark);

      // This first loop do not modify the map, but only the attributes
      // (by calling when required the onmerge functors).
      for ( ; I1.cont(); ++I1, ++I2 )
      {
        CGAL_assertion( I2.cont() );
        if ( is_marked(I1,m) )
          Helper::template Foreach_enabled_attributes_except
              <internal::Group_attribute_functor<Self, 1>, 1>::
              run(this, I1, I2);
        else
          Helper::template Foreach_enabled_attributes_except
              <internal::Group_attribute_functor<Self, 0>, 1>::
              run(this, I1, I2);
      }

      // Now we update the beta links.
      negate_mark( mark );
      for ( I1.rewind(), I2.rewind(); I1.cont(); ++I1, ++I2 )
      {
        if ( is_marked(I1,m) ) basic_link_beta_1(I1, I2);
        else                   basic_link_beta_0(I1, I2);
      }

      for ( typename std::deque<Dart_handle>::iterator it=dartv.begin();
            it!=dartv.end(); ++it )
      { unmark(*it,m); }
      CGAL_assertion( is_whole_map_unmarked(m) );
      free_mark(m);

      negate_mark( mark );
      CGAL_assertion( is_whole_map_unmarked(mark) );
      free_mark(mark);
    }

    /** Sew by betai the two given darts plus all the required darts
     * to satisfy the combinatorial map validity, and updates enabled
     * attributes when necessary so that the final map is valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<i>(adart1, adart2).
     * @pre 2<=i<=dimension.
     * @post is_valid()
     */
    template<unsigned int i>
    void sew_for_involution(Dart_handle adart1, Dart_handle adart2)
    {
      CGAL_assertion( 2<=i && i<=dimension );
      CGAL_assertion( (is_sewable<i>(adart1,adart2)) );

      int mark=get_new_mark();
      CGAL_assertion( mark!=-1 );

      CGAL::CMap_dart_iterator_basic_of_involution<Self, i>
          I1(*this, adart1, mark);
      CGAL::CMap_dart_iterator_basic_of_involution_inv<Self, i>
          I2(*this, adart2, mark);

      // This first loop do not modify the map, but only the attributes
      // (by calling when required the onmerge functors).
      for ( ; I1.cont(); ++I1, ++I2 )
      {
        Helper::template Foreach_enabled_attributes_except
            <CGAL::internal::Group_attribute_functor<Self, i>, i>::
            run(this, I1, I2);
      }

      // Now we update the beta links.
      negate_mark( mark );
      for ( I1.rewind(), I2.rewind(); I1.cont(); ++I1, ++I2 )
      {
        basic_link_beta_for_involution<i>(I1, I2);
      }

      negate_mark( mark );
      CGAL_assertion( is_whole_map_unmarked(mark) );
      free_mark(mark);
    }

    /** Sew by betai the two given darts plus all the required darts
     * to satisfy the combinatorial map validity, and updates enabled
     * attributes when necessary so that the final map is valid.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @pre is_sewable<i>(adart1, adart2).
     * @post is_valid()
     */
    template<unsigned int i>
    void sew(Dart_handle adart1, Dart_handle adart2)
    {
      if ( i==0 ) sew_0(adart1, adart2);
      else if ( i==1 ) sew_1(adart1, adart2);
      else sew_for_involution<i>(adart1, adart2);
    }

    /** Sew by betai the two given darts plus all the required darts
     * to satisfy the combinatorial map validity. Enabled attributes
     * are updated only if update_attributes==true.
     * @param adart1 the first dart.
     * @param adart2 the second dart.
     * @param update_attributes a boolean to update the enabled attributes
     * @pre is_sewable<i>(adart1, adart2).
     */
    template<unsigned int i>
    void sew(Dart_handle adart1, Dart_handle adart2, bool update_attributes)
    {
      if ( update_attributes ) sew<i>(adart1, adart2);
      else topo_sew<i>(adart1, adart2);
    }

    /** Topological unsew by beta1 the given dart plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid
     * @param adart first dart.
     * @pre !adart->is_free(1).
     */
    void topo_unsew_1(Dart_handle adart)
    {
      CGAL_assertion( adart!=NULL && !adart->template is_free<1>() );

      int m = get_new_mark();
      std::deque<Dart_handle> dartv;
      for ( CGAL::CMap_dart_iterator_basic_of_cell<Self,0> it(*this, adart, m);
            it.cont(); ++it )
      {
        mark(*it,m);
        dartv.push_back(*it);
      }

      for ( CGAL::CMap_dart_iterator_of_involution<Self,1> it(*this, adart);
            it.cont(); ++it )
      {
        if ( is_marked(*it,m) ) unlink_beta_1(*it);
        else unlink_beta_0(*it);
      }

      for ( typename std::deque<Dart_handle>::iterator it=dartv.begin();
            it!=dartv.end(); ++it )
      { unmark(*it,m); }
      CGAL_assertion( is_whole_map_unmarked(m) );
      free_mark(m);
    }

    /** Topological unsew by beta0 the given dart plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid
     * @param adart first dart.
     * @pre !adart->is_free(0).
     */
    void topo_unsew_0(Dart_handle adart)
    {
      CGAL_assertion( adart!=NULL && !adart->template is_free<0>() );
      topo_unsew_1( adart->template beta<0>() );
    }

    /** Topological unsew by betai the given dart plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid
     * @param adart first dart.
     * @pre !adart->is_free(i).
     * @pre 2<=i<=dimension.
     */
    template<unsigned int i>
    void topo_unsew_for_involution(Dart_handle adart)
    {
      CGAL_assertion( adart!=NULL && !adart->template is_free<i>() );
      CGAL_assertion( 2<=i && i<=Self::dimension );

      for ( CGAL::CMap_dart_iterator_of_involution<Self,i> it(*this, adart);
            it.cont(); ++it )
      { unlink_beta<i>(*it); }
    }

    /** Topological unsew by betai the given dart plus all the required darts
     * to satisfy the combinatorial map validity: but do not update attributes
     * thus the map can be non valid
     * @param adart first dart.
     * @pre !adart->is_free(i).
     */
    template<unsigned int i>
    void topo_unsew(Dart_handle adart)
    {
      if ( i==0 ) topo_unsew_0(adart);
      else if ( i==1 ) topo_unsew_1(adart);
      else topo_unsew_for_involution<i>(adart);
    }

    /** Unsew by beta0 the given dart plus all the required darts
     * to satisfy the combinatorial map validity, and update enabled
     * attributes when necessary so that the final map is valid.
     * @param adart first dart.
     * @pre !adart->is_free(0).
     * @post is_valid()
     */
    void unsew_0(Dart_handle adart)
    {
      CGAL_assertion( adart!=NULL && !adart->template is_free<0>() );
      Dart_handle d2=NULL;

      int m=get_new_mark();
      std::deque<Dart_handle> dartv;
      std::deque<Dart_handle> modified_darts;
      std::deque<Dart_handle> modified_darts2;

      for ( CGAL::CMap_dart_iterator_basic_of_cell<Self,0> it(*this, adart, m);
            it.cont(); ++it )
      {
        mark(it, m);
        dartv.push_back(it);
      }

      for ( CGAL::CMap_dart_iterator_of_involution<Self,1> it(*this, adart);
            it.cont(); ++it )
      {
        if ( is_marked(it, m) )
        {
          modified_darts.push_back(it);
          modified_darts2.push_back(it->template beta<0>());
          unlink_beta_0(it);
        }
        else
        {
          modified_darts2.push_back(it);
          modified_darts.push_back(it->template beta<1>());
          unlink_beta_1(it);
        }
      }

      for ( typename std::deque<Dart_handle>::iterator it=dartv.begin();
            it!=dartv.end(); ++it )
      { unmark(*it,m); }

      CGAL_assertion( is_whole_map_unmarked(m) );
      free_mark(m);

      // We test the split of all the incident cells for all the non
      // void attributes.
      Helper::template Foreach_enabled_attributes_except
          <CGAL::internal::Test_split_attribute_functor<Self,0>, 1>::
          run(this, modified_darts, modified_darts2);
    }

    /** Unsew by beta1 the given dart plus all the required darts
     * to satisfy the combinatorial map validity, and update enabled
     * attributes when necessary so that the final map is valid.
     * @param adart first dart.
     * @pre !adart->is_free(1).
     * @post is_valid()
     */
    void unsew_1(Dart_handle adart)
    {
      CGAL_assertion( adart!=NULL && !adart->is_free(1) );
      Dart_handle d2 = NULL;

      int m = get_new_mark();
      std::deque<Dart_handle> dartv;
      std::deque<Dart_handle> modified_darts;
      std::deque<Dart_handle> modified_darts2;

      for ( CGAL::CMap_dart_iterator_basic_of_cell<Self,0>
            it(*this, adart, m); it.cont(); ++it)
      {
        mark(it, m);
        dartv.push_back(it);
      }

      for ( CGAL::CMap_dart_iterator_of_involution<Self, 1> it(*this, adart);
            it.cont(); ++it )
      {
        if ( is_marked(it, m) )
        {
          modified_darts2.push_back(it);
          modified_darts.push_back(it->template beta<1>());
          unlink_beta_1(it);
        }
        else
        {
          modified_darts.push_back(it);
          modified_darts2.push_back(it->template beta<0>());
          unlink_beta_0(it);
        }
      }

      for ( typename std::deque<Dart_handle>::iterator
             it=dartv.begin(); it!=dartv.end(); ++it)
      { unmark(*it, m); }
      CGAL_assertion( is_whole_map_unmarked(m) );
      free_mark(m);

      // We test the split of all the incident cells for all the non
      // void attributes.
      Helper::template Foreach_enabled_attributes_except
          <CGAL::internal::Test_split_attribute_functor<Self,1>, 1>::
          run(this, modified_darts, modified_darts2);
    }

    /** Unsew by betai the given dart plus all the required darts
     * to satisfy the combinatorial map validity, and update enabled
     * attributes when necessary so that the final map is valid.
     * @param adart first dart.
     * @pre !adart->is_free(i).
     * @post is_valid()
     * @pre 2<=i<=dimension
     */
    template<unsigned int i>
    void unsew_for_involution(Dart_handle adart)
    {
      CGAL_assertion(2<=i && i<=Self::dimension);
      CGAL_assertion( adart!=NULL && !adart->is_free(i) );

      std::deque<Dart_handle> modified_darts;

      for ( CGAL::CMap_dart_iterator_of_involution<Self, i> it(*this, adart);
            it.cont(); ++it )
      {
        modified_darts.push_back(it);
        modified_darts.push_back(it->template beta<i>());
        unlink_beta_for_involution<i>(it);
      }

      // We test the split of all the incident cells for all the non
      // void attributes.
      Helper::template Foreach_enabled_attributes_except
          <CGAL::internal::Test_split_attribute_functor<Self, i>, i>::
          run(this, modified_darts);
    }

    /** Unsew by betai the given dart plus all the required darts
     * to satisfy the combinatorial map validity, and update enabled
     * attributes when necessary so that the final map is valid.
     * @param adart first dart.
     * @pre !adart->is_free(i).
     * @post is_valid()
     */
    template<unsigned int i>
    void unsew(Dart_handle adart)
    {
      if ( i==0 ) unsew_0(adart);
      else if ( i==1 ) unsew_1(adart);
      else unsew_for_involution<i>(adart);
    }

    /** Unsew by betai the given dart plus all the required darts
     * to satisfy the combinatorial map validity. Enabled attributes
     * are updated only if update_attributes==true.
     * @param adart first dart.
     * @param update_attributes a boolean to update the enabled attributes
     * @pre !adart->is_free(i).
     */
    template<unsigned int i>
    void unsew(Dart_handle adart, bool update_attributes)
    {
      if ( update_attributes ) unsew<i>(adart);
      else topo_unsew<i>(adart);
    }

    /** Count the marked cells (at least one marked dart).
     * @param amark the mark to consider.
     * @param avector containing the dimensions of the cells to count.
     * @return a vector containing the number of cells.
     */
    std::vector<unsigned int>
    count_marked_cells(int amark, const std::vector<unsigned int>& acells) const
    {
      std::vector<unsigned int> res(dimension+2);
      std::vector<int> marks(dimension+2);

      // Initialization of the result
      for ( unsigned int i=0; i<dimension+2; ++i)
      {
        res[i]=0;
        marks[i]=-1;
      }

      // Mark reservation
      for ( unsigned int i=0; i<acells.size(); ++i)
      {
        CGAL_assertion(acells[i]<=dimension+1);
        if ( marks[acells[i]]==-1 )
        {
          marks[acells[i]] = get_new_mark();
        }
      }

      // Counting and marking cells
      for ( typename Dart_range::const_iterator it(darts().begin()),
             itend(darts().end()); it!=itend; ++it)
      {
        if ( is_marked(it, amark) )
        {
          CGAL::internal::Foreach_static
            <CGAL::internal::Count_cell_functor<Self>,dimension+1>::
            run(this, it, &marks, &res);
        }
      }

      // Unmarking darts
      std::vector<unsigned int> tounmark;
      for ( unsigned int i=0; i<acells.size(); ++i)
      {
        if ( is_whole_map_marked(marks[acells[i]]) ||
             is_whole_map_unmarked(marks[acells[i]]))
        {
          free_mark(marks[acells[i]]);
        }
        else
        {
          tounmark.push_back(marks[acells[i]]);
        }
      }

      if ( tounmark.size() > 0 )
      {
        for ( typename Dart_range::const_iterator it(darts().begin()),
               itend(darts().end()); it!=itend; ++it)
        {
          for ( unsigned int i=0; i<tounmark.size(); ++i)
            unmark(it, tounmark[i]);
        }
        for ( unsigned int i=0; i<tounmark.size(); ++i)
        {
          CGAL_assertion(is_whole_map_unmarked(tounmark[i]));
          free_mark(tounmark[i]);
        }
      }

      return res;
    }

    /** Count the number of given cells
     * @param avector containing the dimensions of the cells to count.
     * @return a vector containing the number of cells.
     */
    std::vector<unsigned int>
    count_cells(const std::vector<unsigned int>& acells) const
    {
      std::vector<unsigned int> res;
      int m = get_new_mark();
      negate_mark(m); // We mark all the cells.

      res = count_marked_cells(m, acells);

      negate_mark(m); // We unmark the cells
      free_mark(m);

      return res;
    }

    /** Count the number of cells in each dimension.
     * @return a vector containing the number of cells.
     */
    std::vector<unsigned int> count_all_cells() const
    {
      std::vector<unsigned int> dim(dimension+2);

      for ( unsigned int i=0; i<dimension+2; ++i)
        dim[i]=i;

      return count_cells(dim);
    }

  protected:
    /** Set simultaneously all the marks of a given dart.
     * @param adart the dart.
     * @param amarks the marks to set.
     */
    void set_marks(Dart_handle adart,
                   const std::bitset<NB_MARKS> & amarks) const
    {
      CGAL_assertion(adart != NULL && adart!=null_dart_handle);
      adart->set_marks(amarks ^ mmask_marks);
    }

    /** Get simultaneously all the marks of a given dart.
     * @param adart the dart.
     * @return allt the marks of adart.
     */
    std::bitset<NB_MARKS> get_marks(Dart_handle adart) const
    {
      CGAL_assertion(adart != NULL && adart!=null_dart_handle);
      return adart->get_marks() ^ mmask_marks;
    }

    /** Get the mask associated to a given mark.
     * @param amark the mark.
     * @return the mask associated to mark amark.
     */
    bool get_mask_mark(int amark) const
    {
      CGAL_assertion(amark>=0 && (size_type)amark<NB_MARKS);
      return mmask_marks[(size_type)amark];
    }

  public:
    /** Erase marked darts from the map.
     * Marked darts are unlinked before to be removed, thus surviving darts
     * are correctly linked, but the map is not necessarily valid depending
     * on the configuration of removed darts. User must check carefully marked
     * darts before calling this method.
     * @param amark the mark of darts to erase.
     * @return the number of removed darts.
     */
    unsigned int erase_marked_darts(int amark)
    {
      unsigned int res = 0, i = 0;
      Dart_handle d;
      for ( typename Dart_range::iterator it(darts().begin()),
             itend(darts().end()); it!=itend; )
      {
        d = it++;
        if (is_marked(d, amark))
        {
          for ( i = 0; i <= dimension; ++i)
          { if (!d->is_free(i)) unlink_beta(d, i); }
          erase_dart(d); ++res;
        }
      }
      return res;
    }

#ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
    //**************************************************************************
    // Dart_of_orbit_basic_range
    template<unsigned int ... Beta>
    struct Dart_of_orbit_basic_range : public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_basic_of_orbit<Self,Beta...>,
     CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,Beta...> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_basic_of_orbit<Self,Beta...>,
       CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,Beta...> > Base;

      Dart_of_orbit_basic_range(Self &amap, Dart_handle adart, int amark=-1):
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_basic_const_range
    template<unsigned int ... Beta>
    struct Dart_of_orbit_basic_const_range : public CGAL::CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,Beta...> >
    {
      typedef CGAL::CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,Beta...> >
      Base;

      Dart_of_orbit_basic_const_range(const Self &amap, Dart_const_handle
                                      adart, int amark=-1):
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_range
    template<unsigned int ... Beta>
    struct Dart_of_orbit_range : public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_of_orbit<Self,Beta...>,
     CGAL::CMap_dart_const_iterator_of_orbit<Self,Beta...> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_of_orbit<Self,Beta...>,
       CGAL::CMap_dart_const_iterator_of_orbit<Self,Beta...> > Base;

      Dart_of_orbit_range(Self &amap, Dart_handle adart) : Base(amap,adart)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_const_range
    template<unsigned int ... Beta>
    struct Dart_of_orbit_const_range : public CGAL::CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_of_orbit<Self,Beta...> >
    {
      typedef CGAL::CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_of_orbit<Self,Beta...> > Base;

      Dart_of_orbit_const_range(const Self &amap, Dart_const_handle adart):
        Base(amap,adart)
      {}
    };
    //**************************************************************************
    /// @return a range on all the darts of the given orbit
    template<unsigned int ... Beta>
    Dart_of_orbit_range<Beta...> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<Beta...>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int ... Beta>
    Dart_of_orbit_const_range<Beta...>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<Beta...>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int ... Beta>
    Dart_of_orbit_basic_range<Beta...> darts_of_orbit_basic(Dart_handle adart,
                                                            int amark=-1)
    { return Dart_of_orbit_basic_range<Beta...>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int ... Beta>
    Dart_of_orbit_basic_const_range<Beta...>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<Beta...>(*this,adart,amark); }
    //**************************************************************************
#else
    //**************************************************************************
    // Dart_of_orbit_basic_range
    template<int B1=-1,int B2=-1,int B3=-1,int B4=-1,int B5=-1,
             int B6=-1,int B7=-1,int B8=-1,int B9=-1>
    struct Dart_of_orbit_basic_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_basic_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
        B8,B9>,
     CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
        B8,B9> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_basic_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
      B8,B9>,
       CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,B1,B2,B3,B4,B5,
                                               B6,B7,B8,B9> > Base;

      Dart_of_orbit_basic_range(Self &amap, Dart_handle adart,
                                int /*amark*/=-1):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_basic_const_range
    template<int B1=-1,int B2=-1,int B3=-1,int B4=-1,int B5=-1,
             int B6=-1,int B7=-1,int B8=-1,int B9=-1>
    struct Dart_of_orbit_basic_const_range: public CMap_const_range
    <Self,
     CGAL::CMap_dart_const_iterator_basic_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
        B8,B9> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_basic_of_orbit
       <Self,B1,B2,B3,B4,B5,B6,B7,B8,B9> > Base;

      Dart_of_orbit_basic_const_range(const Self &amap,
                                      Dart_const_handle adart, int amark=-1):
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_range
    template<int B1=-1,int B2=-1,int B3=-1,int B4=-1,int B5=-1,
             int B6=-1,int B7=-1,int B8=-1,int B9=-1>
    struct Dart_of_orbit_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,B8,B9>,
     CGAL::CMap_dart_const_iterator_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,B8,B9> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
      B8,B9>,
       CGAL::CMap_dart_const_iterator_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
      B8,B9> >
      Base;

      Dart_of_orbit_range(Self &amap, Dart_handle adart):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // Dart_of_orbit_const_range
    template<int B1=-1,int B2=-1,int B3=-1,int B4=-1,int B5=-1,
             int B6=-1,int B7=-1,int B8=-1,int B9=-1>
    struct Dart_of_orbit_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_of_orbit<Self,B1,B2,B3,B4,B5,B6,B7,
        B8,B9> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_of_orbit
       <Self,B1,B2,B3,B4,B5,B6,B7,B8,B9> > Base;

      Dart_of_orbit_const_range(const Self &amap, Dart_const_handle adart):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    /// @return a range on all the darts of the given orbit
    Dart_of_orbit_range<> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1>
    Dart_of_orbit_range<B1> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2>
    Dart_of_orbit_range<B1,B2> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3>
    Dart_of_orbit_range<B1,B2,B3> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4>
    Dart_of_orbit_range<B1,B2,B3,B4> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5>
    Dart_of_orbit_range<B1,B2,B3,B4,B5> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4,B5>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6>
    Dart_of_orbit_range<B1,B2,B3,B4,B5,B6> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4,B5,B6>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7>
    Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7> darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8>
    Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7,B8> darts_of_orbit
    (Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7,B8>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8,
              unsigned int B9>
    Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
    darts_of_orbit(Dart_handle adart)
    { return Dart_of_orbit_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>(*this,adart); }
    //--------------------------------------------------------------------------
    // Const versions.
    Dart_of_orbit_const_range<> darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1>
    Dart_of_orbit_const_range<B1> darts_of_orbit(Dart_const_handle
                                                 adart) const
    { return Dart_of_orbit_const_range<B1>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2>
    Dart_of_orbit_const_range<B1,B2> darts_of_orbit(Dart_const_handle
                                                    adart) const
    { return Dart_of_orbit_const_range<B1,B2>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3>
    Dart_of_orbit_const_range<B1,B2,B3> darts_of_orbit
    (Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4>
    Dart_of_orbit_const_range<B1,B2,B3,B4>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5>
    Dart_of_orbit_const_range<B1,B2,B3,B4,B5>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4,B5>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6>
    Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7>
    Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8>
    Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7,B8>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7,B8>(*this,adart); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8,
              unsigned int B9>
    Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
    darts_of_orbit(Dart_const_handle adart) const
    { return Dart_of_orbit_const_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
        (*this,adart); }
    //--------------------------------------------------------------------------
    // Basic versions
    Dart_of_orbit_basic_range<> darts_of_orbit_basic(Dart_handle adart,
                                                     int amark=-1)
    { return Dart_of_orbit_basic_range<>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    Dart_of_orbit_basic_const_range<> darts_of_orbit_basic
    (Dart_const_handle adart,int amark=-1) const
    { return Dart_of_orbit_basic_const_range<>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1>
    Dart_of_orbit_basic_range<B1> darts_of_orbit_basic(Dart_handle adart,
                                                       int amark=-1)
    { return Dart_of_orbit_basic_range<B1>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1>
    Dart_of_orbit_basic_const_range<B1> darts_of_orbit_basic
    (Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2>
    Dart_of_orbit_basic_range<B1,B2> darts_of_orbit_basic(Dart_handle adart,
                                                          int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2>
    Dart_of_orbit_basic_const_range<B1,B2> darts_of_orbit_basic
    (Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3>
    Dart_of_orbit_basic_range<B1,B2,B3> darts_of_orbit_basic(Dart_handle adart,
                                                             int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3>
    Dart_of_orbit_basic_const_range<B1,B2,B3> darts_of_orbit_basic
    (Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4>
    Dart_of_orbit_basic_range<B1,B2,B3,B4> darts_of_orbit_basic
    (Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5>
    Dart_of_orbit_basic_range<B1,B2,B3,B4,B5> darts_of_orbit_basic
    (Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4,B5>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6>
    Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6> darts_of_orbit_basic
    (Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7>
    Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7> darts_of_orbit_basic
    (Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8>
    Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7,B8> darts_of_orbit
    (Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7,B8>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7,B8>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7,B8>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8,
              unsigned int B9>
    Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
    darts_of_orbit_basic(Dart_handle adart, int amark=-1)
    { return Dart_of_orbit_basic_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template <unsigned int B1,unsigned int B2,unsigned int B3,unsigned int B4,
              unsigned int B5,unsigned int B6,unsigned int B7,unsigned int B8,
              unsigned int B9>
    Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
    darts_of_orbit_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_orbit_basic_const_range<B1,B2,B3,B4,B5,B6,B7,B8,B9>
        (*this,adart,amark); }
    //**************************************************************************
#endif //CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
    //**************************************************************************
    // Dart_of_cell_basic_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_cell_basic_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_basic_of_cell<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_basic_of_cell<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_basic_of_cell<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_basic_of_cell<Self,i,dim> > Base;

      Dart_of_cell_basic_range(Self &amap, Dart_handle adart, int amark=-1) :
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_cell_basic_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_cell_basic_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_basic_of_cell<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_basic_of_cell<Self,i,dim> > Base;

      Dart_of_cell_basic_const_range(const Self &amap, Dart_const_handle adart,
                                     int amark=-1) :
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_cell_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_cell_range: public CGAL::CMap_range
    <Self,CMap_dart_iterator_of_cell<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_of_cell<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self,CMap_dart_iterator_of_cell<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_of_cell<Self,i,dim> > Base;

      Dart_of_cell_range(Self &amap, Dart_handle adart) :
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // Dart_of_cell_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_cell_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_of_cell<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_of_cell<Self,i,dim> > Base;

      Dart_of_cell_const_range(const Self &amap, Dart_const_handle adart) :
        Base(amap, adart)
      {}
    };
    //--------------------------------------------------------------------------
    /// @return a range on all the darts of the given i-cell
    template<unsigned int i, int dim>
    Dart_of_cell_basic_range<i,dim> darts_of_cell_basic(Dart_handle adart,
                                                        int amark=-1)
    { return Dart_of_cell_basic_range<i,dim>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i, int dim>
    Dart_of_cell_basic_const_range<i,dim> darts_of_cell_basic
    (Dart_const_handle adart, int amark=-1) const
    { return Dart_of_cell_basic_const_range<i,dim>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_cell_basic_range<i,Self::dimension>
    darts_of_cell_basic(Dart_handle adart, int amark=-1)
    { return darts_of_cell_basic<i,Self::dimension>(adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_cell_basic_const_range<i,Self::dimension>
    darts_of_cell_basic(Dart_const_handle adart, int amark=-1) const
    { return darts_of_cell_basic<i,Self::dimension>(adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i, int dim>
    Dart_of_cell_range<i,dim> darts_of_cell(Dart_handle adart)
    { return Dart_of_cell_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i, int dim>
    Dart_of_cell_const_range<i,dim> darts_of_cell(Dart_const_handle adart) const
    { return Dart_of_cell_const_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_cell_range<i,Self::dimension> darts_of_cell(Dart_handle adart)
    { return darts_of_cell<i,Self::dimension>(adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_cell_const_range<i,Self::dimension>
    darts_of_cell(Dart_const_handle adart) const
    { return darts_of_cell<i,Self::dimension>(adart); }
    //**************************************************************************
    // Dart_of_involution_basic_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_basic_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_basic_of_involution<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_basic_of_involution<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_basic_of_involution<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_basic_of_involution<Self,i,dim> > Base;

      Dart_of_involution_basic_range(Self &amap, Dart_handle adart,
                                     int amark=-1):
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_involution_basic_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_basic_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_basic_of_involution<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_basic_of_involution<Self,i,dim> >
      Base;

      Dart_of_involution_basic_const_range(const Self &amap,
                                           Dart_const_handle adart,
                                           int amark=-1) :
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    template<unsigned int i,int dim>
    Dart_of_involution_basic_range<i,dim>
    darts_of_involution_basic(Dart_handle adart, int amark=-1)
    { return Dart_of_involution_basic_range<i,dim>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i,int dim>
    Dart_of_involution_basic_const_range<i,dim>
    darts_of_involution_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_involution_basic_const_range<i,dim>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_basic_range<i,Self::dimension>
    darts_of_involution_basic(Dart_handle adart, int amark=-1)
    { return Dart_of_involution_basic_range<i,Self::dimension>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_basic_const_range<i,Self::dimension>
    darts_of_involution_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_involution_basic_const_range<i,Self::dimension>
        (*this,adart,amark); }
    //**************************************************************************
    // Dart_of_involution_inv_basic_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_inv_basic_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_basic_of_involution_inv<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_basic_of_involution_inv<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_basic_of_involution_inv<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_basic_of_involution_inv<Self,i,dim> >
      Base;

      Dart_of_involution_inv_basic_range(Self &amap, Dart_handle adart,
                                         int amark=-1):
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    // Dart_of_involution_inv_basic_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_inv_basic_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_basic_of_involution_inv<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_basic_of_involution_inv
      <Self,i,dim> >
      Base;

      Dart_of_involution_inv_basic_const_range(const Self &amap,
                                               Dart_const_handle adart,
                                               int amark=-1) :
        Base(amap, adart, amark)
      {}
    };
    //**************************************************************************
    template<unsigned int i,int dim>
    Dart_of_involution_inv_basic_range<i,dim>
    darts_of_involution_inv_basic(Dart_handle adart, int amark=-1)
    { return Dart_of_involution_inv_basic_range<i,dim>(*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i,int dim>
    Dart_of_involution_inv_basic_const_range<i,dim>
    darts_of_involution_inv_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_involution_inv_basic_const_range<i,dim>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_inv_basic_range<i,Self::dimension>
    darts_of_involution_inv_basic(Dart_handle adart, int amark=-1)
    { return Dart_of_involution_inv_basic_range<i,Self::dimension>
        (*this,adart,amark); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_inv_basic_const_range<i,Self::dimension>
    darts_of_involution_inv_basic(Dart_const_handle adart, int amark=-1) const
    { return Dart_of_involution_inv_basic_const_range<i,Self::dimension>
        (*this,adart,amark); }
    //**************************************************************************
    // Dart_of_involution_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_of_involution<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_of_involution<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_of_involution<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_of_involution<Self,i,dim> > Base;

      Dart_of_involution_range(Self &amap, Dart_handle adart) :
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // Dart_of_involution_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_of_involution<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_of_involution<Self,i,dim> > Base;

      Dart_of_involution_const_range(const Self &amap,
                                     Dart_const_handle adart):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    template<unsigned int i,int dim>
    Dart_of_involution_range<i,dim>
    darts_of_involution(Dart_handle adart)
    { return Dart_of_involution_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i,int dim>
    Dart_of_involution_const_range<i,dim>
    darts_of_involution(Dart_const_handle adart) const
    { return Dart_of_involution_const_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_range<i,Self::dimension>
    darts_of_involution(Dart_handle adart)
    { return Dart_of_involution_range<i,Self::dimension>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_const_range<i,Self::dimension>
    darts_of_involution(Dart_const_handle adart) const
    { return Dart_of_involution_const_range<i,Self::dimension>(*this,adart); }
    //**************************************************************************
    // Dart_of_involution_inv_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_inv_range: public CGAL::CMap_range
    <Self, CGAL::CMap_dart_iterator_of_involution_inv<Self,i,dim>,
     CGAL::CMap_dart_const_iterator_of_involution_inv<Self,i,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_dart_iterator_of_involution_inv<Self,i,dim>,
       CGAL::CMap_dart_const_iterator_of_involution_inv<Self,i,dim> > Base;

      Dart_of_involution_inv_range(Self &amap, Dart_handle adart) :
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // Dart_of_involution_inv_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct Dart_of_involution_inv_const_range: public CMap_const_range
    <Self, CGAL::CMap_dart_const_iterator_of_involution_inv<Self,i,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_dart_const_iterator_of_involution_inv<Self,i,dim> >
      Base;

      Dart_of_involution_inv_const_range(const Self &amap,
                                         Dart_const_handle adart):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    template<unsigned int i,int dim>
    Dart_of_involution_inv_range<i,dim>
    darts_of_involution_inv(Dart_handle adart)
    { return Dart_of_involution_inv_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i,int dim>
    Dart_of_involution_inv_const_range<i,dim>
    darts_of_involution_inv(Dart_const_handle adart) const
    { return Dart_of_involution_inv_const_range<i,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_inv_range<i,Self::dimension>
    darts_of_involution_inv(Dart_handle adart)
    { return Dart_of_involution_inv_range<i,Self::dimension>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    Dart_of_involution_inv_const_range<i,Self::dimension>
    darts_of_involution_inv(Dart_const_handle adart) const
    { return Dart_of_involution_inv_const_range<i,Self::dimension>
        (*this,adart); }
    //**************************************************************************
    // Dart_basic_range
    struct Dart_basic_range {
      typedef CGAL::CMap_dart_iterator_basic_of_all<Self> iterator;
      typedef CGAL::CMap_dart_const_iterator_basic_of_all<Self> const_iterator;
      Dart_basic_range(Self &amap) : mmap(amap)
      {}
      iterator begin() { return iterator(mmap); }
      iterator end()   { return iterator(mmap,NULL); }
      const_iterator begin() const { return const_iterator(mmap); }
      const_iterator end() const   { return const_iterator(mmap,NULL); }
      size_type size()
      { return mmap.number_of_darts(); }
      bool empty() const
      { return mmap.is_empty(); }
    private:
      Self & mmap;
    };
    //**************************************************************************
    // Dart_basic_const_range
    struct Dart_basic_const_range {
      typedef CGAL::CMap_dart_const_iterator_basic_of_all<Self> const_iterator;
      Dart_basic_const_range(Self &amap) : mmap(amap)
      {}
      const_iterator begin() const { return const_iterator(mmap); }
      const_iterator end() const   { return const_iterator(mmap,NULL); }
      size_type size() const
      { return mmap.number_of_darts(); }
      bool empty() const
      { return mmap.is_empty(); }
    private:
      const Self & mmap;
    };
    //**************************************************************************
    Dart_basic_range darts_basic()
    { return Dart_basic_range(*this); }
    //--------------------------------------------------------------------------
    Dart_basic_const_range darts_basic() const
    { return Dart_basic_const_range(*this); }
    //**************************************************************************
    // One_dart_per_incident_cell_range
    template<unsigned int i,unsigned int j,int dim=Self::dimension>
    struct One_dart_per_incident_cell_range: public CGAL::CMap_range
    <Self, CGAL::CMap_one_dart_per_incident_cell_iterator<Self,i,j,dim>,
     CGAL::CMap_one_dart_per_incident_cell_const_iterator<Self,i,j,dim> >
    {
      typedef CGAL::CMap_range
      <Self, CGAL::CMap_one_dart_per_incident_cell_iterator<Self,i,j,dim>,
       CGAL::CMap_one_dart_per_incident_cell_const_iterator<Self,i,j,dim> >
      Base;

      One_dart_per_incident_cell_range(Self &amap, Dart_handle adart):
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // One_dart_per_incident_cell_const_range
    template<unsigned int i,unsigned int j,int dim=Self::dimension>
    struct One_dart_per_incident_cell_const_range: public CMap_const_range
    <Self, CGAL::CMap_one_dart_per_incident_cell_const_iterator<Self,i,j,dim> >
    {
      typedef CMap_const_range
      <Self, CGAL::CMap_one_dart_per_incident_cell_const_iterator
      <Self,i,j,dim> > Base;

      One_dart_per_incident_cell_const_range(const Self &amap,
                                             Dart_const_handle adart) :
        Base(amap, adart)
      {}
    };
    //**************************************************************************
    // One_dart_per_cell_range
    template<unsigned int i,int dim=Self::dimension>
    struct One_dart_per_cell_range {
      typedef CGAL::CMap_one_dart_per_cell_iterator<Self,i,dim> iterator;
      typedef CGAL::CMap_one_dart_per_cell_const_iterator<Self,i,dim>
      const_iterator;
      One_dart_per_cell_range(Self &amap) : mmap(amap), msize(0)
      {}
      iterator begin() { return iterator(mmap); }
      iterator end()   { return iterator(mmap,NULL); }
      const_iterator begin() const { return const_iterator(mmap); }
      const_iterator end() const   { return const_iterator(mmap,NULL); }
      size_type size()
      {
        if (msize==0)
          for ( const_iterator it=begin(); it!=end(); ++it)
            ++msize;
        return msize;
      }
      bool empty() const
      { return mmap.is_empty(); }
    private:
      Self & mmap;
      size_type msize;
    };
    //**************************************************************************
    // One_dart_per_cell_const_range
    template<unsigned int i,int dim=Self::dimension>
    struct One_dart_per_cell_const_range {
      typedef CGAL::CMap_one_dart_per_cell_const_iterator<Self,i,dim>
      const_iterator;
      One_dart_per_cell_const_range(const Self &amap) : mmap(amap), msize(0)
      {}
      const_iterator begin() const { return const_iterator(mmap); }
      const_iterator end() const   { return const_iterator(mmap,NULL); }
      size_type size()
      {
        if (msize==0)
          for ( const_iterator it=begin(); it!=end(); ++it)
            ++msize;
        return msize;
      }
      bool empty() const
      { return mmap.is_empty(); }
    private:
      const Self & mmap;
      size_type msize;
    };
    //**************************************************************************
    /// @return a range on the i-cells incindent to the given j-cell.
    template<unsigned int i, unsigned int j, int dim>
    One_dart_per_incident_cell_range<i,j,dim>
    one_dart_per_incident_cell(Dart_handle adart)
    { return One_dart_per_incident_cell_range<i,j,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i, unsigned int j, int dim>
    One_dart_per_incident_cell_const_range<i,j,dim>
    one_dart_per_incident_cell(Dart_const_handle adart) const
    { return One_dart_per_incident_cell_const_range<i,j,dim>(*this,adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i, unsigned int j>
    One_dart_per_incident_cell_range<i,j,Self::dimension>
    one_dart_per_incident_cell(Dart_handle adart)
    { return one_dart_per_incident_cell<i,j,Self::dimension>(adart); }
    //--------------------------------------------------------------------------
    template<unsigned int i, unsigned int j>
    One_dart_per_incident_cell_const_range<i,j,Self::dimension>
    one_dart_per_incident_cell(Dart_const_handle adart) const
    { return one_dart_per_incident_cell<i,j,Self::dimension>(adart); }
    //--------------------------------------------------------------------------
    /// @return a range on all the i-cells
    template<unsigned int i, int dim>
    One_dart_per_cell_range<i,dim> one_dart_per_cell()
    { return One_dart_per_cell_range<i,dim>(*this); }
    //--------------------------------------------------------------------------
    template<unsigned int i, int dim>
    One_dart_per_cell_const_range<i,dim> one_dart_per_cell() const
    { return One_dart_per_cell_const_range<i,dim>(*this); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    One_dart_per_cell_range<i,Self::dimension> one_dart_per_cell()
    { return one_dart_per_cell<i,Self::dimension>(); }
    //--------------------------------------------------------------------------
    template<unsigned int i>
    One_dart_per_cell_const_range<i,Self::dimension> one_dart_per_cell() const
    { return one_dart_per_cell<i,Self::dimension>(); }
    //--------------------------------------------------------------------------

  public:

    /** Compute the dual of a Combinatorial_map.
     * @param amap the cmap in which we build the dual of this map.
     * @param adart a dart of the initial map, NULL by default.
     * @return adart of the dual map, the dual of adart if adart!=NULL,
     *         any dart otherwise.
     * As soon as we don't modify this map and amap map, we can iterate
     * simultaneously through all the darts of the two maps and we have
     * each time of the iteration two "dual" darts.
     */
    Dart_handle dual(Self& amap, Dart_handle adart=NULL)
    {
      CGAL_assertion( is_without_boundary(dimension) );

      CGAL::Unique_hash_map< Dart_handle, Dart_handle > dual;
      Dart_handle d, d2, res = NULL;

      // We clear amap. TODO return a new amap ? (but we need to make
      // a copy contructor and =operator...)
      amap.clear();

      // We create a copy of all the dart of the map.
      for ( typename Dart_range::iterator it=darts().begin();
            it!=darts().end(); ++it)
      {
        dual[it] = amap.create_dart();
        if ( it==adart && res==NULL ) res = dual[it];
      }

      // Then we link the darts by using the dual formula :
      // G(B,b1,b2,...,bn-1,bn) =>
      //    dual(G)=(B, b(n-1)obn, b(n-2)obn,...,b1obn, bn)
      // We suppose darts are run in the same order for both maps.
      typename Dart_range::iterator it2=amap.darts().begin();
      for ( typename Dart_range::iterator it=darts().begin();
            it!=darts().end(); ++it, ++it2)
      {
        d = it2; // The supposition on the order allows to avoid d=dual[it];
        CGAL_assertion( it2==dual[it] );

        // First case outside the loop since we need to use link_beta1
        if ( d->template is_free<1>() && it->template beta<dimension>()->
             template beta<dimension-1>()!=null_dart_handle )
          amap.basic_link_beta_1(d, dual[it->template beta<dimension>()->
                                 template beta<dimension-1>()]);

        // and during the loop we use link_beta(d1,d2,i)
        for ( unsigned int i=dimension-2; i>=1; --i)
        {
          if ( d->is_free(dimension-i) &&
               it->template beta<dimension>()->beta(i)!=null_dart_handle )
            amap.basic_link_beta(d, dual[it->template beta<dimension>()->
                                 beta(i)], dimension-i);
        }
        if ( d->template is_free<dimension>() )
        {
          CGAL_assertion ( !it->template is_free<dimension>() );
          amap.basic_link_beta(d, dual[it->template beta<dimension>()],
                               dimension);
        }
      }

      //  CGAL_postcondition(amap2.is_valid());

      if ( res==NULL ) res = amap.darts().begin();
      return res;
    }

    /// Void dart. A dart d is i-free if beta_i(d)=null_dart_handle.
    static Dart_handle null_dart_handle;

  protected:
    /// Dart container.
    Dart_container mdarts;

    /// Container for the null_dart_handle, static data member.
    static Dart_container mnull_dart_container;

    /// Number of times each mark is reserved. 0 if the mark is free.
    mutable size_type mnb_times_reserved_marks[NB_MARKS];

    /// Mask marks to know the value of unmark dart, for each index i.
    mutable std::bitset<NB_MARKS> mmask_marks;

    /// Number of used marks.
    mutable size_type mnb_used_marks;

    /// Index of each mark, in mfree_marks_stack or in mfree_marks_stack.
    mutable size_type mindex_marks[NB_MARKS];

    /// "Stack" of free marks.
    mutable int mfree_marks_stack[NB_MARKS];

    /// "Stack" of used marks.
    mutable int mused_marks_stack[NB_MARKS];

    /// Number of marked darts for each used marks.
    mutable size_type mnb_marked_darts[NB_MARKS];

    /// Tuple of attributes containers
    typename Helper::Attribute_containers mattribute_containers;
  };

  /// Allocation of static data members
  /// mnull_dart_container
  template < unsigned int d_, class Refs, class Items_, class Alloc_ >
  typename Combinatorial_map_base<d_, Refs, Items_, Alloc_>::Dart_container
  Combinatorial_map_base<d_, Refs, Items_, Alloc_>::mnull_dart_container;

  /// null_dart_handle
  template < unsigned int d_, class Refs, class Items_, class Alloc_ >
  typename Combinatorial_map_base<d_, Refs, Items_, Alloc_>::Dart_handle
  Combinatorial_map_base<d_, Refs, Items_, Alloc_>::null_dart_handle;
  // =  mnull_dart_container.emplace( std::bitset<NB_MARKS>() );
  // Does not work on windows => segfault
  // Thus we initialize null_dart_handle in the Combinatorial_map constructor

  template < unsigned int d_,
             class Items_=Combinatorial_map_min_items<d_>,
             class Alloc_=CGAL_ALLOCATOR(int) >
  class Combinatorial_map :
    public Combinatorial_map_base<d_,
                                  Combinatorial_map<d_,Items_,Alloc_>,
                                  Items_, Alloc_ >
  {
  public:
    typedef Combinatorial_map<d_, Items_,Alloc_>  Self;
    typedef Combinatorial_map_base<d_, Self, Items_, Alloc_> Base;

    typedef typename Base::Dart_handle Dart_handle;
    typedef typename Base::Dart_const_handle Dart_const_handle;
    typedef typename Base::Alloc Alloc;
  };

} // namespace CGAL

#endif // CGAL_COMBINATORIAL_MAP_H //
// EOF //