// Copyright (c) 1997-2013 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Periodic_2_triangulation_2/include/CGAL/Periodic_2_triangulation_iterators_2.h $
// $Id: include/CGAL/Periodic_2_triangulation_iterators_2.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Nico Kruithof <Nico@nghk.nl>

#ifndef CGAL_PERIODIC_2_TRIANGULATION_ITERATORS_2_H
#define CGAL_PERIODIC_2_TRIANGULATION_ITERATORS_2_H

#include <CGAL/license/Periodic_2_triangulation_2.h>

#include <CGAL/assertions.h>
#include <CGAL/iterator.h>
#include <CGAL/array.h>

namespace CGAL {

template < class T >
class Periodic_2_triangulation_triangle_iterator_2
{
  // Iterates over the primitives in a periodic triangulation.
  // Options:
  // - STORED: output each primitive from the Tds exactly once
  // - UNIQUE: output exactly one periodic copy of each primitive, no matter
  //     whether the current tds stores a n-sheeted covering for n!=1.
  // - STORED_COVER_DOMAIN: output each primitive whose intersection with the
  //     actually used periodic domain is non-zero.
  // - UNIQUE_COVER_DOMAIN: output each primitive whose intersection
  //     with the original domain that the user has given is non-zero
  //
  // Comments:
  // When computing in 1-sheeted covering, there will be no difference in the
  // result of STORED and UNIQUE as well as STORED_COVER_DOMAIN and
  // UNIQUE_COVER_DOMAIN.

public:

  typedef typename T::Periodic_triangle                   value_type;
  typedef const typename T::Periodic_triangle *           pointer;
  typedef const typename T::Periodic_triangle &           reference;
  typedef std::size_t                                     size_type;
  typedef std::ptrdiff_t                                  difference_type;
  typedef std::bidirectional_iterator_tag                 iterator_category;

  typedef typename T::Periodic_triangle                   Periodic_triangle;
  typedef Periodic_2_triangulation_triangle_iterator_2<T> Periodic_triangle_iterator;
  typedef typename T::Face                                Face;
  typedef typename T::Face_iterator                       Face_iterator;

  typedef typename T::Offset                              Offset;
  typedef typename T::Iterator_type                       Iterator_type;

  Periodic_2_triangulation_triangle_iterator_2(Iterator_type it = T::STORED)
    : _t(nullptr), _it(it), _off(0) {}

  Periodic_2_triangulation_triangle_iterator_2(const T * t,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->faces_begin()), _it(it), _off(0)
  {
    if (_it == T::UNIQUE || _it == T::UNIQUE_COVER_DOMAIN)
      {
        while (pos != _t->faces_end() && !_t->is_canonical(pos) )
          ++pos;
      }
  }

  // used to initialize the past-the-end iterator
  Periodic_2_triangulation_triangle_iterator_2(const T* t, int,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->faces_end()), _it(it), _off(0) {}

  Periodic_triangle_iterator& operator++()
  {
    switch (_it)
      {
      case T::STORED:
        ++pos;
        break;
      case T::UNIQUE:
        do
          {
            ++pos;
          }
        while (pos != _t->faces_end() && !_t->is_canonical(pos));
        break;
      case T::STORED_COVER_DOMAIN:
      case T::UNIQUE_COVER_DOMAIN:
        increment_domain();
        break;
      default:
        CGAL_assertion(false);
      };
    return *this;
  }

  Periodic_triangle_iterator& operator--()
  {
    switch (_it)
      {
      case T::STORED:
        --pos;
        break;
      case T::UNIQUE:
        do
          {
            --pos;
          }
        while (pos != _t->faces_begin() && !_t->is_canonical(pos));
        break;
      case T::STORED_COVER_DOMAIN:
      case T::UNIQUE_COVER_DOMAIN:
        decrement_domain();
      };
    return *this;
  }

  Periodic_triangle_iterator operator++(int)
  {
    Periodic_triangle_iterator tmp(*this);
    ++(*this);
    return tmp;
  }

  Periodic_triangle_iterator operator--(int)
  {
    Periodic_triangle_iterator tmp(*this);
    --(*this);
    return tmp;
  }

  bool operator==(const Periodic_triangle_iterator& ti) const
  {
    // We are only allowed to compare iterators of the same type.
    CGAL_assertion(_it == ti._it);
    return _t == ti._t && pos == ti.pos && _off == ti._off;
  }

  bool operator!=(const Periodic_triangle_iterator& ti) const
  {
    return !(*this == ti);
  }

  reference operator*() const
  {
    periodic_triangle = construct_periodic_triangle();
    return periodic_triangle;
  }

  pointer operator->() const
  {
    periodic_triangle = construct_periodic_triangle();
    return &periodic_triangle;
  }

  Face_iterator get_face() const
  {
    return pos;
  }

private:
  const T*  _t;
  Face_iterator pos; // current face.
  Iterator_type _it;
  int _off; // current offset
  mutable Periodic_triangle periodic_triangle; // current triangle.

private:
  // Artificial incrementation function that takes periodic
  // copies into account.
  void increment_domain()
  {
    int off = get_drawing_offsets();
    CGAL_assertion(_off <= off);
    if (_off == off)
      {
        _off = 0;
        do
          {
            ++pos;
          }
        while (_it == T::UNIQUE_COVER_DOMAIN
               && pos != _t->faces_end() && !_t->is_canonical(pos));
      }
    else
      {
        do
          {
            ++_off;
          }
        while ((((~_off) | off) & 3) != 3); // Increment until a valid
        // offset has been found
      }
  }

  // Artificial decrementation function that takes periodic
  // copies into account.
  void decrement_domain()
  {
    if (_off == 0)
      {
        if (pos == _t->faces_begin()) return;
        do
          {
            --pos;
          }
        while (_it == T::UNIQUE_COVER_DOMAIN && !_t->is_canonical(pos));
        _off = get_drawing_offsets();
      }
    else
      {
        int off = get_drawing_offsets();
        do
          {
            --_off;
          }
        while ((((~_off) | off) & 3) != 3); // Decrement until a valid
        // offset has been found
      }
  }

  // return an integer that encodes the translations which have to be
  // applied to the edge *pos
  int get_drawing_offsets()
  {
    Offset off0, off1, off2;
    // Choose edges that are to be duplicated. These are edges that
    // intersect the boundary of the periodic domain. In UNIQUE mode
    // this means that the offset with respect to drawing should
    // differ in some entries. Otherwise we consider the offsets
    // internally stored inside the face telling us that this face
    // wraps around the domain.
    if (_it == T::UNIQUE_COVER_DOMAIN)
      _t->get_offsets(pos, off0, off1, off2);
    else
      {
        CGAL_assertion(_it == T::STORED_COVER_DOMAIN);
        off0 = _t->int_to_off(pos->offset(0));
        off1 = _t->int_to_off(pos->offset(1));
        off2 = _t->int_to_off(pos->offset(2));
      }

    CGAL_assertion(off0.x() == 0 || off0.x() == 1);
    CGAL_assertion(off0.y() == 0 || off0.y() == 1);
    CGAL_assertion(off1.x() == 0 || off1.x() == 1);
    CGAL_assertion(off1.y() == 0 || off1.y() == 1);
    CGAL_assertion(off2.x() == 0 || off2.x() == 1);
    CGAL_assertion(off2.y() == 0 || off2.y() == 1);

    int offx = ( ((off0.x() == 0 && off1.x() == 0
                   && off2.x() == 0)
                  || (off0.x() == 1 && off1.x() == 1
                      && off2.x() == 1)) ? 0 : 1);
    int offy = ( ((off0.y() == 0 && off1.y() == 0
                   && off2.y() == 0)
                  || (off0.y() == 1 && off1.y() == 1
                      && off2.y() == 1)) ? 0 : 1);

    return( 2 * offx + offy );
  }

  Periodic_triangle construct_periodic_triangle() const
  {
    CGAL_assertion(pos != typename T::Face_handle());
    Offset off0, off1, off2;
    _t->get_offsets(pos, off0, off1, off2);
    Offset transl_off = Offset((((_off >> 1) & 1) == 1 ? -1 : 0),
                               (((_off   ) & 1) == 1 ? -1 : 0));
    if (_it == T::STORED_COVER_DOMAIN)
      {
        off0 = _t->combine_offsets(off0, transl_off);
        off1 = _t->combine_offsets(off1, transl_off);
        off2 = _t->combine_offsets(off2, transl_off);
      }
    if (_it == T::UNIQUE_COVER_DOMAIN)
      {
        off0 += transl_off;
        off1 += transl_off;
        off2 += transl_off;
      }
    return make_array(std::make_pair(pos->vertex(0)->point(), off0),
                      std::make_pair(pos->vertex(1)->point(), off1),
                      std::make_pair(pos->vertex(2)->point(), off2));
  }
};

template < class T >
class Periodic_2_triangulation_segment_iterator_2
{
  // Iterates over the primitives in a periodic triangulation.
  // Options:
  // - STORED: output each primitive from the Tds exactly once
  // - UNIQUE: output exactly one periodic copy of each primitive, no matter
  //     whether the current tds stores a n-sheeted covering for n!=1.
  // - STORED_COVER_DOMAIN: output each primitive whose intersection with the
  //     actually used periodic domain is non-zero.
  // - UNIQUE_COVER_DOMAIN: output each primitive whose intersection
  //     with the original domain that the user has given is non-zero
  //
  // Comments:
  // When computing in 1-sheeted covering, there will be no difference in the
  // result of STORED and UNIQUE as well as STORED_COVER_DOMAIN and
  // UNIQUE_COVER_DOMAIN.

public:

  typedef typename T::Periodic_segment                    value_type;
  typedef const typename T::Periodic_segment *            pointer;
  typedef const typename T::Periodic_segment &            reference;
  typedef std::size_t                                     size_type;
  typedef std::ptrdiff_t                                  difference_type;
  typedef std::bidirectional_iterator_tag                 iterator_category;

  typedef typename T::Periodic_segment                    Periodic_segment;
  typedef Periodic_2_triangulation_segment_iterator_2<T>
  Periodic_segment_iterator;
  typedef typename T::Edge                                Edge;
  typedef typename T::Edge_iterator                       Edge_iterator;

  typedef typename T::Offset                              Offset;
  typedef typename T::Iterator_type                       Iterator_type;

  Periodic_2_triangulation_segment_iterator_2(Iterator_type it = T::STORED)
    : _t(nullptr), _it(it), _off(0) {}

  Periodic_2_triangulation_segment_iterator_2(const T * t,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->edges_begin()), _it(it), _off(0)
  {
    if (_it == T::UNIQUE || _it == T::UNIQUE_COVER_DOMAIN)
      {
        while (pos != _t->edges_end() && !_t->is_canonical(*pos) )
          ++pos;
      }
  }

  // used to initialize the past-the-end iterator
  Periodic_2_triangulation_segment_iterator_2(const T* t, int,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->edges_end()), _it(it), _off(0) {}

  Periodic_segment_iterator& operator++()
  {
    switch (_it)
      {
      case T::STORED:
        ++pos;
        break;
      case T::UNIQUE:
        do
          {
            ++pos;
          }
        while (pos != _t->edges_end() && !_t->is_canonical(*pos));
        break;
      case T::STORED_COVER_DOMAIN:
      case T::UNIQUE_COVER_DOMAIN:
        increment_domain();
        break;
      default:
        CGAL_assertion(false);
      };
    return *this;
  }

  Periodic_segment_iterator& operator--()
  {
    switch (_it)
      {
      case T::STORED:
        --pos;
        break;
      case T::UNIQUE:
        do
          {
            --pos;
          }
        while (pos != _t->edges_begin() && !_t->is_canonical(*pos));
        break;
      case T::STORED_COVER_DOMAIN:
      case T::UNIQUE_COVER_DOMAIN:
        decrement_domain();
      };
    return *this;
  }

  Periodic_segment_iterator operator++(int)
  {
    Periodic_segment_iterator tmp(*this);
    ++(*this);
    return tmp;
  }

  Periodic_segment_iterator operator--(int)
  {
    Periodic_segment_iterator tmp(*this);
    --(*this);
    return tmp;
  }

  bool operator==(const Periodic_segment_iterator& ti) const
  {
    // We are only allowed to compare iterators of the same type.
    CGAL_assertion(_it == ti._it);
    return _t == ti._t && pos == ti.pos && _off == ti._off;
  }

  bool operator!=(const Periodic_segment_iterator& ti) const
  {
    return !(*this == ti);
  }

  reference operator*() const
  {
    periodic_segment = construct_periodic_segment();
    return periodic_segment;
  }

  pointer operator->() const
  {
    periodic_segment = construct_periodic_segment();
    return &periodic_segment;
  }

  Edge_iterator get_edge() const
  {
    return pos;
  }
private:
  const T*  _t;
  Edge_iterator pos; // current edge.
  Iterator_type _it;
  int _off; // current offset
  mutable Periodic_segment periodic_segment; // current segment.

private:
  // Artificial incrementation function that takes periodic
  // copies into account.
  void increment_domain()
  {
    int off = get_drawing_offsets();
    CGAL_assertion(_off <= off);
    if (_off == off)
      {
        _off = 0;
        do
          {
            ++pos;
          }
        while (_it == T::UNIQUE_COVER_DOMAIN
               && pos != _t->edges_end() && !_t->is_canonical(*pos));
      }
    else
      {
        do
          {
            ++_off;
          }
        while ((((~_off) | off) & 3) != 3); // Increment until a valid
        // offset has been found
      }
  }

  // Artificial decrementation function that takes periodic
  // copies into account.
  void decrement_domain()
  {
    if (_off == 0)
      {
        if (pos == _t->edges_begin()) return;
        do
          {
            --pos;
          }
        while (_it == T::UNIQUE_COVER_DOMAIN && !_t->is_canonical(*pos));
        _off = get_drawing_offsets();
      }
    else
      {
        int off = get_drawing_offsets();
        do
          {
            --_off;
          }
        while ((((~_off) | off) & 3) != 3); // Decrement until a valid
        // offset has been found
      }
  }

  // return an integer that encodes the translations which have to be
  // applied to the edge *pos
  int get_drawing_offsets()
  {
    Offset off0, off1;
    // Choose edges that are to be duplicated. These are edges that
    // intersect the boundary of the periodic domain. In UNIQUE mode
    // this means that the offset with respect to drawing should
    // differ in some entries. Otherwise we consider the offsets
    // internally stored inside the face telling us that this face
    // wraps around the domain.
    if (_it == T::UNIQUE_COVER_DOMAIN)
      _t->get_offsets(*pos, off0, off1);
    else
      {
        CGAL_assertion(_it == T::STORED_COVER_DOMAIN);
        off0 = _t->int_to_off(pos->first->offset(_t->cw(pos->second)));
        off1 = _t->int_to_off(pos->first->offset(_t->ccw(pos->second)));
      }
    Offset diff_off = off0 - off1;

    CGAL_assertion(diff_off.x() >= -1 || diff_off.x() <= 1);
    CGAL_assertion(diff_off.y() >= -1 || diff_off.y() <= 1);

    return( 2 * (diff_off.x() == 0 ? 0 : 1)
            + (diff_off.y() == 0 ? 0 : 1));
  }

  Periodic_segment construct_periodic_segment() const
  {
    CGAL_assertion(pos->first != typename T::Face_handle());
    Offset off0, off1;
    _t->get_offsets(*pos, off0, off1);
    Offset transl_off = Offset((((_off >> 1) & 1) == 1 ? -1 : 0),
                               (( _off    & 1) == 1 ? -1 : 0));
    if (_it == T::STORED_COVER_DOMAIN)
      {
        off0 = _t->combine_offsets(off0, transl_off);
        off1 = _t->combine_offsets(off1, transl_off);
      }
    if (_it == T::UNIQUE_COVER_DOMAIN)
      {
        off0 += transl_off;
        off1 += transl_off;
      }
    return make_array(
             std::make_pair(pos->first->vertex(_t->cw(pos->second))->point(), off0),
             std::make_pair(pos->first->vertex(_t->ccw(pos->second))->point(), off1));
  }
};

template < class T >
class Periodic_2_triangulation_point_iterator_2
{
  // Iterates over the primitives in a periodic triangulation.
  // Options:
  // - STORED: output each primitive from the Tds exactly once
  // - UNIQUE: output exactly one periodic copy of each primitive, no matter
  //     whether the current tds stores a n-sheeted covering for n!=1.
  // - STORED_COVER_DOMAIN: output each primitive whose intersection with the
  //     actually used periodic domain is non-zero.
  // - UNIQUE_COVER_DOMAIN: output each primitive whose intersection
  //     with the original domain that the user has given is non-zero
  //
  // Comments:
  // When computing in 1-sheeted covering, there will be no difference in the
  // result of STORED and UNIQUE as well as STORED_COVER_DOMAIN and
  // UNIQUE_COVER_DOMAIN.

public:
  typedef typename T::Periodic_point                      value_type;
  typedef const typename T::Periodic_point *              pointer;
  typedef const typename T::Periodic_point &              reference;
  typedef std::size_t                                     size_type;
  typedef std::ptrdiff_t                                  difference_type;
  typedef std::bidirectional_iterator_tag                 iterator_category;

  typedef typename T::Periodic_point                      Periodic_point;
  typedef Periodic_2_triangulation_point_iterator_2<T>  Periodic_point_iterator;

  typedef typename T::Vertex                              Vertex;
  typedef typename T::Vertex_iterator                     Vertex_iterator;

  typedef typename T::Offset                              Offset;
  typedef typename T::Iterator_type                       Iterator_type;

  Periodic_2_triangulation_point_iterator_2(Iterator_type it = T::STORED)
    : _t(nullptr), _it(it) {}

  Periodic_2_triangulation_point_iterator_2(const T * t,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->vertices_begin()), _it(it)
  {
    if (_it == T::UNIQUE || _it == T::UNIQUE_COVER_DOMAIN)
      {
        while (pos != _t->vertices_end() && !_t->is_canonical(pos) )
          ++pos;
      }
  }

  // used to initialize the past-the-end iterator
  Periodic_2_triangulation_point_iterator_2(const T* t, int,
      Iterator_type it = T::STORED)
    : _t(t), pos(_t->vertices_end()), _it(it) {}

  Periodic_point_iterator& operator++()
  {
    switch (_it)
      {
      case T::STORED:
      case T::STORED_COVER_DOMAIN:
        ++pos;
        break;
      case T::UNIQUE:
      case T::UNIQUE_COVER_DOMAIN:
        do
          {
            ++pos;
          }
        while (pos != _t->vertices_end() && !_t->is_canonical(pos));
        break;
      default:
        CGAL_assertion(false);
      };
    return *this;
  }

  Periodic_point_iterator& operator--()
  {
    switch (_it)
      {
      case T::STORED:
      case T::STORED_COVER_DOMAIN:
        --pos;
        break;
      case T::UNIQUE:
      case T::UNIQUE_COVER_DOMAIN:
        do
          {
            --pos;
          }
        while (pos != _t->vertices_begin() && !_t->is_canonical(pos));
        break;
      default:
        CGAL_assertion(false);
      };
    return *this;
  }

  Periodic_point_iterator operator++(int)
  {
    Periodic_point_iterator tmp(*this);
    ++(*this);
    return tmp;
  }

  Periodic_point_iterator operator--(int)
  {
    Periodic_point_iterator tmp(*this);
    --(*this);
    return tmp;
  }

  bool operator==(const Periodic_point_iterator& pi) const
  {
    // We are only allowed to compare iterators of the same type.
    CGAL_assertion(_it == pi._it);
    return _t == pi._t && pos == pi.pos;
  }

  bool operator!=(const Periodic_point_iterator& pi) const
  {
    return !(*this == pi);
  }

  reference operator*() const
  {
    periodic_point = construct_periodic_point();
    return periodic_point;
  }

  pointer operator->() const
  {
    periodic_point = construct_periodic_point();
    return &periodic_point;
  }

  Vertex_iterator get_vertex() const
  {
    return pos;
  }
private:
  const T*  _t;
  Vertex_iterator pos; // current vertex.
  Iterator_type _it;
  int _off; // current offset
  mutable Periodic_point periodic_point; // current point.

private:
  Periodic_point construct_periodic_point() const
  {
    CGAL_assertion(pos != typename T::Vertex_handle());
    Offset off = _t->get_offset(pos);
    return std::make_pair(pos->point(), off);
  }
};

namespace Periodic_2_triangulation_2_internal {

// returns `true` if the simplex is not canonical, and has to be filtered out
template <class T>
class Domain_tester
{
  typedef typename T::Offset                              Offset;

  const T *t;

public:
  Domain_tester() {}
  Domain_tester(const T *tr) : t(tr) {}

  bool operator()(const typename T::Vertex_iterator v) const
  {
    return !(t->get_offset(v).is_null());
  }

  bool operator()(const typename T::Edge_iterator e) const
  {
    Offset eo_0 = t->int_to_off(e->first->offset(t->cw(e->second)));
    Offset eo_1 = t->int_to_off(e->first->offset(t->ccw(e->second)));

    Offset diff_off((eo_0.x() == 1 && eo_1.x() == 1) ? -1 : 0,
                    (eo_0.y() == 1 && eo_1.y() == 1) ? -1 : 0);
    Offset off0 = t->combine_offsets(t->get_offset(e->first, t->cw(e->second)), diff_off);
    Offset off1 = t->combine_offsets(t->get_offset(e->first, t->ccw(e->second)), diff_off);

    if (t->number_of_sheets() != make_array(1, 1))
    {
      // If there is one offset with entries larger than 1 then we are
      // talking about a vertex that is too far away from the original
      // domain to belong to a canonical edge.
      if (off0.x() > 1) return true;
      if (off0.y() > 1) return true;
      if (off1.x() > 1) return true;
      if (off1.y() > 1) return true;
    }

    // If there is one direction of space for which all offsets are
    // non-zero then the edge is not canonical because we can
    // take the copy closer towards the origin in that direction.
    int offx = off0.x() & off1.x();
    int offy = off0.y() & off1.y();

    return (offx != 0 || offy != 0);
  }

  bool operator()(const typename T::Face_iterator f) const
  {
    Offset fo_0 = t->int_to_off(f->offset(0));
    Offset fo_1 = t->int_to_off(f->offset(1));
    Offset fo_2 = t->int_to_off(f->offset(2));

    Offset diff_off((fo_0.x() == 1 && fo_1.x() == 1 && fo_2.x() == 1) ? -1 : 0,
                    (fo_0.y() == 1 && fo_1.y() == 1 && fo_2.y() == 1) ? -1 : 0);
    Offset off0 = t->combine_offsets(t->get_offset(f, 0), diff_off);
    Offset off1 = t->combine_offsets(t->get_offset(f, 1), diff_off);
    Offset off2 = t->combine_offsets(t->get_offset(f, 2), diff_off);

    if (t->number_of_sheets() != make_array(1, 1))
    {
      // If there is one offset with entries larger than 1 then we are
      // talking about a vertex that is too far away from the original
      // domain to belong to a canonical triangle.
      if (off0.x() > 1) return true;
      if (off0.y() > 1) return true;
      if (off1.x() > 1) return true;
      if (off1.y() > 1) return true;
      if (off2.x() > 1) return true;
      if (off2.y() > 1) return true;
    }

    // If there is one direction of space for which all offsets are
    // non-zero then the edge is not canonical because we can
    // take the copy closer towards the origin in that direction.
    int offx = off0.x() & off1.x() & off2.x();
    int offy = off0.y() & off1.y() & off2.y();

    return (offx != 0 || offy != 0);
  }
};

} // Periodic_2_triangulation_2_internal

// Iterates over the vertices in a periodic triangulation that are
// located inside the original cube.
// Derives from Filter_iterator in order to add a conversion to handle
//
// Comments:
// When computing in 1-sheeted covering, there will be no difference
// between a normal Vertex_iterator and this iterator
template <class T>
class Periodic_2_triangulation_unique_vertex_iterator_2
        : public Filter_iterator<typename T::Vertex_iterator, Periodic_2_triangulation_2_internal::Domain_tester<T> >
{
  typedef typename T::Vertex_handle Vertex_handle;
  typedef typename T::Vertex_iterator Vertex_iterator;

  typedef typename Periodic_2_triangulation_2_internal::Domain_tester<T> Tester;

  typedef Filter_iterator<Vertex_iterator, Tester > Base;
  typedef Periodic_2_triangulation_unique_vertex_iterator_2 Self;

public:
  Periodic_2_triangulation_unique_vertex_iterator_2() : Base() {}
  Periodic_2_triangulation_unique_vertex_iterator_2(const Base &b) : Base(b) {}

  Self & operator++()
  {
    Base::operator++();
    return *this;
  }
  Self & operator--()
  {
    Base::operator--();
    return *this;
  }
  Self operator++(int)
  {
    Self tmp(*this);
    ++(*this);
    return tmp;
  }
  Self operator--(int)
  {
    Self tmp(*this);
    --(*this);
    return tmp;
  }

  operator Vertex_handle() const
  {
    return Base::base();
  }
};

// Iterates over the canonical edges in a periodic triangulation.
// Derives from Filter_iterator in order to add a conversion to handle
//
// Comments:
// When computing in 1-sheeted covering, there will be no difference
// between a normal Edge_iterator and this iterator
template <class T>
class Periodic_2_triangulation_unique_edge_iterator_2
        : public Filter_iterator<typename T::Edge_iterator, Periodic_2_triangulation_2_internal::Domain_tester<T> >
{
  typedef typename T::Edge Edge;
  typedef typename T::Edge_iterator Edge_iterator;

  typedef typename Periodic_2_triangulation_2_internal::Domain_tester<T> Tester;

  typedef Filter_iterator<Edge_iterator, Tester > Base;
  typedef Periodic_2_triangulation_unique_edge_iterator_2 Self;

public:
  Periodic_2_triangulation_unique_edge_iterator_2() : Base() {}
  Periodic_2_triangulation_unique_edge_iterator_2(const Base &b) : Base(b) {}

  Self & operator++()
  {
    Base::operator++();
    return *this;
  }
  Self & operator--()
  {
    Base::operator--();
    return *this;
  }
  Self operator++(int)
  {
    Self tmp(*this);
    ++(*this);
    return tmp;
  }
  Self operator--(int)
  {
    Self tmp(*this);
    --(*this);
    return tmp;
  }

  operator Edge() const
  {
    return Base::base();
  }
};

// Iterates over the canonical faces in a periodic triangulation.
// Derives from Filter_iterator in order to add a conversion to handle
//
// Comments:
// When computing in 1-sheeted covering, there will be no difference
// between a normal Face_iterator and this iterator
template <class T>
class Periodic_2_triangulation_unique_face_iterator_2
        : public Filter_iterator<typename T::Face_iterator, Periodic_2_triangulation_2_internal::Domain_tester<T> >
{
  typedef typename T::Face_handle Face_handle;
  typedef typename T::Face_iterator Face_iterator;

  typedef typename Periodic_2_triangulation_2_internal::Domain_tester<T> Tester;

  typedef Filter_iterator<Face_iterator, Tester > Base;
  typedef Periodic_2_triangulation_unique_face_iterator_2 Self;

public:
  Periodic_2_triangulation_unique_face_iterator_2() : Base() {}
  Periodic_2_triangulation_unique_face_iterator_2(const Base &b) : Base(b) {}

  Self & operator++()
  {
    Base::operator++();
    return *this;
  }
  Self & operator--()
  {
    Base::operator--();
    return *this;
  }
  Self operator++(int)
  {
    Self tmp(*this);
    ++(*this);
    return tmp;
  }
  Self operator--(int)
  {
    Self tmp(*this);
    --(*this);
    return tmp;
  }

  operator Face_handle() const
  {
    return Base::base();
  }
};

} // namespace CGAL

#endif // CGAL_PERIODIC_2_TRIANGULATION_ITERATORS_2_H

