// Copyright (c) 2009-2010 INRIA Sophia-Antipolis (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
// 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)     : Stéphane Tayeb, Laurent Rineau
//
//******************************************************************************
// File Description :
//
//******************************************************************************

#ifndef CGAL_MESH_DOMAIN_WITH_POLYLINE_FEATURES_3_H
#define CGAL_MESH_DOMAIN_WITH_POLYLINE_FEATURES_3_H

#include <CGAL/iterator.h>
#include <CGAL/enum.h>
#include <CGAL/number_utils.h>
#include <CGAL/AABB_tree.h>
#include <CGAL/AABB_traits.h>
#include <CGAL/is_streamable.h>

#include <vector>
#include <set>
#include <map>
#include <boost/next_prior.hpp> // for boost::prior and boost::next
#include <boost/variant.hpp>
#include <boost/foreach.hpp>

namespace CGAL {


namespace internal {
namespace Mesh_3 {

template <typename Kernel>
class Polyline
{
  typedef typename Kernel::Point_3  Point_3;
  typedef typename Kernel::Segment_3 Segment_3;
  typedef typename Kernel::FT       FT;

  typedef std::vector<Point_3>      Data;

public:
  typedef typename Data::const_iterator const_iterator;

  Polyline() {}
  ~Polyline() {}

  /// Add a point at the end of the polyline
  void add_point(const Point_3& p)
  {
    if( points_.empty() || p != end_point() ) {
      points_.push_back(p);
    }
  }

  /// Returns the starting point of the polyline
  const Point_3& start_point() const
  {
    CGAL_assertion( ! points_.empty() );
    return points_.front();
  }

  /// Returns the ending point of the polyline
  const Point_3& end_point() const
  {
    CGAL_assertion( ! points_.empty() );
    return points_.back();
  }

  /// Returns true if the polyline is not degenerated
  bool is_valid() const
  {
    return points_.size() > 1;
  }

  /// Returns true if polyline is a cycle
  bool is_cycle() const
  {
    return start_point() == end_point();
  }

  /// Returns the length of the polyline
  FT length() const
  {
    //TODO: cache result
    FT result (0);
    const_iterator it = points_.begin();
    const_iterator previous = it++;

    for ( const_iterator end = points_.end() ; it != end ; ++it, ++previous )
    {
      result += distance(*previous,*it);
    }

    return result;
  }

  /// Returns signed geodesic distance between \c p and \c q
  FT geodesic_distance(const Point_3& p, const Point_3& q,
                       bool /*treat_cycle*/=true) const
  {
    CGAL_precondition(is_valid());

    // Locate p & q on polyline
    const_iterator pit = locate(p);
    const_iterator qit = locate(q,false);

    // Compute geodesic distance
    FT result = (pit <= qit) ? geodesic_distance(p,q,pit,qit)
                             : -geodesic_distance(q,p,qit,pit);

    // Treat cycles: return a positive value
    if ( is_cycle() && (p==q || result < FT(0)) )
    {
      result = length() + result;
    }

    return result;
  }


  /// Returns a point at geodesic distance \c distance from p along the
  /// polyline. The polyline is oriented from starting point to end point.
  /// The distance could be negative.
  Point_3 point_at(const Point_3& p, FT distance) const
  {
    // use first point of the polyline instead of p
    distance += geodesic_distance(start_point(),p,false);

    // If polyline is a cycle, ensure that distance is given from start_point()
    if ( is_cycle() )
    {
      if ( distance < FT(0) ) { distance += length(); }
      else if ( distance > length() ) { distance -= length(); }
    }

    CGAL_assertion( distance >= FT(0) );
    CGAL_assertion( distance <= length() );

    // Initialize iterators
    const_iterator pit = points_.begin();
    const_iterator previous = pit++;

    // Iterate to find which segment contains the point we want to construct
    FT segment_length = this->distance(*previous,*pit);
    while ( distance > segment_length )
    {
      distance -= segment_length;

      // Increment iterators and update length
      ++previous;
      ++pit;
      CGAL_assertion(pit != points_.end());

      segment_length = this->distance(*previous,*pit);
    }

    // return point at distance from current segment source
    typedef typename Kernel::Vector_3 Vector_3;
    Vector_3 v (*previous, *pit);

    return (*previous) + (distance / CGAL::sqrt(v.squared_length())) * v;
  }

  bool are_ordered_along(const Point_3& p, const Point_3& q) const
  {
    CGAL_precondition(!is_cycle());

    // Locate p & q on polyline
    const_iterator pit = locate(p);
    const_iterator qit = locate(q,true);

    // Points are not located on the same segment
    if ( pit != qit ) { return (pit <= qit); }

    // pit == qit, then we have to sort p&q along (pit,pit+1)
    return ( compare_distance(*pit,p,q) != CGAL::LARGER );
  }

private:
  const_iterator first_segment_source() const
  {
    CGAL_precondition(is_valid());
    return points_.begin();
  }

  const_iterator last_segment_source() const
  {
    CGAL_precondition(is_valid());
    return (points_.end() - 2);
  }

  FT geodesic_distance(const Point_3& p, const Point_3& q,
                       const_iterator pit, const_iterator qit) const
  {
    CGAL_precondition(std::distance(pit,qit) >= 0);

    // If p and q are in the same segment of the polyline
    if ( pit == qit )
    {
      FT result = distance(p,q);

      // Find the closest point to *pit
      if ( compare_distance(*pit,p,q) != CGAL::LARGER )
      { return result; }
      else
      { return -result; }
    }

    // p is inside [pit,pit+1], pit+1 != qit, q is inside [qit,qit+1]
    FT result = distance(p,*(pit+1));
    result += distance(*qit,q);

    // Add segments between pit+1 and qit to result
    for ( const_iterator it = (pit+1) ; it != qit ; ++it )
    {
      result += distance(*it,*(it+1));
    }

    return result;
  }

  /// Returns an iterator on the starting point of the segment of the
  /// polyline which contains p
  /// if end_point_first is true, then --end is returned instead of begin
  /// if p is the starting point of a cycle.
  const_iterator locate(const Point_3& p, bool end_point_first=false) const
  {
    CGAL_precondition(is_valid());

    // First look if p is one of the points of the polyline
    const_iterator result = std::find(points_.begin(), points_.end(), p);
    if ( result != points_.end() )
    {
      if ( result != points_.begin() )
      { return --result; }
      else
      {
        // Treat cycles
        if ( end_point_first && p == end_point() )
        { return last_segment_source(); }
        else
        { return result; }
      }
    }

    CGAL_assertion(result == points_.end());

    // Get result by projecting p on the polyline
    const_iterator it = points_.begin();
    const_iterator previous = it;
    Segment_3 nearest_segment;
    const_iterator nearest_vertex = it;
    result = nearest_vertex;
    bool nearest_is_a_segment = false;

    while ( ++it != points_.end() )
    {
      Segment_3 seg (*previous, *it);

      if(nearest_is_a_segment)
      {
        if(compare_distance(p, seg, nearest_segment) == CGAL::SMALLER)
        {
          nearest_segment = seg;
          result = previous;
        }
        if(compare_distance(p, *it, nearest_segment) == CGAL::SMALLER)
        {
          nearest_vertex = it;
          nearest_is_a_segment = false;
          result = it;
        }
      }
      else {
        if(compare_distance(p, *it, *nearest_vertex) == CGAL::SMALLER)
        {
          nearest_vertex = it;
          result = it;
        }
        if(compare_distance(p, seg, *nearest_vertex) == CGAL::SMALLER)
        {
          nearest_segment = seg;
          nearest_is_a_segment = true;
          result = previous;
        }
      }
      previous = it;
    } // end the while loop on the vertices of the polyline


    if(result == points_.begin()) {
      return (end_point_first && !nearest_is_a_segment) ? last_segment_source() : points_.begin();
    } else {
      return result;
    }
  }

  // FT squared_distance(const Point_3& p, const Point_3& q) const
  // {
  //   typename Kernel::Compute_squared_distance_3 sq_distance =
  //     Kernel().compute_squared_distance_3_object();
  //   return sq_distance(p,q);
  // }

  FT distance(const Point_3& p, const Point_3& q) const
  {
    return CGAL::sqrt(squared_distance(p, q));
  }

  Angle angle(const Point_3& p,
              const Point_3& angle_vertex_point,
              const Point_3& q) const
  {
    typename Kernel::Angle_3 compute_angle =  Kernel().angle_3_object();
    return compute_angle(p,angle_vertex_point,q);
  }

  template <typename T1, typename T2>
  CGAL::Sign compare_distance(const Point_3& p,
                              const T1& obj1,
                              const T2& obj2) const
  {
    typename Kernel::Compare_distance_3 compare_distance =
      Kernel().compare_distance_3_object();
    return compare_distance(p,obj1,obj2);
  }

public:
  Data points_;
}; // end class Polyline


template <typename Gt, typename MapIterator>
struct Mesh_domain_segment_of_curve_primitive{
  typedef typename std::iterator_traits<MapIterator>::value_type Map_value_type;
  typedef typename Map_value_type::first_type Curve_id;
  typedef typename Map_value_type::second_type Polyline;

  typedef std::pair<MapIterator,
                    typename Polyline::const_iterator> Id;

  typedef typename std::iterator_traits<
    typename Polyline::const_iterator>::value_type Point;

  typedef typename Gt::Segment_3 Datum;

  Id id_;

  Mesh_domain_segment_of_curve_primitive(Id id) : id_(id) {}

  const Id& id() const { return id_; }

  const Point& reference_point() const {
    return *(id_.second);
  }

  Datum datum() const {
    return Datum(*id_.second, *(id_.second+1));
  }
}; // end Mesh_domain_segment_of_curve_primitive

template <typename MDwPF, bool patch_id_is_streamable>
struct Display_incidences_to_patches_aux {
  template <typename Container>
  void operator()(std::ostream& os, typename MDwPF::Curve_segment_index id,
                  const Container&) const;
};

template <typename MDwPF> //specialization when patch_id_is_streamable == false
struct Display_incidences_to_patches_aux<MDwPF, false> {
  template <typename Container>
  void operator()(std::ostream& os,
                  typename MDwPF::Curve_segment_index id,
                  const Container&) const;
};

template <typename MDwPF, bool curve_id_is_streamable>
struct Display_incidences_to_curves_aux {
  template <typename Container>
  void operator()(std::ostream& os, typename MDwPF::Curve_segment_index id,
                  const Container&) const;
};

template <typename MDwPF> //specialization when curve_id_is_streamable == false
struct Display_incidences_to_curves_aux<MDwPF, false> {
  template <typename Container>
  void operator()(std::ostream& os, typename MDwPF::Curve_segment_index id,
                  const Container&) const;
};

} // end of namespace CGAL::internal::Mesh_3
} // end of namespace CGAL::internal





/**
 * @class Mesh_domain_with_polyline_features_3
 *
 *
 */
template < typename MeshDomain >
class Mesh_domain_with_polyline_features_3
  : public MeshDomain
{
  typedef MeshDomain Base;

public:
  // Index types
  typedef typename Base::Index    Index;

  typedef typename Base::Surface_patch_index
                                  Surface_patch_index;

  typedef int                     Curve_segment_index;
  typedef int                     Corner_index;

  typedef typename Base::R         Gt;
  typedef Gt                       R;
  typedef typename Base::Point_3   Point_3;
  typedef typename Gt::FT          FT;

  typedef CGAL::Tag_true           Has_features;


#ifndef CGAL_CFG_NO_CPP0X_VARIADIC_TEMPLATES
  template <typename ... T>
  Mesh_domain_with_polyline_features_3(const T& ...t)
    : Base(t...)
    , current_corner_index_(1)
    , current_curve_index_(1)
    , curves_aabb_tree_is_built(false) {}
#else
  /// Constructors
  /// Call the base class constructor
  Mesh_domain_with_polyline_features_3()
    : Base()
    , current_corner_index_(1)
    , current_curve_index_(1)
    , curves_aabb_tree_is_built(false) {}

  template <typename T1>
  Mesh_domain_with_polyline_features_3(const T1& o1)
    : Base(o1)
    , current_corner_index_(1)
    , current_curve_index_(1)
    , curves_aabb_tree_is_built(false) {}

  template <typename T1, typename T2>
  Mesh_domain_with_polyline_features_3(const T1& o1, const T2& o2)
    : Base(o1, o2)
    , current_corner_index_(1)
    , current_curve_index_(1)
    , curves_aabb_tree_is_built(false) {}

  template <typename T1, typename T2, typename T3>
  Mesh_domain_with_polyline_features_3(const T1& o1, const T2& o2,
                                       const T3& o3)
    : Base(o1, o2, o3)
    , current_corner_index_(1)
    , current_curve_index_(1)
    , curves_aabb_tree_is_built(false) {}
#endif

  /// Destructor
  ~Mesh_domain_with_polyline_features_3() {}

  /// OutputIterator value type is std::pair<Corner_index, Point_3>
  template <typename OutputIterator>
  OutputIterator get_corners(OutputIterator out) const;

  /// OutputIterator value type is CGAL::cpp11::tuple<Curve_segment_index,
  /// std::pair<Point_3,Index>, std::pair<Point_3,Index> >
  template <typename OutputIterator>
  OutputIterator get_curve_segments(OutputIterator out) const;

  /// Returns the geodesic distance between points p and q of curve
  /// \c curve_index
  FT geodesic_distance(const Point_3& p, const Point_3& q,
                       const Curve_segment_index& curve_index) const;

  /// Construct a point on curve \c curve_index at geodesic distance \c distance
  /// of \c starting_point
  Point_3
  construct_point_on_curve_segment(const Point_3& starting_point,
                                   const Curve_segment_index& curve_index,
                                   FT distance) const;

  /// Returns the sign of the orientation of p,q,r along curve segment
  /// of index \c index
  CGAL::Sign distance_sign_along_cycle(const Point_3& p,
                                       const Point_3& q,
                                       const Point_3& r,
                                       const Curve_segment_index& index) const;

  /// Returns true if curve \c curve_index is a cycle
  bool is_cycle(const Point_3&, const Curve_segment_index& index) const;

  /// Returns an Index from a Curve_segment_index
  Index index_from_curve_segment_index(const Curve_segment_index& index) const
  { return Index(index); }

  /// Returns an Curve_segment_index from an Index
  Curve_segment_index curve_segment_index(const Index& index) const
  { return boost::get<Curve_segment_index>(index); }

  /// Returns an Index from a Corner_index
  Index index_from_corner_index(const Corner_index& index) const
  { return Index(index); }

  /// Returns an Corner_index from an Index
  Corner_index corner_index(const Index& index) const
  { return boost::get<Corner_index>(index); }

  /// Insert a bunch of edges into domain
  ///   + InputIterator type should have begin() and end() function
  ///   + InputIterator::iterator value type must be Point_3
  //    + IndicesOutputIterator is an output iterator of value_type equal
  ///   to Curve_segment_index
  template <typename InputIterator, typename IndicesOutputIterator>
  IndicesOutputIterator
  add_features(InputIterator first, InputIterator last,
               IndicesOutputIterator out /*= CGAL::Emptyset_iterator()*/);

  template <typename InputIterator, typename IndicesOutputIterator>
  IndicesOutputIterator
  add_features_with_context(InputIterator first, InputIterator last,
                            IndicesOutputIterator out /*=
                                                        CGAL::Emptyset_iterator()*/);

  template <typename IndicesOutputIterator>
  IndicesOutputIterator
  get_incidences(Curve_segment_index id, IndicesOutputIterator out) const;

  template <typename IndicesOutputIterator>
  IndicesOutputIterator
  get_corner_incidences(Curve_segment_index id, IndicesOutputIterator out) const;

  typedef std::set<Surface_patch_index> Surface_patch_index_set;

  const Surface_patch_index_set&
  get_incidences(Curve_segment_index id) const;

  void display_corner_incidences(std::ostream& os, Corner_index id);

  template <typename InputIterator>
  void
  add_features(InputIterator first, InputIterator last)
  { add_features(first, last, CGAL::Emptyset_iterator()); }

  /// Insert one edge into domain
  /// InputIterator value type is Point_3
  template <typename InputIterator>
  Curve_segment_index insert_edge(InputIterator first, InputIterator last);

private:
  void register_corner(const Point_3& p, const Curve_segment_index& index);
  void compute_corners_incidences();

  /// Returns the sign of the geodesic distance between \c p and \c q
  /// Precondition: index is not a cycle
  CGAL::Sign distance_sign(const Point_3& p, const Point_3& q,
                           const Curve_segment_index& index) const;

  /// Returns Index associated to p (p must be the coordinates of a corner
  /// point)
  Index point_corner_index(const Point_3& p) const;

private:
  typedef std::map<Point_3,Corner_index> Corners;

  typedef internal::Mesh_3::Polyline<Gt> Polyline;
  typedef std::map<Curve_segment_index, Polyline> Edges;
  typedef std::map<Curve_segment_index, Surface_patch_index_set > Edges_incidences;
  typedef std::map<Corner_index, std::set<Curve_segment_index> > Corners_tmp_incidences;
  typedef std::map<Corner_index, Surface_patch_index_set > Corners_incidences;

  typedef internal::Mesh_3::Mesh_domain_segment_of_curve_primitive<
    Gt,
    typename Edges::const_iterator> Curves_primitives;

  typedef CGAL::AABB_traits<Gt,
                            Curves_primitives> AABB_curves_traits;

  Corners corners_;
  Corners_tmp_incidences corners_tmp_incidences_;
  Corner_index current_corner_index_;
  Corners_incidences corners_incidences_;

  Edges edges_;
  Curve_segment_index current_curve_index_;
  Edges_incidences edges_incidences_;

public:
  typedef CGAL::AABB_tree<AABB_curves_traits> Curves_AABB_tree;

private:
  mutable Curves_AABB_tree curves_aabb_tree_;
  mutable bool curves_aabb_tree_is_built;

public:
  const Curves_AABB_tree& curves_aabb_tree() const {
    if(!curves_aabb_tree_is_built) build_curves_aabb_tree();
    return curves_aabb_tree_;
  }

  void build_curves_aabb_tree() const {
    std::cerr << "Building curves AABB tree...\n";
    curves_aabb_tree_.clear();
    for(typename Edges::const_iterator
          edges_it = edges_.begin(),
          edges_end = edges_.end();
        edges_it != edges_end; ++edges_it)
    {
      const Polyline& polyline = edges_it->second;
      for(typename Polyline::const_iterator
            pit = polyline.points_.begin(),
            end = polyline.points_.end() - 1;
          pit != end; ++pit)
      {
        curves_aabb_tree_.insert(std::make_pair(edges_it, pit));
      }
    }
    curves_aabb_tree_.build();
    curves_aabb_tree_is_built = true;
  } // end build_curves_aabb_tree()

private:
  // Disabled copy constructor & assignment operator
  typedef Mesh_domain_with_polyline_features_3 Self;
  Mesh_domain_with_polyline_features_3(const Self& src);
  Self& operator=(const Self& src);

};  // end class Mesh_domain_with_polyline_features_3



template <class MD_>
template <typename OutputIterator>
OutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
get_corners(OutputIterator out) const
{
  for ( typename Corners::const_iterator
       cit = corners_.begin(), end = corners_.end() ; cit != end ; ++cit )
  {
    *out++ = std::make_pair(cit->second,cit->first);
  }

  return out;
}

template <class MD_>
template <typename OutputIterator>
OutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
get_curve_segments(OutputIterator out) const
{
  for ( typename Edges::const_iterator
       eit = edges_.begin(), end = edges_.end() ; eit != end ; ++eit )
  {
    CGAL_assertion( eit->second.is_valid() );

    const Point_3& p = eit->second.start_point();
    const Point_3& q = eit->second.end_point();

    Index p_index, q_index;
    if ( ! eit->second.is_cycle() )
    {
      p_index = point_corner_index(p);
      q_index = point_corner_index(q);
    }
    else
    {
      p_index = index_from_curve_segment_index(eit->first);
      q_index = p_index;
    }

    *out++ = CGAL::cpp11::make_tuple(eit->first,
                                     std::make_pair(p,p_index),
                                     std::make_pair(q,q_index));
  }

  return out;
}


template <class MD_>
typename Mesh_domain_with_polyline_features_3<MD_>::Index
Mesh_domain_with_polyline_features_3<MD_>::
point_corner_index(const Point_3& p) const
{
  typename Corners::const_iterator p_index_it = corners_.find(p);
  if ( p_index_it == corners_.end() )
  {
    CGAL_assertion(false);
    return Index();
  }

  return p_index_it->second;
}


template <class MD_>
typename Mesh_domain_with_polyline_features_3<MD_>::FT
Mesh_domain_with_polyline_features_3<MD_>::
geodesic_distance(const Point_3& p, const Point_3& q,
                  const Curve_segment_index& curve_index) const
{
  // Get corresponding polyline
  typename Edges::const_iterator eit = edges_.find(curve_index);
  CGAL_assertion(eit != edges_.end());

  // Compute geodesic_distance
  return eit->second.geodesic_distance(p,q);
}


template <class MD_>
typename Mesh_domain_with_polyline_features_3<MD_>::Point_3
Mesh_domain_with_polyline_features_3<MD_>::
construct_point_on_curve_segment(const Point_3& starting_point,
                                 const Curve_segment_index& curve_index,
                                 FT distance) const
{
  // Get corresponding polyline
  typename Edges::const_iterator eit = edges_.find(curve_index);
  CGAL_assertion(eit != edges_.end());

  // Return point at geodesic_distance distance from starting_point
  return eit->second.point_at(starting_point,distance);
}



template <class MD_>
template <typename InputIterator, typename IndicesOutputIterator>
IndicesOutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
add_features(InputIterator first, InputIterator last,
             IndicesOutputIterator indices_out)
{
  // Insert one edge for each element
  while ( first != last )
  {
    *indices_out++ = insert_edge(first->begin(), first->end());
    ++first;
  }
  compute_corners_incidences();
  return indices_out;
}

template <class MD_>
template <typename InputIterator, typename IndicesOutputIterator>
IndicesOutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
add_features_with_context(InputIterator first, InputIterator last,
                          IndicesOutputIterator indices_out)
{
  // Insert one edge for each element
  for( ; first != last ; ++first )
  {
    Curve_segment_index curve_id =
      insert_edge(first->polyline_content.begin(), first->polyline_content.end());
    edges_incidences_[curve_id] = first->context.adjacent_patches_ids;
    *indices_out++ = curve_id;
  }
  compute_corners_incidences();
  return indices_out;
}

template <class MD_>
template <typename IndicesOutputIterator>
IndicesOutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
get_incidences(Curve_segment_index id,
               IndicesOutputIterator indices_out) const
{
  typename Edges_incidences::const_iterator it = edges_incidences_.find(id);

  if(it == edges_incidences_.end()) return indices_out;

  const Surface_patch_index_set& incidences = it->second;

  return std::copy(incidences.begin(), incidences.end(), indices_out);
}

template <class MD_>
template <typename IndicesOutputIterator>
IndicesOutputIterator
Mesh_domain_with_polyline_features_3<MD_>::
get_corner_incidences(Corner_index id,
                      IndicesOutputIterator indices_out) const
{
  typename Corners_incidences::const_iterator it = corners_incidences_.find(id);
  const Surface_patch_index_set& incidences = it->second;
  return std::copy(incidences.begin(), incidences.end(), indices_out);
}

namespace internal { namespace Mesh_3 {

template <typename MDwPF_, bool curve_id_is_streamable>
// here 'curve_id_is_streamable' is true
template <typename Container2>
void
Display_incidences_to_curves_aux<MDwPF_,curve_id_is_streamable>::
operator()(std::ostream& os, typename MDwPF_::Curve_segment_index id,
           const Container2& corners_tmp_incidences_of_id) const
{
  os << "Corner #" << id << " is incident to the following curves: {";
  BOOST_FOREACH(typename MDwPF_::Curve_segment_index curve_index,
                corners_tmp_incidences_of_id)
  {
    os << " " << curve_index;
  }
  os << " }\n";
}

template <class MDwPF_>
// here 'curve_id_is_streamable' is false
template <typename Container2>
void
Display_incidences_to_curves_aux<MDwPF_,false>::
operator()(std::ostream& os, typename MDwPF_::Curve_segment_index id,
           const Container2& corners_tmp_incidences_of_id) const
{
  os << "Corner #" << id << " is incident to "
     << corners_tmp_incidences_of_id .size()
     << " curve(s).\n";
}

template <typename MDwPF_, bool patch_id_is_streamable>
// here 'patch_id_is_streamable' is true
template <typename Container>
void
Display_incidences_to_patches_aux<MDwPF_,patch_id_is_streamable>::
operator()(std::ostream& os, typename MDwPF_::Curve_segment_index id,
           const Container& corners_incidences_of_id) const
{
  os << "Corner #" << id << " is incident to the following patches: {";
  BOOST_FOREACH(typename MDwPF_::Surface_patch_index i,
                corners_incidences_of_id)
  {
    os << " " << i;
  }
  os << " }\n";
}

template <class MDwPF_>
// here 'patch_id_is_streamable' is false
template <typename Container>
void
Display_incidences_to_patches_aux<MDwPF_,false>::
operator()(std::ostream& os, typename MDwPF_::Curve_segment_index id,
           const Container& corners_incidences_id) const
{
  os << "Corner #" << id << " is incident to "
     << corners_incidences_id.size()
     << " surface patch(es).\n";
}

}} // end namespaces internal::Mesh_3:: and internal::

template <class MD_>
void
Mesh_domain_with_polyline_features_3<MD_>::
display_corner_incidences(std::ostream& os, Corner_index id)
{
  typedef Mesh_domain_with_polyline_features_3<MD_> Mdwpf;
  typedef is_streamable<Surface_patch_index> i_s_spi;
  typedef is_streamable<Curve_segment_index> i_s_csi;

  using namespace internal::Mesh_3;
  typedef Display_incidences_to_curves_aux<Mdwpf,i_s_csi::value> D_i_t_c;
  typedef Display_incidences_to_patches_aux<Mdwpf,i_s_spi::value> D_i_t_p;
  D_i_t_c()(os, id, corners_tmp_incidences_[id]);
  D_i_t_p()(os, id, corners_incidences_[id]);
}

template <class MD_>
void
Mesh_domain_with_polyline_features_3<MD_>::
compute_corners_incidences()
{
  for(typename Corners::iterator
        cit = corners_.begin(), end = corners_.end();
      cit != end; /* the loop variable is incremented in the  body */)
  {
    const Corner_index id = cit->second;

    const typename Corners_tmp_incidences::mapped_type&
      corner_tmp_incidences = corners_tmp_incidences_[id];

    // If the corner is incident to only one curve, and that curve is a
    // cycle, then remove the corner from the set.
    if(corner_tmp_incidences.size() == 1 &&
       is_cycle(Point_3(), *corner_tmp_incidences.begin()))
    {
      typename Corners::iterator to_erase = cit;
      ++cit;
      corners_.erase(to_erase);
      continue;
    }

    Surface_patch_index_set& incidences = corners_incidences_[id];
    // That should be an empty set.

    BOOST_FOREACH(Curve_segment_index curve_index, corner_tmp_incidences)
    {
      get_incidences(curve_index,
                     std::inserter(incidences,
                                   incidences.begin()));
    }
#ifdef CGAL_MESH_3_PROTECTION_DEBUG
    display_corner_incidences(std::cerr, id);
#endif // CGAL_MESH_3_PROTECTION_DEBUG

    // increment the loop variable
    ++cit;
  }
}

template <class MD_>
const typename Mesh_domain_with_polyline_features_3<MD_>::Surface_patch_index_set&
Mesh_domain_with_polyline_features_3<MD_>::
get_incidences(Curve_segment_index id) const
{
  typename Edges_incidences::const_iterator it = edges_incidences_.find(id);
  return it->second;
}

template <class MD_>
void
Mesh_domain_with_polyline_features_3<MD_>::
register_corner(const Point_3& p, const Curve_segment_index& curve_index)
{

  typename Corners::iterator cit = corners_.lower_bound(p);

  // If the corner already exists, returns...
  if(cit != corners_.end() && !(corners_.key_comp()(p, cit->first))) {
    corners_tmp_incidences_[cit->second].insert(curve_index);
    return;
  }

  // ...else insert it!

  const Corner_index index = current_corner_index_;
  ++current_corner_index_;

  corners_.insert(cit, std::make_pair(p, index));
  corners_tmp_incidences_[index].insert(curve_index);
}

template <class MD_>
template <typename InputIterator>
typename Mesh_domain_with_polyline_features_3<MD_>::Curve_segment_index
Mesh_domain_with_polyline_features_3<MD_>::
insert_edge(InputIterator first, InputIterator last)
{
  CGAL_assertion(std::distance(first,last) > 1);

  const Curve_segment_index curve_index = current_curve_index_++;

  // Fill corners
  //
  // For a cycle, the "first" point of the cycle is registered as a
  // corner. If at the end, during the call to
  // 'compute_corners_incidences()', that corner is incident only to a
  // cycle, then it will be removed from the set of corners.
  register_corner(*first, curve_index);
  if ( *first != *boost::prior(last) )
  {
    register_corner(*boost::prior(last), curve_index);
  }

  // Create a new polyline
  std::pair<typename Edges::iterator,bool> insertion =
    edges_.insert(std::make_pair(curve_index,Polyline()));

  // Fill polyline with data
  while ( first != last )
  {
    insertion.first->second.add_point(*first++);
  }
  return curve_index;
}


template <class MD_>
CGAL::Sign
Mesh_domain_with_polyline_features_3<MD_>::
distance_sign(const Point_3& p, const Point_3& q,
              const Curve_segment_index& index) const
{
  typename Edges::const_iterator eit = edges_.find(index);
  CGAL_assertion(eit != edges_.end());
  CGAL_precondition( ! eit->second.is_cycle() );

  if ( p == q )
    return CGAL::ZERO;
  else if ( eit->second.are_ordered_along(p,q) )
    return CGAL::POSITIVE;
  else
    return CGAL::NEGATIVE;
}

template <class MD_>
CGAL::Sign
Mesh_domain_with_polyline_features_3<MD_>::
distance_sign_along_cycle(const Point_3& p,
                          const Point_3& q,
                          const Point_3& r,
                          const Curve_segment_index& index) const
{
  // Find edge
  typename Edges::const_iterator eit = edges_.find(index);
  CGAL_assertion(eit != edges_.end());

  // If eit is not a cycle, then the orientation corresponds to the sign
  // of the distance
  if ( ! eit->second.is_cycle() )
  {
    return distance_sign(p,r,index);
  }

  // If p and r are the same point, it correspond to a complete loop on a cycle
  if ( p == r ) { return CGAL::POSITIVE; }

  // We are on a cycle without any clue (p==q). Return the shortest path as
  // orientation.
  if ( p == q )
  {
    FT pr = eit->second.geodesic_distance(p,r);
    FT rp = eit->second.geodesic_distance(r,p);
    if ( pr < rp ) { return CGAL::POSITIVE; }
    else { return CGAL::NEGATIVE; }
  }

  // If pq or pr is negative, edge is not a cycle, thus geodesic_distance
  // gives the answer.
  FT pq = eit->second.geodesic_distance(p,q);
  FT pr = eit->second.geodesic_distance(p,r);
  CGAL_assertion(pq > FT(0));
  CGAL_assertion(pr > FT(0));

  // Compare pq and pr
  if ( pq <= pr ) { return CGAL::POSITIVE; }
  else { return CGAL::NEGATIVE; }
}

template <class MD_>
bool
Mesh_domain_with_polyline_features_3<MD_>::
is_cycle(const Point_3&, const Curve_segment_index& index) const
{
  // Find edge
  typename Edges::const_iterator eit = edges_.find(index);
  CGAL_assertion(eit != edges_.end());

  return eit->second.is_cycle();
}


} //namespace CGAL


#endif // CGAL_MESH_DOMAIN_WITH_POLYLINE_FEATURES_3_H
