// Copyright (c) 2006-2008 Fernando Luis Cacciola Carballal. All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// 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)     : Fernando Cacciola <fernando_cacciola@ciudad.com.ar>
//
#ifndef CGAL_STRAIGHT_SKELETON_BUILDER_2_H
#define CGAL_STRAIGHT_SKELETON_BUILDER_2_H 1

#include <list>
#include <queue>
#include <exception>
#include <string>
#include <map>

#define _USE_MATH_DEFINES  // Needed so M_PI gets defined
#include <cmath>

#include <boost/tuple/tuple.hpp>
#include <boost/intrusive_ptr.hpp>
#include <boost/shared_ptr.hpp>
#include <boost/scoped_ptr.hpp>

#include <CGAL/algorithm.h>
#include <CGAL/Straight_skeleton_2/Straight_skeleton_aux.h>
#include <CGAL/Straight_skeleton_2/Straight_skeleton_builder_events_2.h>
#include <CGAL/Straight_skeleton_2.h>
#include <CGAL/Straight_skeleton_builder_traits_2.h>
#include <CGAL/HalfedgeDS_const_decorator.h>
#include <CGAL/enum.h>


CGAL_BEGIN_NAMESPACE

template<class SSkel_>
struct Dummy_straight_skeleton_builder_2_visitor
{
  typedef SSkel_ SSkel ;

  typedef typename SSkel::Halfedge_const_handle Halfedge_const_handle ;
  typedef typename SSkel::Vertex_const_handle   Vertex_const_handle ;

  void on_contour_edge_entered ( Halfedge_const_handle const&  ) const {}
                               
  void on_initialization_started( std::size_t /* size_of_vertices */ ) const {}
  
  void on_initial_events_collected( Vertex_const_handle const& , bool /* is_reflex */, bool /*is_degenerate*/ )  const  {}
  
  void on_edge_event_created( Vertex_const_handle const& /* lnode */
             			    , Vertex_const_handle const& /* rnode */
                            )  const {}

  void on_split_event_created( Vertex_const_handle const&  )  const {}

  void on_pseudo_split_event_created( Vertex_const_handle const& /* lnode */
                                    , Vertex_const_handle const& /* rnode */
                                    )  const {}
                                    
  void on_initialization_finished() const {}
  
  void on_propagation_started() const {}
  
  void on_anihiliation_event_processed ( Vertex_const_handle const& /* node0 */
                                       , Vertex_const_handle const& /* node1 */
                                       )  const  {}


  void on_edge_event_processed( Vertex_const_handle const& /* lseed */
                              , Vertex_const_handle const& /* rseed */
                              , Vertex_const_handle const& /* node */
                              )  const {} 

  void on_split_event_processed( Vertex_const_handle const& /* seed */
                               , Vertex_const_handle const& /* node0 */
                               , Vertex_const_handle const& /* node1 */
                               )  const {}

  void on_pseudo_split_event_processed( Vertex_const_handle const& /* lseed */
                                      , Vertex_const_handle const& /* rseed */
                                      , Vertex_const_handle const& /* node0 */
                                      , Vertex_const_handle const& /* node1 */
                                      )  const {}

  void on_vertex_processed( Vertex_const_handle const& )  const {}
  
  void on_propagation_finished() const {}
  
  void on_cleanup_started() const {}
  
  void on_cleanup_finished() const {}
  
  void on_algorithm_finished ( bool /* finished_ok */ ) const {}
  
  void on_error( char const* ) const {}
} ;

template<class Traits_, class SSkel_, class Visitor_ = Dummy_straight_skeleton_builder_2_visitor<SSkel_> >
class Straight_skeleton_builder_2
{
public:

  typedef Traits_  Traits ;
  typedef SSkel_   SSkel ;
  typedef Visitor_ Visitor ;

  typedef boost::shared_ptr<SSkel> SSkelPtr ;

private :

  typedef typename Traits::Kernel K ;
  
  typedef typename Traits::FT               FT ;
  typedef typename Traits::Point_2          Point_2 ;
  typedef typename Traits::Vector_2         Vector_2 ;
  typedef typename Traits::Direction_2      Direction_2 ;
  typedef typename Traits::Segment_2        Segment_2 ;
  typedef typename Traits::Trisegment_2     Trisegment_2 ;
  typedef typename Traits::Trisegment_2_ptr Trisegment_2_ptr ;
  
  typedef typename SSkel::Vertex   Vertex ;
  typedef typename SSkel::Halfedge Halfedge ;
  typedef typename SSkel::Face     Face ;

  typedef typename SSkel::Vertex_const_handle   Vertex_const_handle ;
  typedef typename SSkel::Halfedge_const_handle Halfedge_const_handle ;
  typedef typename SSkel::Face_const_handle     Face_const_handle ;

  typedef typename SSkel::Vertex_const_iterator   Vertex_const_iterator ;
  typedef typename SSkel::Halfedge_const_iterator Halfedge_const_iterator ;
  typedef typename SSkel::Face_const_iterator     Face_const_iterator ;

  typedef typename SSkel::Vertex_handle   Vertex_handle ;
  typedef typename SSkel::Halfedge_handle Halfedge_handle ;
  typedef typename SSkel::Face_handle     Face_handle ;

  typedef typename SSkel::Vertex_iterator   Vertex_iterator ;
  typedef typename SSkel::Halfedge_iterator Halfedge_iterator ;
  typedef typename SSkel::Face_iterator     Face_iterator ;

  typedef typename Vertex::Halfedge_around_vertex_circulator Halfedge_around_vertex_circulator ;
  
  typedef typename SSkel::size_type size_type ;

  typedef CGAL_SS_i::Triedge<Halfedge_handle> Triedge ;
  
  typedef CGAL_SS_i::Event_2             <SSkel,Traits> Event ;
  typedef CGAL_SS_i::Edge_event_2        <SSkel,Traits> EdgeEvent ;
  typedef CGAL_SS_i::Split_event_2       <SSkel,Traits> SplitEvent ;
  typedef CGAL_SS_i::Pseudo_split_event_2<SSkel,Traits> PseudoSplitEvent ;

  typedef boost::intrusive_ptr<Event> EventPtr ;

  typedef std::pair<Vertex_handle,Vertex_handle> Vertex_handle_pair ;
  
  typedef std::vector<EventPtr>           EventPtr_Vector ;
  typedef std::vector<Halfedge_handle>    Halfedge_handle_vector ;
  typedef std::vector<Vertex_handle>      Vertex_handle_vector ;
  typedef std::vector<Vertex_handle_pair> Vertex_handle_pair_vector ;
  
  typedef typename Halfedge_handle_vector   ::iterator Halfedge_handle_vector_iterator ;
  typedef typename Vertex_handle_vector     ::iterator Vertex_handle_vector_iterator ;
  typedef typename Vertex_handle_pair_vector::iterator Vertex_handle_pair_vector_iterator ;
  
  typedef typename EventPtr_Vector::const_iterator event_const_iterator ;

  typedef Straight_skeleton_builder_2<Traits,SSkel,Visitor> Self ;
  
  typedef typename Halfedge::Base_base HBase_base ;
  typedef typename Halfedge::Base      HBase ;
  typedef typename Vertex::Base        VBase ;
  typedef typename Face::Base          FBase ;
  
  enum Site { AT_SOURCE = -1 , INSIDE = 0, AT_TARGET = +1 } ;
  
  struct Multinode : public Ref_counted_base
  {
    Multinode ( Halfedge_handle b, Halfedge_handle e )
      :
       begin(b)
      ,end  (e)
      ,v    (b->vertex())
      ,size (0)
    {}
      
    Halfedge_handle        begin ;
    Halfedge_handle        end ;
    Vertex_handle          v ;
    std::size_t            size ;
    Halfedge_handle_vector bisectors_to_relink ;
    Halfedge_handle_vector bisectors_to_remove ;
    Vertex_handle_vector   nodes_to_remove ;
  } ;  
  
  typedef boost::intrusive_ptr<Multinode> MultinodePtr ;
  
  struct MultinodeComparer
  {
    bool operator() ( MultinodePtr const& x, MultinodePtr const& y ) { return x->size > y->size ; }
  } ;
  
  typedef std::vector<MultinodePtr> MultinodeVector ;

  struct Halfedge_ID_compare : std::binary_function<bool,Halfedge_handle,Halfedge_handle>
  {
    bool operator() ( Halfedge_handle const& aA, Halfedge_handle const& aB ) const
    {
      return aA->id() < aB->id() ;
    }
  } ;
  
public:

  Straight_skeleton_builder_2 ( boost::optional<FT> aMaxTime = boost::none
                              , Traits const&                = Traits()
                              , Visitor const& aVisitor      = Visitor() 
                              ) ;
  
  SSkelPtr construct_skeleton( bool aNull_if_failed = true ) ;

private :

  
  class Event_compare : public std::binary_function<bool,EventPtr,EventPtr>
  {
  public:

    Event_compare ( Self const* aBuilder ) : mBuilder(aBuilder) {}

    bool operator() ( EventPtr const& aA, EventPtr const& aB ) const
    {
      return mBuilder->CompareEvents(aA,aB) == LARGER ;
    }

  private:

    Self const* mBuilder ;
  } ;

  typedef std::priority_queue<EventPtr,std::vector<EventPtr>,Event_compare> PQ ;


  struct Vertex_data : public Ref_counted_base
  {
    Vertex_data ( Vertex_handle aVertex, Event_compare const& aComparer )
      :
        mVertex(aVertex)
      , mIsTerminal(false)  
      , mIsReflex(false)
      , mIsDegenerate(false)
      , mIsProcessed(false)
      , mIsExcluded(false)
      , mPrevInLAV(-1)
      , mNextInLAV(-1)
      , mNextSplitEventInMainPQ(false)
      , mSplitEvents(aComparer)
    {}

    Vertex_handle     mVertex ;
    bool              mIsTerminal ;
    bool              mIsReflex ;
    bool              mIsDegenerate ;
    bool              mIsProcessed ;
    bool              mIsExcluded ;
    int               mPrevInLAV ;
    int               mNextInLAV ;
    bool              mNextSplitEventInMainPQ;
    PQ                mSplitEvents ;
    Triedge           mTriedge ; // Here, E0,E1 corresponds to the vertex (unlike *event* triedges). Terminal vertices woud have only E0 or E1
    Trisegment_2_ptr  mTrisegment ; // Skeleton nodes cache the full trisegment tree that defines the originating event
  } ;
  
  typedef boost::intrusive_ptr<Vertex_data> Vertex_data_ptr ;
  
private :

  Halfedge_handle validate( Halfedge_handle aH ) const ;
  Vertex_handle   validate( Vertex_handle   aH ) const ;

  void InitVertexData( Vertex_handle aV )
  {
    mVertexData.push_back( Vertex_data_ptr( new Vertex_data(aV,mEventCompare) ) ) ;
  } 
  
  Vertex_data const& GetVertexData( Vertex_const_handle aV ) const 
  { 
    CGAL_precondition( handle_assigned(aV) ) ; 
    return *mVertexData[aV->id()]; 
  }
  
  Vertex_data&  GetVertexData( Vertex_const_handle aV )      
  { 
    CGAL_precondition( handle_assigned(aV) ) ; 
    return *mVertexData[aV->id()]; 
  }
  
  Vertex_handle GetVertex ( int aIdx )
  {
    return aIdx >= 0 ? mVertexData[aIdx]->mVertex : Vertex_handle() ;
  }

  // Null if aV is a contour or infinite node
  Trisegment_2_ptr const& GetTrisegment ( Vertex_handle aV ) const
  {
    return GetVertexData(aV).mTrisegment ;
  }
  
  void SetTrisegment ( Vertex_handle aV, Trisegment_2_ptr const& aTrisegment )
  {
    GetVertexData(aV).mTrisegment = aTrisegment ;
  }
  
  Triedge GetVertexTriedge ( Vertex_handle aV ) const
  {
    Triedge rTriedge = GetVertexData(aV).mTriedge ;
    
    return rTriedge ;
  }
  
  void SetVertexTriedge ( Vertex_handle aV, Triedge const& aTriedge )
  {
    GetVertexData(aV).mTriedge = aTriedge ;
  }
  
  Segment_2 CreateSegment ( Halfedge_const_handle aH ) const
  {
    Point_2 s = aH->opposite()->vertex()->point() ;
    Point_2 t = aH->vertex()->point() ;
    return K().construct_segment_2_object()(s,t);
  }
  
  Vector_2 CreateVector ( Halfedge_const_handle aH ) const
  {
    Point_2 s = aH->opposite()->vertex()->point() ;
    Point_2 t = aH->vertex()->point() ;
    return K().construct_vector_2_object()(s,t);
  }
  
  Direction_2 CreateDirection ( Halfedge_const_handle aH ) const
  {
    return K().construct_direction_2_object()( CreateVector(aH) );
  }

  Trisegment_2_ptr CreateTrisegment ( Triedge const& aTriedge ) const
  {
    CGAL_precondition(aTriedge.is_valid() && aTriedge.is_skeleton());
    
    Trisegment_2_ptr r = Construct_ss_trisegment_2(mTraits)(CreateSegment(aTriedge.e0())
                                                           ,aTriedge.e0()->weight()
                                                           ,CreateSegment(aTriedge.e1())
                                                           ,aTriedge.e1()->weight()
                                                           ,CreateSegment(aTriedge.e2())
                                                           ,aTriedge.e2()->weight()
                                                           );
                                                                        
    CGAL_STSKEL_BUILDER_TRACE(6,"Trisegment for " << aTriedge << ":" << r ) ;
    
    CGAL_postcondition_msg(r, "Unable to determine edges collinearity");
      
    return r ;  
  }
  
  Trisegment_2_ptr CreateTrisegment ( Triedge const& aTriedge, Vertex_handle aLSeed ) const
  {
    Trisegment_2_ptr r = CreateTrisegment( aTriedge ) ;
    r->set_child_l( GetTrisegment(aLSeed) ) ;
    return r ;
  }
  
  Trisegment_2_ptr CreateTrisegment ( Triedge const& aTriedge, Vertex_handle aLSeed, Vertex_handle aRSeed ) const
  {
    Trisegment_2_ptr r = CreateTrisegment( aTriedge ) ;
    r->set_child_l( GetTrisegment(aLSeed) ) ;
    r->set_child_r( GetTrisegment(aRSeed) ) ;
    return r ;
  }
  
  Vertex_handle GetPrevInLAV ( Vertex_handle aV )
  {
    return GetVertex ( GetVertexData(aV).mPrevInLAV ) ;
  }

  Vertex_handle GetNextInLAV ( Vertex_handle aV )
  {
    return GetVertex ( GetVertexData(aV).mNextInLAV ) ;
  }

  bool IsLeftTerminal( Vertex_handle aV )
  {
    return ! handle_assigned( GetPrevInLAV(aV) ) ;  
  }
  
  bool IsRightTerminal( Vertex_handle aV )
  {
    return ! handle_assigned( GetNextInLAV(aV) ) ;  
  }
  
  void SetPrevInLAV ( Vertex_handle aV, Vertex_handle aPrev )
  {
    GetVertexData(aV).mPrevInLAV = aPrev->id();
  }

  void SetNextInLAV ( Vertex_handle aV, Vertex_handle aPrev )
  {
    GetVertexData(aV).mNextInLAV = aPrev->id();
  }

  Halfedge_handle GetEdgeEndingAt ( Vertex_handle aV )
  {
    return GetVertexTriedge(aV).e0();
  }
  
  Halfedge_handle GetEdgeStartingAt ( Vertex_handle aV )
  {
    Vertex_handle lN = GetNextInLAV(aV) ; return handle_assigned(lN) ? GetEdgeEndingAt(lN) : Halfedge_handle() ;
  }
  
  void Exclude ( Vertex_handle aV )
  {
    GetVertexData(aV).mIsExcluded = true ;
  }
  bool IsExcluded ( Vertex_const_handle aV ) const
  {
    return GetVertexData(aV).mIsExcluded ;
  }

  void SetIsTerminal ( Vertex_handle aV )
  {
    GetVertexData(aV).mIsTerminal = true ;
  }

  bool IsTerminal ( Vertex_handle aV )
  {
    return GetVertexData(aV).mIsTerminal ;
  }
  
  void SetIsReflex ( Vertex_handle aV )
  {
    GetVertexData(aV).mIsReflex = true ;
  }

  bool IsReflex ( Vertex_handle aV )
  {
    return GetVertexData(aV).mIsReflex ;
  }
  
  void SetIsDegenerate ( Vertex_handle aV )
  {
    GetVertexData(aV).mIsDegenerate = true ;
  }

  bool IsDegenerate ( Vertex_handle aV )
  {
    return GetVertexData(aV).mIsDegenerate ;
  }
  
  void SetIsProcessed ( Vertex_handle aV )
  {
    GetVertexData(aV).mIsProcessed = true ;

    mVisitor.on_vertex_processed(aV);
  }

  bool IsConvex ( Vertex_handle aV )
  {
    Vertex_data const& lData = GetVertexData(aV) ;
    return !lData.mIsReflex && !lData.mIsDegenerate ;
  }
  
  bool IsProcessed ( Vertex_handle aV )
  {
    return GetVertexData(aV).mIsProcessed ;
  }

  Vertex_handle NewInfNode()
  {
    Vertex_handle rInfNode = mSSkel->SSkel::Base::vertices_push_back( Vertex( mVertexID++ ) ) ;
    InitVertexData(rInfNode);
    CGAL_assertion(rInfNode->has_null_point());
    return rInfNode ;
  }
  
  void AddSplitEvent ( Vertex_handle aV, EventPtr aEvent )
  {
    CGAL_STSKEL_BUILDER_TRACE(2, "V" << aV->id() << " PQ: " << *aEvent);
    GetVertexData(aV).mSplitEvents.push(aEvent);
  }
  
  EventPtr PopNextSplitEvent ( Vertex_handle aV )
  {
    EventPtr rEvent ;
    Vertex_data& lData = GetVertexData(aV) ;
    if ( !lData.mNextSplitEventInMainPQ )
    {
      PQ& lPQ = lData.mSplitEvents ;
      if ( !lPQ.empty() )
      {
        rEvent = lPQ.top(); 
        lPQ.pop();
        lData.mNextSplitEventInMainPQ = true ;
      }
    }
    return rEvent ;
  }

  void AllowNextSplitEvent ( Vertex_handle aV )
  {
    GetVertexData(aV).mNextSplitEventInMainPQ = false ;
  }  
  
  void InsertEventInPQ( EventPtr aEvent ) ;

  EventPtr PopEventFromPQ() ;

  bool ExistEvent ( Trisegment_2_ptr const& aS )
  {
    return Do_ss_event_exist_2(mTraits)(aS,mMaxTime);
  }  
  
  bool IsOppositeEdgeFacingTheSplitSeed( Vertex_handle aSeed, Halfedge_handle aOpposite ) const
  {
    if ( aSeed->is_skeleton() )
         return Is_edge_facing_ss_node_2(mTraits)( GetTrisegment(aSeed), CreateSegment(aOpposite), aOpposite->weight() ) ;
    else return Is_edge_facing_ss_node_2(mTraits)( aSeed->point()      , CreateSegment(aOpposite), aOpposite->weight() ) ;
  }
  
  Oriented_side EventPointOrientedSideOfBisector( Event const&          aEvent
                                                , Halfedge_const_handle aE0
                                                , Halfedge_const_handle aE1
                                                , Vertex_handle         aV01
                                                , bool                  aE0isPrimary
                                                ) const
  {
    return Oriented_side_of_event_point_wrt_bisector_2(mTraits)( aEvent.trisegment()
                                                               , CreateSegment(aE0)
                                                               , aE0->weight()
                                                               , CreateSegment(aE1)
                                                               , aE1->weight()
                                                               , GetTrisegment(aV01) // Can be null
                                                               , aE0isPrimary
                                                               ) ;
  }

  Comparison_result CompareEvents ( Trisegment_2_ptr const& aA, Trisegment_2_ptr const& aB ) const
  {
    return Compare_ss_event_times_2(mTraits)(aA,aB) ;
  }

  Comparison_result CompareEvents ( EventPtr const& aA, EventPtr const& aB ) const
  {
    Comparison_result rR = aA->triedge() != aB->triedge() ? CompareEvents( aA->trisegment(), aB->trisegment() ) : EQUAL ;
    
    CGAL_STSKEL_BUILDER_TRACE(6,"Comparing events: {" << *aA << "} and {" << *aB << "} = " << ( rR == EQUAL ? "EQUAL" : ( rR == LARGER ? "LARGER"  : "SMALLER" )  ) ) ;
    
    return rR ;
  }
  
  bool AreEventsSimultaneous( Trisegment_2_ptr const& x, Trisegment_2_ptr const& y ) const
  {
    return Are_ss_events_simultaneous_2(mTraits)(x,y) ;
  }
  
  bool AreEventsSimultaneous( EventPtr const& x, EventPtr const& y ) const
  {
    return AreEventsSimultaneous(x->trisegment(),y->trisegment());
  }
  
  bool AreContourNodesCoincident( Vertex_handle aX, Vertex_handle aY ) const
  {
    CGAL_precondition( aX->is_contour() );
    CGAL_precondition( aY->is_contour() );
    
    return CGAL::compare_xy(aX->point(),aY->point()) == EQUAL ;
  }

  bool AreSkeletonNodesCoincident( Vertex_handle aX, Vertex_handle aY ) const
  {
    CGAL_precondition(  aX->is_skeleton() );
    CGAL_precondition(  aY->is_skeleton() );
    CGAL_precondition( !aX->has_infinite_time() );
    CGAL_precondition( !aY->has_infinite_time() );
    
    return AreEventsSimultaneous( GetTrisegment(aX),  GetTrisegment(aY) ) ;
  }
  
  Comparison_result CompareEvents( Trisegment_2_ptr const& aTrisegment, Vertex_handle aSeedNode ) const
  {
    return aSeedNode->is_skeleton() ? aSeedNode->has_infinite_time() ? SMALLER
                                                                     : CompareEvents( aTrisegment, GetTrisegment(aSeedNode) )
                                    : LARGER  ;
  }
  
  void SetBisectorSlope ( Halfedge_handle aBisector, Sign aSlope )
  {
    aBisector->HBase_base::set_slope(aSlope);
  }
  
  void SetBisectorSlope ( Vertex_handle aA, Vertex_handle aB )
  {
    Halfedge_handle lOBisector = aA->primary_bisector();
    Halfedge_handle lIBisector = lOBisector->opposite();

    CGAL_precondition( !aA->is_contour() || !aB->is_contour() ) ;
        
    if ( aA->is_contour() )
    {
      SetBisectorSlope(lOBisector,POSITIVE);
      SetBisectorSlope(lIBisector,NEGATIVE);
    }
    else if ( aB->is_contour())
    {
      SetBisectorSlope(lOBisector,NEGATIVE);
      SetBisectorSlope(lIBisector,POSITIVE);
    }
    else
    {
      if ( aA->has_infinite_time() )
      {
        CGAL_precondition( !aB->has_infinite_time());
        
        SetBisectorSlope(lOBisector,NEGATIVE);
        SetBisectorSlope(lIBisector,POSITIVE);
      }
      else if ( aB->has_infinite_time())
      {
        CGAL_precondition( !aA->has_infinite_time());
        
        SetBisectorSlope(lOBisector,NEGATIVE);
        SetBisectorSlope(lIBisector,POSITIVE);
      }
      else
      {
        CGAL_precondition( !aA->has_infinite_time());
        CGAL_precondition( !aB->has_infinite_time());
        
        Sign lSlope = CompareEvents(GetTrisegment(aB),GetTrisegment(aA));
        SetBisectorSlope(lOBisector,lSlope);
        SetBisectorSlope(lIBisector,opposite(lSlope));
      }
    }
  }

  boost::tuple<FT,Point_2> ConstructEventTimeAndPoint( Trisegment_2_ptr const& aS ) const
  {
    boost::optional< boost::tuple<FT,Point_2> > r = Construct_ss_event_time_and_point_2(mTraits)(aS);
    
    CGAL_postcondition_msg(!!r, "Unable to compute skeleton node coordinates");
    return *r ;  
  }

  void SetEventTimeAndPoint( Event& aE )
  {
    FT      lTime ;
    Point_2 lP ;
    boost::tie(lTime,lP) = ConstructEventTimeAndPoint(aE.trisegment());
    
    aE.SetTimeAndPoint(lTime,lP);
  }

  
  void EraseBisector( Halfedge_handle aB )
  {
    CGAL_STSKEL_BUILDER_TRACE(1,"Dangling B" << aB->id() << " and B" << aB->opposite()->id() << " removed.");
    
    mSSkel->SSkel::Base::edges_erase(aB);
  }

#ifdef CGAL_STSKEL_TRACE_ON
  std::string wavefront2str( Vertex_handle v )
  {
    std::ostringstream ss ; 
    
    ss << "N" << hid(GetPrevInLAV(v)) << "->N" << hid(v) << "->N" << hid(GetNextInLAV(v)) 
       << "  E" << hid(GetVertexTriedge(v).e0()) << "->E" << hid(GetVertexTriedge(v).e1()) ;
       
    return ss.str() ;
    
  } 
#endif
  
  void Link( Halfedge_handle aH, Face_handle aF )
  {
    aH->HBase_base::set_face(aF);
  }
  
  void Link( Halfedge_handle aH, Vertex_handle aV )
  {
    aH->HBase_base::set_vertex(aV);
  }
  
  void Link( Vertex_handle aV, Halfedge_handle aH )
  {
    aV->VBase::set_halfedge(aH);
  }
  
  void CrossLinkFwd( Halfedge_handle aPrev, Halfedge_handle aNext )
  {
    aPrev->HBase_base::set_next(aNext);
    aNext->HBase_base::set_prev(aPrev);
  }
  
  void CrossLink( Halfedge_handle aH, Vertex_handle aV )
  {
    Link(aH,aV);
    Link(aV,aH);
  }
  
  Triedge GetCommonTriedge( Vertex_handle aA, Vertex_handle aB ) ;

  bool AreBisectorsCoincident ( Halfedge_const_handle aA, Halfedge_const_handle aB ) const ;
                                    
  EventPtr IsPseudoSplitEvent( EventPtr const& aEvent, Vertex_handle_pair aOpp, Site const& aSite ) ;
  
  void CollectSplitEvent( Vertex_handle aNode, Triedge const& aTriedge ) ;

  void CollectSplitEvents( Vertex_handle aNode, Triedge const& aPrevEventTriedge ) ;

  EventPtr FindEdgeEvent( Vertex_handle aLNode, Vertex_handle aRNode, Triedge const& aPrevEventTriedge ) ;

  void HandleSimultaneousEdgeEvent( Vertex_handle aA, Vertex_handle aB ) ;

  void CollectNewEvents( Vertex_handle aNode, Triedge const& aPrevEventTriedge ) ;
  void UpdatePQ( Vertex_handle aV, Triedge const& aPrevEventTriedge ) ;
  void CreateInitialEvents();
  void CreateContourBisectors();
  void InitPhase();

  void SetupNewNode( Vertex_handle aNode );

  Vertex_handle_pair LookupOnSLAV ( Halfedge_handle aOBorder, EventPtr const& aEvent, Site& rSite ) ;

  Vertex_handle      ConstructEdgeEventNode         ( EdgeEvent&   aEvent ) ;
  Vertex_handle_pair ConstructSplitEventNodes       ( SplitEvent&  aEvent, Vertex_handle aOppR ) ;
  Vertex_handle_pair ConstructPseudoSplitEventNodes ( PseudoSplitEvent& aEvent ) ;

  bool IsValidEdgeEvent        ( EdgeEvent        const& aEvent ) ;
  bool IsValidSplitEvent       ( SplitEvent       const& aEvent, Vertex_handle_pair aOpp ) ;
  bool IsValidPseudoSplitEvent ( PseudoSplitEvent const& aEvent ) ;
  
  void HandleEdgeEvent               ( EventPtr aEvent ) ;
  void HandleSplitEvent              ( EventPtr aEvent, Vertex_handle_pair aOpp ) ;
  void HandlePseudoSplitEvent        ( EventPtr aEvent ) ;
  void HandleSplitOrPseudoSplitEvent ( EventPtr aEvent ) ;
  
  void InsertNextSplitEventInPQ( Vertex_handle v ) ;
  void InsertNextSplitEventsInPQ() ;
  
  bool IsProcessed( EventPtr aEvent ) ;

  void Propagate();
  
  void EraseNode ( Vertex_handle aNode ) ;

  void MergeSplitNodes ( Vertex_handle_pair aSplitNodes ) ;
  
  void RelinkBisectorsAroundMultinode( Vertex_handle const& v0, Halfedge_handle_vector& aLinks ) ;
  
  void PreprocessMultinode( Multinode& aMN ) ;
                          
  void ProcessMultinode( Multinode& aMN, Halfedge_handle_vector& rHalfedgesToRemove , Vertex_handle_vector& rNodesToRemove ) ;

  MultinodePtr CreateMultinode( Halfedge_handle begin, Halfedge_handle end ) ;
  
  void MergeCoincidentNodes() ;
  
  bool FinishUp();

  bool Run();

private:

  //Input
  Traits  mTraits ;

  Visitor const& mVisitor ;

  std::vector<Vertex_data_ptr> mVertexData ;
  
  Vertex_handle_vector   mReflexVertices ;
  Halfedge_handle_vector mDanglingBisectors ;
  Halfedge_handle_vector mBoundaryHalfedges ;

  std::list<Vertex_handle> mGLAV ;

  Vertex_handle_pair_vector mSplitNodes ;

  Event_compare mEventCompare ;

  int mVertexID ;
  int mEdgeID   ;
  int mFaceID   ;
  int mEventID  ;
  int mStepID   ;

  boost::optional<FT> mMaxTime ;
   
  PQ mPQ ;

  //Output
  SSkelPtr mSSkel ;

private :  

  template<class InputPointIterator, class Converter>
  Halfedge_handle enter_valid_contour ( InputPointIterator aBegin, InputPointIterator aEnd, bool aIsClosed, Converter const& cvt )
  {
    CGAL_STSKEL_BUILDER_TRACE(0,"Inserting " << ( aIsClosed ? "Closed" : "Open" ) << " Connected Component of the Boundary....");
    
    Halfedge_handle lNULL ;

    Halfedge_handle lFirstBoundaryFwdHE ;
    Halfedge_handle lPrevBoundaryFwdHE ;
    Halfedge_handle lNextBoundaryBckHE ;
    Halfedge_handle lBoundaryFwdHE ;
    Halfedge_handle lBoundaryBckHE ;
    Vertex_handle   lFirstVertex ;
    Vertex_handle   lPrevVertex ;

    InputPointIterator lCurr = aBegin ;
    InputPointIterator lPrev = aBegin ;
    
    InputPointIterator lSecond = aBegin ; ++ lSecond ;
    
    int c = 0 ;
    
    while ( lCurr != aEnd )
    {
      Vertex_handle lVertex = mSSkel->SSkel::Base::vertices_push_back( Vertex(mVertexID++,cvt(*lCurr)) ) ;
      CGAL_STSKEL_BUILDER_TRACE(1,"Vertex: N" << lVertex->id() << " at " << lVertex->point() );
      InitVertexData(lVertex);
      
      if ( aIsClosed || lCurr != aBegin )
      {
        lBoundaryFwdHE = mSSkel->SSkel::Base::edges_push_back ( Halfedge::NewBoundary(mEdgeID),Halfedge::NewBoundary(mEdgeID+1)  );
        lBoundaryBckHE = lBoundaryFwdHE->opposite();
        mEdgeID += 2 ;

        mBoundaryHalfedges.push_back(lBoundaryFwdHE);

        Face_handle lFace = mSSkel->SSkel::Base::faces_push_back( Face(mFaceID++) ) ;
        
        lBoundaryFwdHE->HBase_base::set_face(lFace);
        lFace         ->FBase     ::set_halfedge(lBoundaryFwdHE);

        lVertex       ->VBase     ::set_halfedge(lBoundaryFwdHE);
        lBoundaryFwdHE->HBase_base::set_vertex(lVertex);
        
        CGAL_STSKEL_BUILDER_TRACE(1,"Boundary Fwd E" << lBoundaryFwdHE->id() << " Bck E" << lBoundaryBckHE->id() << " Face F" << lFace->id() ) ;
      }

      ++ c ;

      if ( lCurr == aBegin )
      {
        lFirstVertex = lVertex ;
        
        if ( aIsClosed )
          lFirstBoundaryFwdHE = lBoundaryFwdHE ;
      }
      else
      {
        if ( ! aIsClosed && lCurr == lSecond )
          lFirstBoundaryFwdHE = lBoundaryFwdHE ;
        
        SetPrevInLAV(lVertex    ,lPrevVertex);
        SetNextInLAV(lPrevVertex,lVertex    );

        SetVertexTriedge(lPrevVertex, Triedge(lPrevBoundaryFwdHE,lBoundaryFwdHE) ) ;
        
        lBoundaryBckHE->HBase_base::set_vertex(lPrevVertex);

        if ( handle_assigned(lPrevBoundaryFwdHE) )
        {
          lBoundaryFwdHE    ->HBase_base::set_prev(lPrevBoundaryFwdHE);
          lPrevBoundaryFwdHE->HBase_base::set_next(lBoundaryFwdHE);

          lNextBoundaryBckHE->HBase_base::set_prev(lBoundaryBckHE);
          lBoundaryBckHE    ->HBase_base::set_next(lNextBoundaryBckHE);
        }

        CGAL_STSKEL_BUILDER_TRACE(1,"E" << lBoundaryFwdHE->id() << ' ' << lPrevVertex->point() << " -> " << lVertex    ->point() );
        CGAL_STSKEL_BUILDER_TRACE(1,"E" << lBoundaryBckHE->id() << ' ' << lVertex    ->point() << " -> " << lPrevVertex->point() );
        
        mVisitor.on_contour_edge_entered(lBoundaryFwdHE);

      }

      lPrev = lCurr ;
      
      ++ lCurr ;

      lPrevVertex        = lVertex ;
      lPrevBoundaryFwdHE = lBoundaryFwdHE ;
      lNextBoundaryBckHE = lBoundaryBckHE ;
    }

    if ( aIsClosed )
    {
      SetPrevInLAV(lFirstVertex,lPrevVertex );
      SetNextInLAV(lPrevVertex ,lFirstVertex);

      SetVertexTriedge( lPrevVertex, Triedge(lPrevBoundaryFwdHE,lFirstBoundaryFwdHE) ) ;

      lFirstBoundaryFwdHE->opposite()->HBase_base::set_vertex(lPrevVertex);

      lFirstBoundaryFwdHE->HBase_base::set_prev(lPrevBoundaryFwdHE);
      lPrevBoundaryFwdHE ->HBase_base::set_next(lFirstBoundaryFwdHE);

      lPrevBoundaryFwdHE ->opposite()->HBase_base::set_prev(lFirstBoundaryFwdHE->opposite());
      lFirstBoundaryFwdHE->opposite()->HBase_base::set_next(lPrevBoundaryFwdHE ->opposite());
      
      CGAL_STSKEL_BUILDER_TRACE(1
                               ,  "E" << lFirstBoundaryFwdHE->id()             << ' ' << lPrevVertex ->point() << " -> " << lFirstVertex->point() << '\n'
                               << "E" << lFirstBoundaryFwdHE->opposite()->id() << ' ' << lFirstVertex->point() << " -> " << lPrevVertex ->point()
                               );
                               
      mVisitor.on_contour_edge_entered(lFirstBoundaryFwdHE);
      
      CGAL_precondition_msg( c >= 3, "The closed contour must have at least 3 _distinct_ vertices" ) ;
    }
    else
    {
      SetVertexTriedge( lFirstVertex, Triedge(lFirstBoundaryFwdHE,lFirstBoundaryFwdHE) ) ;
      SetVertexTriedge( lPrevVertex , Triedge(lPrevBoundaryFwdHE ,lPrevBoundaryFwdHE ) ) ;
      
      CGAL_precondition_msg( c >= 2, "The open contour must have at least 2 _distinct_ vertices" ) ;
    }
    
    return lFirstBoundaryFwdHE ;
    
  }

  template<class InputPointIterator, class InputWeightIterator, class Converter>
  Halfedge_handle enter_valid_contour ( InputPointIterator  aPBegin
                                      , InputPointIterator  aPEnd
                                      , InputWeightIterator aWBegin
                                      , InputWeightIterator aWEnd
                                      , bool                aIsClosed
                                      , Converter const&    aCvt 
                                      ) 
  {
	  Halfedge_handle rHead = enter_valid_contour(aPBegin, aPEnd, aIsClosed, aCvt ) ;
	  
	  if ( aWBegin != aWEnd )
	  {
	    InputWeightIterator wit = aWBegin ;
  	  
	    Halfedge_handle lH = rHead ;
	    
	    do
	    {
        CGAL_STSKEL_BUILDER_TRACE(1, "E" << hid(lH) << " is given weight " << ( wit != aWEnd ? *wit : -1 ) );
  		  lH->HBase_base::set_weight(*wit);
	      Halfedge_handle lN = lH->next();
	      if ( !handle_assigned(lN) || lN == rHead )
	        break ;
        lH = lN ;
	    }
	    while ( ++ wit != aWEnd ) ;
	  }
	  
	  return rHead ;
  }
  
public:
  
  // This compares INPUT vertices so there is no need to filter it.
  struct AreVerticesEqual
  {
    template<class P>
    bool operator() ( P const&x, P const& y ) const
    {
      return CGAL::compare_xy(x,y) == EQUAL ;
    }
  } ; 
  
  template<class InputPointIterator, class Converter>
  Straight_skeleton_builder_2& enter_contour ( InputPointIterator aBegin
                                             , InputPointIterator aEnd
                                             , bool               aIsClosed
                                             , Converter const&   aCvt
                                             , bool               aCheckValidity = true 
                                             )
  {
    if ( aCheckValidity )
    {
      typedef typename std::iterator_traits<InputPointIterator>::value_type Input_point;
      
      typedef std::vector<Input_point> Input_point_vector ;
      typedef typename Input_point_vector::iterator Input_point_iterator ;
     
      // Remove coincident consecutive vertices
      Input_point_vector lList;
      std::unique_copy(aBegin,aEnd,std::back_inserter(lList),AreVerticesEqual());

      while ( lList.size() > 0 && CGAL::compare_xy(lList.front(),lList.back()) == EQUAL ) 
        lList.pop_back();
      
      if ( lList.size() >= ( aIsClosed ? 3u : 2u ) )
      {
        enter_valid_contour(lList.begin(), lList.end(), aIsClosed, aCvt);
      }
      else
      {
        CGAL_STSKEL_BUILDER_TRACE(0,"Degenerate contour (less than 3 non-degenerate vertices).");
      }
    }
    else
    {
      enter_valid_contour(aBegin, aEnd, aIsClosed, aCvt);
    } 

    return *this ;
  }
  
  template<class InputPointIterator, class InputWeightIterator, class Converter>
  Straight_skeleton_builder_2& enter_contour ( InputPointIterator  aPBegin
                                             , InputPointIterator  aPEnd
                                             , InputWeightIterator aWBegin
                                             , InputWeightIterator aWEnd
                                             , bool                aIsClosed      = true
                                             , Converter const&    aCvt           = Converter()
                                             , bool                aCheckValidity = true 
                                             )
  {
    if ( aCheckValidity )
    {
      typedef typename std::iterator_traits<InputPointIterator> ::value_type Input_point;
      typedef typename std::iterator_traits<InputWeightIterator>::value_type Input_weight;
      
      typedef std::vector<Input_point>  Input_point_vector ;
      typedef std::vector<Input_weight> Input_weight_vector ;
     
      //
      // Remove coincident consecutive vertices
      //
      Input_point_vector  lPList;
      Input_weight_vector lWList ;
      
      InputWeightIterator wit = aWBegin;
      for ( InputPointIterator pit = aPBegin; pit != aPEnd; ++ pit ) 
      {
        if( lPList.empty() || CGAL::compare_xy(lPList.back(),*pit) != EQUAL ) 
        {
	        lPList.push_back(*pit);
	        
	        if ( wit != aWEnd )
	             lWList.push_back(*wit);
	        else lWList.push_back( Input_weight(1.0) );
        }
        
        if ( wit != aWEnd )
          ++ wit ;  
      }      

      while ( lPList.size() > 0 && CGAL::compare_xy(lPList.front(),lPList.back()) == EQUAL ) 
      {
        lPList.pop_back();
        lWList.pop_back();
      }
      
      if ( lPList.size() >= ( aIsClosed ? 3u : 2u ) )
      {
        enter_valid_contour(lPList.begin(), lPList.end(), lWList.begin(), lWList.end(), aIsClosed, aCvt);
      }
      else
      {
        CGAL_STSKEL_BUILDER_TRACE(0,"Degenerate contour (less than 3 non-degenerate vertices).");
      }
    }
    else
    {
      enter_valid_contour(aPBegin, aPEnd, aWBegin, aWEnd, aIsClosed, aCvt);
    } 

    return *this ;
  }
  
  template<class InputPointIterator>
  Straight_skeleton_builder_2& enter_contour ( InputPointIterator aBegin
                                             , InputPointIterator aEnd
                                             , bool               aIsClosed      = true
                                             , bool               aCheckValidity = true 
                                             )
  {
    return enter_contour(aBegin, aEnd, aIsClosed, Cartesian_converter<K,K>(), aCheckValidity);
  }                                             
  
  template<class InputPointIterator, class InputWeightIterator>
  Straight_skeleton_builder_2& enter_contour ( InputPointIterator  aPBegin
                                             , InputPointIterator  aPEnd
                                             , InputWeightIterator aWBegin
                                             , InputWeightIterator aWEnd
                                             , bool                aIsClosed      = true
                                             , bool                aCheckValidity = true 
                                             )
  {
    return enter_contour(aPBegin, aPEnd, aWBegin, aWEnd, aIsClosed, Cartesian_converter<K,K>(), aCheckValidity ) ;
  }                                             

} ;

CGAL_END_NAMESPACE

#include <CGAL/Straight_skeleton_2/Straight_skeleton_builder_2_impl.h>


#endif // CGAL_STRAIGHT_SKELETON_BUILDER_2_H //
// EOF //