// Copyright (c) 1999  Max-Planck-Institute Saarbruecken (Germany).
// 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)     : Stefan Schirra


#ifndef CGAL_CH_AKL_TOUSSAINT_C
#define CGAL_CH_AKL_TOUSSAINT_C

#ifndef CGAL_CH_AKL_TOUSSAINT_H
#include <CGAL/ch_akl_toussaint.h>
#endif // CGAL_CH_AKL_TOUSSAINT_H

#ifndef CGAL_CH_NO_POSTCONDITIONS
#include <CGAL/convexity_check_2.h>
#endif // CGAL_CH_NO_POSTCONDITIONS

#include <CGAL/ch_assertions.h>
#include <CGAL/ch_selected_extreme_points_2.h>
#include <CGAL/ch_graham_andrew.h>
#include <CGAL/algorithm.h>
#include <CGAL/functional.h>
#include <CGAL/IO/Tee_for_output_iterator.h>

CGAL_BEGIN_NAMESPACE
template <class ForwardIterator, class OutputIterator, class Traits>
OutputIterator
ch_akl_toussaint(ForwardIterator first, ForwardIterator last, 
                 OutputIterator  result,
                 const Traits&   ch_traits)
{
  typedef  typename Traits::Point_2                    Point_2;    
  typedef  typename Traits::Left_turn_2                Left_of_line;
  // added 
  typedef  typename Traits::Equal_2                    Equal_2;
  
  Left_of_line  left_turn        = ch_traits.left_turn_2_object();
  Equal_2       equal_points     = ch_traits.equal_2_object();  

  if (first == last) return result;
  ForwardIterator n, s, e, w;
  ch_nswe_point( first, last, n, s, w, e, ch_traits);
  if (equal_points(*n, *s) )
  {
      *result = *w;  ++result;
      return result;
  }

  std::vector< Point_2 > region1;
  std::vector< Point_2 > region2;
  std::vector< Point_2 > region3;
  std::vector< Point_2 > region4;
  region1.reserve(16);
  region2.reserve(16);
  region3.reserve(16);
  region4.reserve(16);
  region1.push_back( *w);
  region2.push_back( *s);
  region3.push_back( *e);
  region4.push_back( *n);

  CGAL_ch_postcondition_code( ForwardIterator save_first = first; )

  for ( ; first != last; ++first )
  {
      if ( left_turn(*e, *w, *first ) )   
      {
          if ( left_turn( *s, *w, *first ) )       region1.push_back( *first );
          else if ( left_turn( *e, *s, *first ) )  region2.push_back( *first );
      }
      else
      {
          if ( left_turn( *n, *e, *first ) )       region3.push_back( *first );
          else if ( left_turn( *w, *n, *first ) )  region4.push_back( *first );
      }
  }

  #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) \
    || defined(NDEBUG)
  OutputIterator  res(result);
  #else
  Tee_for_output_iterator<OutputIterator,Point_2> res(result);
  #endif // no postconditions ...
  std::sort( successor(region1.begin() ), region1.end(), 
             ch_traits.less_xy_2_object() );
  std::sort( successor(region2.begin() ), region2.end(), 
             ch_traits.less_xy_2_object() );
  std::sort( successor(region3.begin() ), region3.end(),
             swap_1(ch_traits.less_xy_2_object()) );
  std::sort( successor(region4.begin() ), region4.end(), 
             swap_1(ch_traits.less_xy_2_object()) );

  if (! equal_points(*w,*s) )
  {
      region1.push_back( *s );
      ch__ref_graham_andrew_scan( region1.begin(), region1.end(), 
                                       res, ch_traits);
  }
  if (! equal_points(*s,*e) )
  {
      region2.push_back( *e );
      ch__ref_graham_andrew_scan( region2.begin(), region2.end(),
                                       res, ch_traits);
  }
  if (! equal_points(*e,*n) )
  {
      region3.push_back( *n );
      ch__ref_graham_andrew_scan( region3.begin(), region3.end(),
                                       res, ch_traits);
  }
  if (! equal_points(*n,*w) )
  {
      region4.push_back( *w );
      ch__ref_graham_andrew_scan( region4.begin(), region4.end(),
                                       res, ch_traits);
  }

  CGAL_ch_postcondition_code( first = save_first; )
  CGAL_ch_postcondition( \
      is_ccw_strongly_convex_2( res.output_so_far_begin(), \
                                     res.output_so_far_end(), \
                                     ch_traits));
  CGAL_ch_expensive_postcondition( \
      ch_brute_force_check_2( \
          first, last, \
          res.output_so_far_begin(), res.output_so_far_end(), \
          ch_traits)
  );
  #if defined(CGAL_CH_NO_POSTCONDITIONS) || defined(CGAL_NO_POSTCONDITIONS) \
    || defined(NDEBUG)
  return res;
  #else
  return res.to_output_iterator();
  #endif // no postconditions ...

}

CGAL_END_NAMESPACE

#endif // CGAL_CH_AKL_TOUSSAINT_C