// Copyright (c) 1999  Max-Planck-Institute Saarbruecken (Germany).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.0.2/Convex_hull_2/include/CGAL/ch_selected_extreme_points_2.h $
// $Id: include/CGAL/ch_selected_extreme_points_2.h e13ef800cb7 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Stefan Schirra


#ifndef CGAL_CH_SELECTED_EXTREME_POINTS_2_H
#define CGAL_CH_SELECTED_EXTREME_POINTS_2_H

#include <CGAL/license/Convex_hull_2.h>


#include <CGAL/basic.h>
#include <iterator>


namespace CGAL {


// traverses the range [|first|,|last|). After execution, the value of |n| is
// an iterator in the range such that |*n| $\ge_{\rm yx}$ |*it| for
// all iterators |it| in the range. Similarly, for |s|, |w|, and |e|
// the inequations |*s| $\le_{\rm yx}$ |*it|, |*w| $\le_{\rm xy}$ |*it|,
// and |*e| $\ge_{\rm yx}$ |*it| hold respectively for all iterators
// |it| in the range.
// {\sc traits}: uses |Traits::Less_xy_2| and |Traits::Less_yx_2|.
template <class ForwardIterator, class Traits>
void
ch_nswe_point( ForwardIterator first, ForwardIterator last,
               ForwardIterator& n,
               ForwardIterator& s,
               ForwardIterator& w,
               ForwardIterator& e,
               const Traits& ch_traits);

template <class ForwardIterator>
inline
void
ch_nswe_point( ForwardIterator first, ForwardIterator last,
               ForwardIterator& n,
               ForwardIterator& s,
               ForwardIterator& w,
               ForwardIterator& e)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_nswe_point(first, last, n, s, w, e, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |n| is
// an iterator in the range such that |*n| $\ge_{\rm yx}$ |*it| for
// all iterators |it| in the range. Similarly, for |s| the inequation
// |*s| $\le_{\rm yx}$ |*it| holds for all iterators |it| in the range.
// {\sc traits}: uses function object type |Traits::Less_yx_2|.
template <class ForwardIterator, class Traits>
void
ch_ns_point( ForwardIterator first, ForwardIterator last,
             ForwardIterator& n,
             ForwardIterator& s,
             const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_ns_point( ForwardIterator first, ForwardIterator last,
             ForwardIterator& n,
             ForwardIterator& s)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_ns_point(first, last, n, s, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |w| is
// an iterator in the range such that |*w| $\le_{\rm xy}$ |*it| for
// all iterators |it| in the range. Similarly, for |e| the inequation
// |*e| $\ge_{\rm yx}$ |*it| holds for all iterators |it| in the range.
// {\sc traits}: uses function object type |Traits::Less_xy_2|.
template <class ForwardIterator, class Traits>
void
ch_we_point( ForwardIterator first, ForwardIterator last,
             ForwardIterator& w,
             ForwardIterator& e,
             const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_we_point( ForwardIterator first, ForwardIterator last,
             ForwardIterator& w,
             ForwardIterator& e)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_we_point(first, last, w, e, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |n| is
// an iterator in the range such that |*n| $\ge_{\rm yx}$ |*it| for
// all iterators |it| in the range.
// {\sc traits}: uses |Traits::Less_yx_2|.
template <class ForwardIterator, class Traits>
void
ch_n_point( ForwardIterator first, ForwardIterator last,
            ForwardIterator& n,
            const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_n_point( ForwardIterator first, ForwardIterator last, ForwardIterator& n)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_n_point(first, last, n, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |s| is
// an iterator in the range such that |*s| $\le_{\rm yx}$ |*it| for
// all iterators |it| in the range.
// {\sc traits}: uses |Traits::Less_yx_2|.
template <class ForwardIterator, class Traits>
void
ch_s_point( ForwardIterator first, ForwardIterator last,
            ForwardIterator& s,
            const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_s_point( ForwardIterator first, ForwardIterator last, ForwardIterator& s)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_s_point(first, last, s, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |e| is
// an iterator in the range such that |*e| $\ge_{\rm yx}$ |*it| for
// for all iterators |it| in the range.
// {\sc traits}: uses |Traits::Less_xy_2|.
template <class ForwardIterator, class Traits>
void
ch_e_point( ForwardIterator first, ForwardIterator last,
            ForwardIterator& e,
            const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_e_point( ForwardIterator first, ForwardIterator last, ForwardIterator& e)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_e_point(first, last, e, Kernel());
}


// traverses the range [|first|,|last|). After execution, the value of |w| is
// an iterator in the range such that |*w| $\le_{\rm yx}$ |*it| for
// for all iterators |it| in the range.
// {\sc traits}: uses |Traits::Less_yx_2|.
template <class ForwardIterator, class Traits>
void
ch_w_point( ForwardIterator first, ForwardIterator last,
            ForwardIterator& w,
            const Traits& ch_traits );

template <class ForwardIterator>
inline
void
ch_w_point( ForwardIterator first, ForwardIterator last, ForwardIterator& w)
{
    typedef std::iterator_traits<ForwardIterator> ITraits;
    typedef typename ITraits::value_type          value_type;
    typedef CGAL::Kernel_traits<value_type>       KTraits;
    typedef typename KTraits::Kernel              Kernel;
    ch_w_point(first, last, w, Kernel());
}

} //namespace CGAL

#include <CGAL/Convex_hull_2/ch_selected_extreme_points_2_impl.h>

#endif // CGAL_CH_SELECTED_EXTREME_POINTS_2_H
