// Copyright (c) 2012 Geometry Factory. All rights reserved.
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Polyline_simplification_2/include/CGAL/Polyline_simplification_2/Squared_distance_cost.h $
// $Id: include/CGAL/Polyline_simplification_2/Squared_distance_cost.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
// Author(s)     : Andreas Fabri, Fernando Cacciola
//
#ifndef CGAL_POLYLINE_SIMPLIFICATION_2_SQUARED_DISTANCE_COST_H
#define CGAL_POLYLINE_SIMPLIFICATION_2_SQUARED_DISTANCE_COST_H

#include <CGAL/license/Polyline_simplification_2.h>


#include <CGAL/algorithm.h>
#include <CGAL/Constrained_triangulation_plus_2.h>

namespace CGAL {

#ifndef DOXYGEN_RUNNING

template < class Tr >
class Constrained_triangulation_plus_2;

#endif

namespace Polyline_simplification_2
{

/// \ingroup PkgPolylineSimplification2Classes

/// This class is a cost function which calculates the cost as the square of the distance between the original and simplified polylines.
///
/// \cgalModels{PolylineSimplificationCostFunction}
class Squared_distance_cost
{

public:

  /// Initializes the cost function
  Squared_distance_cost() {}

   /// Given a vertex in constraint iterator `vicq` computes `vicp=std::prev(vicq)` and `vicr=std::next(vicq)`,
  /// returns the maximum of the square distances between each point along the original subpolyline,
  /// between `vicp` and `vicr`, and the straight line segment  from `*vicp->point() to *vicr->point()`.
  /// \tparam CDT  must be `CGAL::Constrained_Delaunay_triangulation_2` with a vertex type that
  /// is model of  `PolylineSimplificationVertexBase_2`.

    template<class CDT>
    std::optional<typename CDT::Geom_traits::FT>
    operator()(const Constrained_triangulation_plus_2<CDT>& pct
               , typename Constrained_triangulation_plus_2<CDT>::Vertices_in_constraint_iterator vicq)const
  {
    typedef typename Constrained_triangulation_plus_2<CDT>::Points_in_constraint_iterator Points_in_constraint_iterator;
    typedef typename Constrained_triangulation_plus_2<CDT>::Geom_traits Geom_traits ;
    typedef typename Geom_traits::FT                                  FT;
    typedef typename Geom_traits::Compute_squared_distance_2 Compute_squared_distance ;
    typedef typename Geom_traits::Construct_segment_2        Construct_segment ;
    typedef typename Geom_traits::Segment_2                  Segment ;
    typedef typename Geom_traits::Point_2                    Point ;

    Compute_squared_distance compute_squared_distance = pct.geom_traits().compute_squared_distance_2_object() ;
    Construct_segment        construct_segment        = pct.geom_traits().construct_segment_2_object() ;
    typedef typename Constrained_triangulation_plus_2<CDT>::Vertices_in_constraint_iterator Vertices_in_constraint_iterator;

    Vertices_in_constraint_iterator vicp = std::prev(vicq);
    Vertices_in_constraint_iterator vicr = std::next(vicq);

    Point const& lP = (*vicp)->point();
    Point const& lR = (*vicr)->point();

    Segment lP_R = construct_segment(lP, lR) ;

    FT d1 = 0.0;
    Points_in_constraint_iterator pp(vicp), rr(vicr);
    ++pp;

    for ( ;pp != rr; ++pp )
      d1 = (std::max)(d1, compute_squared_distance( lP_R, *pp ) ) ;

    return d1 ;
  }


};


} // namespace Polyline_simplification_2


} //namespace CGAL

#endif // CGAL_POLYLINE_SIMPLIFICATION_2_SQUARED_DISTANCE_COST_H



