// Copyright (c) 2009 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Mesh_3/include/CGAL/Mesh_3/Triangulation_sizing_field.h $
// $Id: include/CGAL/Mesh_3/Triangulation_sizing_field.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Stephane Tayeb
//
//******************************************************************************
// File Description : Defines a sizing field which use an internal triangulation
// to store the sizes
//******************************************************************************

#ifndef CGAL_MESH_3_TRIANGULATION_SIZING_FIELD_H
#define CGAL_MESH_3_TRIANGULATION_SIZING_FIELD_H

#include <CGAL/license/Mesh_3.h>

#include <CGAL/Triangulation_data_structure_3.h>
#include <CGAL/Regular_triangulation_3.h>
#include <CGAL/Regular_triangulation_cell_base_3.h>
#include <CGAL/Regular_triangulation_vertex_base_3.h>
#include <CGAL/Triangulation_cell_base_3.h>
#include <CGAL/Triangulation_vertex_base_with_info_3.h>

#include <CGAL/functional.h>

#include <CGAL/boost/iterator/transform_iterator.hpp>

namespace CGAL {

namespace Mesh_3
{

/**
 * @class Triangulation_sizing_field
 */
template <typename Tr>
class Triangulation_sizing_field
{
  // Types
  typedef typename Tr::Geom_traits                        GT;
  typedef typename Tr::Bare_point                         Bare_point;
  typedef typename Tr::Weighted_point                     Weighted_point;
  typedef typename GT::FT                                 FT;

  typedef Triangulation_vertex_base_with_info_3<FT, GT>   Vbb;
  typedef Regular_triangulation_vertex_base_3<GT, Vb>     Vb;
  typedef Triangulation_cell_base_3<GT>                   Cbb;
  typedef Regular_triangulation_cell_base_3<
            GT, Cbb, Discard_hidden_points>               Cb;
  typedef Triangulation_data_structure_3<Vb, Cb>          Tds;
  typedef Regular_triangulation_3<GT,Tds>                 Compact_triangulation;
  typedef Compact_triangulation                           Ctr;

  typedef typename Tr::Vertex_handle                      Vertex_handle;
  typedef typename Tr::Cell_handle                        Cell_handle;
  typedef typename Ctr::Cell_handle                       CCell_handle;
  typedef typename Ctr::Vertex_handle                     CVertex_handle;

public:
  // Vertices of mesh triangulation do not need to be updated
  static const bool is_vertex_update_needed = false;

public:
  /**
   * Constructor
   */
  Triangulation_sizing_field(const Tr& tr);

  /**
   * Fills the sizing field, using size associated to point in `value_map`.
   */
  void fill(const std::map<Weighted_point, FT>& value_map);

  /**
   * Returns size at point `p`.
   */
  FT operator()(const Weighted_point& p) const;

  /**
   * Returns size at point `p`. (needed for compatibility)
   */
  template <typename Handle>
  FT operator()(const Weighted_point& p, const Handle&) const
  { return this->operator()(p); }

private:
  /**
   * Returns size at point `p`, by interpolation into tetrahedron.
   */
  FT interpolate_on_cell_vertices(const Weighted_point& p,
                                  const CCell_handle& cell) const;

  /**
   * Returns size at point `p`, by interpolation into facet (`cell` is assumed
   * to be an infinite cell).
   */
  FT interpolate_on_facet_vertices(const Weighted_point& p,
                                   const CCell_handle& cell) const;

  /**
   * Returns a hint for `p` location.
   */
  CCell_handle get_hint(const Weighted_point& p) const
  { return last_cell_; }

  /**
   * A functor which extract the point from a vertex handle.
   * Used by boost transform iterator
   */
  struct Extract_point :
    public CGAL::cpp98::unary_function<typename Tr::Vertex, Weighted_point>
  {
    Weighted_point operator()(const typename Tr::Vertex& v) const { return v.point(); }
  };

private:
  Compact_triangulation ctr_;
  mutable CCell_handle last_cell_;
};


template <typename Tr>
Triangulation_sizing_field<Tr>::
Triangulation_sizing_field(const Tr& tr)
  : ctr_(boost::make_transform_iterator(tr.finite_vertices_begin(),
                                        Extract_point()),
         boost::make_transform_iterator(tr.finite_vertices_end(),
                                        Extract_point()) )
  , last_cell_(CCell_handle())
{
}



template <typename Tr>
void
Triangulation_sizing_field<Tr>::
fill(const std::map<Weighted_point, FT>& value_map)
{
  typedef typename Ctr::Finite_vertices_iterator  Fvi;

  for ( Fvi vit = ctr_.finite_vertices_begin() ;
        vit != ctr_.finite_vertices_end() ;
        ++ vit )
  {
    typename std::map<Weighted_point, FT>::const_iterator find_result =
      value_map.find(ctr_.point(vit));

    if ( find_result != value_map.end() )
      vit->info() = find_result->second;
    else
      vit->info() = FT(0);
  }
}


template <typename Tr>
typename Triangulation_sizing_field<Tr>::FT
Triangulation_sizing_field<Tr>::
operator()(const Weighted_point& p) const
{
  CCell_handle hint = get_hint(p);
  CCell_handle cell = ctr_.locate(p,hint);
  last_cell_ = cell;

  if ( !ctr_.is_infinite(cell) )
    return interpolate_on_cell_vertices(p,cell);
  else
    return interpolate_on_facet_vertices(p,cell);
}


template <typename Tr>
typename Triangulation_sizing_field<Tr>::FT
Triangulation_sizing_field<Tr>::
interpolate_on_cell_vertices(const Weighted_point& p, const CCell_handle& cell) const
{
  typename GT::Construct_point_3 cp = ctr_.geom_traits().construct_point_3_object();
  typename GT::Compute_volume_3 volume = ctr_.geom_traits().compute_volume_3_object();

  // Interpolate value using tet vertices values
  const FT& va = cell->vertex(0)->info();
  const FT& vb = cell->vertex(1)->info();
  const FT& vc = cell->vertex(2)->info();
  const FT& vd = cell->vertex(3)->info();

  const Weighted_point& wa = ctr_.point(cell, 0);
  const Weighted_point& wb = ctr_.point(cell, 1);
  const Weighted_point& wc = ctr_.point(cell, 2);
  const Weighted_point& wd = ctr_.point(cell, 3);
  const Bare_point& a = cp(wa);
  const Bare_point& b = cp(wb);
  const Bare_point& c = cp(wc);
  const Bare_point& d = cp(wd);

  const FT abcp = CGAL::abs(volume(a,b,c,p));
  const FT abdp = CGAL::abs(volume(a,b,d,p));
  const FT acdp = CGAL::abs(volume(a,c,d,p));
  const FT bcdp = CGAL::abs(volume(b,c,d,p));

  // TODO: improve this (static filter ?)
  // If volume is 0, then compute the average value
  if ( is_zero(abcp+abdp+acdp+bcdp) )
    return (va+vb+vc+vd)/4.;

  return ( (abcp*vd + abdp*vc + acdp*vb + bcdp*va) / (abcp+abdp+acdp+bcdp) );
}

template <typename Tr>
typename Triangulation_sizing_field<Tr>::FT
Triangulation_sizing_field<Tr>::
interpolate_on_facet_vertices(const Weighted_point& p, const CCell_handle& cell) const
{
  typename GT::Construct_point_3 cp = ctr_.geom_traits().construct_point_3_object();
  typename GT::Compute_area_3 area = ctr_.geom_traits().compute_area_3_object();

  // Find infinite vertex and put it in k0
  int k0 = 0;
  int k1 = 1;
  int k2 = 2;
  int k3 = 3;

  if ( ctr_.is_infinite(cell->vertex(1)) )
    std::swap(k0,k1);
  if ( ctr_.is_infinite(cell->vertex(2)) )
    std::swap(k0,k2);
  if ( ctr_.is_infinite(cell->vertex(3)) )
    std::swap(k0,k3);

  // Interpolate value using tet vertices values
  const FT& va = cell->vertex(k1)->info();
  const FT& vb = cell->vertex(k2)->info();
  const FT& vc = cell->vertex(k3)->info();

  const Weighted_point& wa = ctr_.point(cell, k1);
  const Weighted_point& wb = ctr_.point(cell, k2);
  const Weighted_point& wc = ctr_.point(cell, k3);
  const Bare_point& a = cp(wa);
  const Bare_point& b = cp(wb);
  const Bare_point& c = cp(wc);

  const FT abp = area(a,b,p);
  const FT acp = area(a,c,p);
  const FT bcp = area(b,c,p);

  // TODO: improve this (static filter ?)
  // If area is 0, then compute the average value
  if ( is_zero(abp+acp+bcp) )
    return (va+vb+vc)/3.;

  return ( (abp*vc + acp*vb + bcp*va ) / (abp+acp+bcp) );
}

} // end namespace Mesh_3


} //namespace CGAL

#endif // CGAL_MESH_3_TRIANGULATION_SIZING_FIELD_H

