// Copyright (c) 2013 INRIA Sophia-Antipolis (France),
//               2014-2015 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Mesh_2/include/CGAL/Mesh_2/Mesh_sizing_field.h $
// $Id: include/CGAL/Mesh_2/Mesh_sizing_field.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s) : Jane Tournois, Pierre Alliez
//

#ifndef CGAL_MESH_2_MESH_SIZING_FIELD_H
#define CGAL_MESH_2_MESH_SIZING_FIELD_H

#include <CGAL/license/Mesh_2.h>


#include <CGAL/Mesh_2/Sizing_field_2.h>
#include <CGAL/squared_distance_2.h>

namespace CGAL {

namespace Mesh_2
{
/**
 * @class Mesh_sizing_field
 */
template <typename Tr, bool Need_vertex_update = true>
class Mesh_sizing_field
  : public virtual Sizing_field_2<Tr>
{
  // Types
  typedef typename Tr::Geom_traits   Gt;
  typedef typename Tr::Point         Point_2;
  typedef typename Gt::FT            FT;

  typedef typename Tr::Vertex_handle      Vertex_handle;
  typedef typename Tr::Face_handle        Face_handle;
  typedef typename Tr::Edge               Edge;

public:
  // update vertices of mesh triangulation ?
  static const bool is_vertex_update_needed = Need_vertex_update;

public:
  /**
   * Constructor
   */
  Mesh_sizing_field(Tr& tr)
  : tr_(tr)
  , last_face_()
  {
    init();
  }

  /**
   * Returns size at point `p`.
   */
  FT operator()(const Point_2& p) const
  { return this->operator()(p, last_face_); }

  /**
   * Returns size at point `p`, using `v` to accelerate `p` location
   * in triangulation
   */
  FT operator()(const Point_2& p, const Vertex_handle& v) const
  { return this->operator()(p, v->face()); }

  /**
   * Returns size at point `p`.
   */
  FT operator()(const Point_2& p, const Face_handle& c) const
  {
    const Face_handle fh = tr_.locate(p,c);
    last_face_ = fh;

    if ( !tr_.is_infinite(fh) )
      return interpolate_on_face_vertices(p,fh);
    else
      return interpolate_on_edge_vertices(p,fh);
  }

  /**
   * Fill sizing field with actual size inside the triangulation
   */
  void init()
  {
    for(typename Tr::Finite_vertices_iterator
        vit = tr_.finite_vertices_begin() ;
        vit != tr_.finite_vertices_end() ;
        ++vit )
    {
      vit->set_sizing_info(average_incident_edge_length(vit));
    }
  }

private:
  /**
   * Returns size at point `p`, by interpolation inside facet.
   */
  FT interpolate_on_face_vertices(const Point_2&
#ifdef CGAL_MESH_2_SIZING_FIELD_USE_BARYCENTRIC_COORDINATES
                                  p
#endif
                                  , const Face_handle& f) const
  {
    // Interpolate value using tet vertices values
    const FT& sa = f->vertex(0)->sizing_info();
    const FT& sb = f->vertex(1)->sizing_info();
    const FT& sc = f->vertex(2)->sizing_info();

#ifdef CGAL_MESH_2_SIZING_FIELD_USE_BARYCENTRIC_COORDINATES
    const Point_2& a = f->vertex(0)->point();
    const Point_2& b = f->vertex(1)->point();
    const Point_2& c = f->vertex(2)->point();
    double abc_inv = 1. / CGAL::area(a, b, c);
    double alpha = CGAL::area(p, b, c) * abc_inv;
    double beta = CGAL::area(a, p, c) * abc_inv;
    double gamma = CGAL::area(a, b, p) * abc_inv;

    return alpha * sa + beta * sb + gamma * sc;
#else
    return ((sa + sb + sc) / 3.);
#endif
  }

  /**
   * Returns size at point `p`, by interpolation inside edge
   * (`f` is assumed to be an infinite face)
   */
  FT interpolate_on_edge_vertices(const Point_2&
#ifdef CGAL_MESH_2_SIZING_FIELD_USE_BARYCENTRIC_COORDINATES
                                  p
#endif
                                  , const Face_handle& f) const
  {
    CGAL_precondition(tr_.is_infinite(f));
    int finite_i = -1;
    for(int i = 0; i < 3; ++i)
    {
      if(!tr_.is_infinite(f, i))
        finite_i = i;
    }
    CGAL_assertion(finite_i != -1);

    const FT& sa = f->vertex(tr_.cw(finite_i))->sizing_info();
    const FT& sb = f->vertex(tr_.ccw(finite_i))->sizing_info();

#ifdef CGAL_MESH_2_SIZING_FIELD_USE_BARYCENTRIC_COORDINATES
    const Point_2& pa = f->vertex(tr_.cw(finite_i))->point();
    const Point_2& pb = f->vertex(tr_.ccw(finite_i))->point();

    FT t = CGAL::sqrt(
      CGAL::squared_distance(pb, pb) / CGAL::squared_distance(pa, pb));
    CGAL_assertion(t <= 1.);

    return t * sa + (1. - t) * sb;
#else
    return 0.5 * (sa + sb);
#endif
  }

  FT average_incident_edge_length(const Vertex_handle& v) const
  {
    typename Tr::Edge_circulator ec = tr_.incident_edges(v);
    typename Tr::Edge_circulator end = ec;

    FT sum_len(0.);
    unsigned int nb = 0;
    do
    {
      Edge e = *ec;
      if(tr_.is_infinite(e))
        continue;

      Face_handle f1 = e.first;
      Face_handle f2 = e.first->neighbor(e.second);
      if(f1->is_in_domain() || f2->is_in_domain())
      {
        sum_len += length(e);
        ++nb;
      }
    }
    while(++ec != end);
    // nb == 0 could happen if there is an isolated point.
    if( 0 != nb )
      return sum_len/FT(nb);
    else
     // Use outside faces to compute size of point
      return 1.;//todo
  }

  FT length(const Edge& e) const
  {
    Point_2 p1 = e.first->vertex(Tr::cw(e.second))->point();
    Point_2 p2 = e.first->vertex(Tr::ccw(e.second))->point();
    return CGAL::sqrt(CGAL::squared_distance(p1, p2));
  }

private:
  /// The triangulation
  Tr& tr_;
  /// A face_handle that is used to accelerate location queries
  mutable Face_handle last_face_;
};

} // end namespace Mesh_2

} //namespace CGAL

#endif // CGAL_MESH_2_MESH_SIZING_FIELD_H

