#include <Rcpp.h>
// 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/Refine_facets_3.h $
// $Id: include/CGAL/Mesh_3/Refine_facets_3.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Laurent Rineau, Stéphane Tayeb
//
//******************************************************************************
// File Description :
// Implements a mesher level for facets.
//******************************************************************************

#ifndef CGAL_MESH_3_REFINE_FACETS_3_H
#define CGAL_MESH_3_REFINE_FACETS_3_H

#include <CGAL/license/Mesh_3.h>

#include <CGAL/disable_warnings.h>

#include <CGAL/Mesh_3/Mesher_level.h>
#include <CGAL/Mesh_3/Mesher_level_default_implementations.h>
#ifdef CGAL_LINKED_WITH_TBB
  #include <tbb/enumerable_thread_specific.h>
  #include <tbb/parallel_for_each.h>
#endif

#include <CGAL/Meshes/Filtered_deque_container.h>
#include <CGAL/Meshes/Filtered_multimap_container.h>
#include <CGAL/Meshes/Double_map_container.h>

#include <CGAL/Meshes/Triangulation_mesher_level_traits_3.h>

#ifdef CGAL_MESH_3_PROFILING
  #include <CGAL/Mesh_3/Profiling_tools.h>
#endif
#include <CGAL/SMDS_3/Dump_c3t3.h>

#include <CGAL/Object.h>

#include <boost/format.hpp>
#include <optional>
#include <boost/optional/optional_io.hpp>
#include <boost/mpl/has_xxx.hpp>

#include <sstream>
#include <atomic>

namespace CGAL {

namespace Mesh_3 {

  template<typename Facet>
  struct Facets_erase_counters
  {
    const Facet f1_;
    const unsigned int f1_erase_counter_;
    const Facet f2_;
    const unsigned int f2_erase_counter_;
  };

  // Predicate to know if a facet in a refinement queue is a zombie
  // A facet is a pair <cell, index of the opposite vertex>.
  // A facet is a "zombie" if at least one of its two adjacent cells
  // has been erased. We test it thanks to the "erase counter" which
  // is inside each cell (incremented by the compact container).
  // In the refinement queue, we store a struct
  // <facet1, facet1_erase counter, facet2, facet2_erase_counter>
  // where facet2 = mirror_facet(facet1) and facetx_erase_counter is
  // the erase_counter of facetx's cell when added to the queue>
  template<typename Facet>
  class Facet_to_refine_is_not_zombie
  {
    typedef Facets_erase_counters<Facet> Facets_ec;

  public:
    Facet_to_refine_is_not_zombie() {}

    bool operator()(const Facets_ec& f) const
    {
#ifdef _DEBUG
      /*
      int f1_current_erase_counter = f.f1_.first->erase_counter();
      int f1_saved_erase_counter = f.f1_erase_counter_;
      int f2_current_erase_counter = f.f2_.first->erase_counter();
      int f2_saved_erase_counter = f.f2_erase_counter_;
      */
      //f1_current_erase_counter - f1_saved_erase_counter + f2_current_erase_counter - f2_saved_erase_counter == 1

      /*if (f1_current_erase_counter - f1_saved_erase_counter + f2_current_erase_counter - f2_saved_erase_counter == 1)
      {
#ifdef CGAL_LINKED_WITH_TBB
        tbb::queuing_mutex mut;
        tbb::queuing_mutex::scoped_lock l(mut);
#endif

        std::stringstream sstr;
        Facet facet = f.f1_;
        sstr << "Facet 1 { " << std::endl
        << "  - " << *facet.first->vertex((facet.second+1)%4)  << std::endl
        << "  - " << *facet.first->vertex((facet.second+2)%4)  << std::endl
        << "  - " << *facet.first->vertex((facet.second+3)%4)  << std::endl
        << "  - 4th vertex in cell: " << *facet.first->vertex(facet.second)  << std::endl
        << "}" << std::endl;

        facet = f.f2_;
        sstr << "Facet 2 { " << std::endl
        << "  - " << *facet.first->vertex((facet.second+1)%4)  << std::endl
        << "  - " << *facet.first->vertex((facet.second+2)%4)  << std::endl
        << "  - " << *facet.first->vertex((facet.second+3)%4)  << std::endl
        << "  - 4th vertex in cell: " << *facet.first->vertex(facet.second)  << std::endl
        << "}" << std::endl;

        std::string s = sstr.str();
        Rcpp::Rcerr << s << std::endl;
      }*/
#endif
      return (f.f1_.first->erase_counter() == f.f1_erase_counter_
           && f.f2_.first->erase_counter() == f.f2_erase_counter_ );
    }
  };

/************************************************
// Class Refine_facets_3_handle_queue_base
// Two versions: sequential / parallel
************************************************/

// Sequential
template <typename Index, typename Facet, typename Concurrency_tag>
class Refine_facets_3_handle_queue_base
{
  typedef Facets_erase_counters<Facet> Facets_counters;

protected:
  Refine_facets_3_handle_queue_base() : m_last_vertex_index() {}

  Index get_last_vertex_index() const
  {
    return m_last_vertex_index;
  }

  void set_last_vertex_index(Index i) const
  {
    m_last_vertex_index = i;
  }

#if defined(CGAL_MESH_3_USE_LAZY_SORTED_REFINEMENT_QUEUE) \
 || defined(CGAL_MESH_3_USE_LAZY_UNSORTED_REFINEMENT_QUEUE)

  Facets_counters
  from_facet_to_refinement_queue_element(const Facet &facet,
                                         const Facet &mirror) const
  {
    return Facets_counters{facet, facet.first->erase_counter(),
                           mirror, mirror.first->erase_counter()};
  }

public:
  template<typename Container_element>
  Facet extract_element_from_container_value(const Container_element &e) const
  {
    // We get the first Facet inside the struct
    return e.f1_;
  }

#else

  Facet
  from_facet_to_refinement_queue_element(const Facet &facet,
                                         const Facet &mirror) const
  {
    // Returns canonical facet
    return (facet < mirror) ? facet : mirror;
  }

public:
  template<typename Container_element>
  Facet extract_element_from_container_value(const Container_element &e) const
  {
    return e;
  }

#endif

protected:
  /// Stores index of vertex that may be inserted into triangulation
  mutable Index m_last_vertex_index;
};

#ifdef CGAL_LINKED_WITH_TBB
// Parallel
template <typename Index, typename Facet>
class Refine_facets_3_handle_queue_base<Index, Facet, Parallel_tag>
{
protected:
  Refine_facets_3_handle_queue_base() : m_last_vertex_index(Index()) {}

  Index get_last_vertex_index() const
  {
    return m_last_vertex_index.local();
  }

  void set_last_vertex_index(Index i) const
  {
    m_last_vertex_index.local() = i;
  }

  Facets_erase_counters<Facet>
  from_facet_to_refinement_queue_element(const Facet &facet,
                                         const Facet &mirror) const
  {
    return Facets_erase_counters<Facet>{facet, facet.first->erase_counter(),
                                        mirror, mirror.first->erase_counter()};
  }

public:
  template<typename Container_element>
  Facet extract_element_from_container_value(const Container_element &e) const
  {
    // We get the first Facet inside the struct
    return e.f1_;
  }

protected:
  /// Stores index of vertex that may be inserted into triangulation
  mutable tbb::enumerable_thread_specific<Index> m_last_vertex_index;
};
#endif // CGAL_LINKED_WITH_TBB

template<class Tr,
         class Criteria,
         class MeshDomain,
         class Complex3InTriangulation3,
         class Concurrency_tag,
         class Container_
         >
class Refine_facets_3_base
  : public Refine_facets_3_handle_queue_base<typename MeshDomain::Index,
                                             typename Tr::Facet,
                                             Concurrency_tag>
  , public Container_
{
  typedef typename Tr::Weighted_point Weighted_point;
  typedef typename Tr::Bare_point Bare_point;

  typedef typename Tr::Facet Facet;
  typedef typename Tr::Vertex_handle Vertex_handle;
  typedef typename Tr::Cell_handle Cell_handle;
  typedef typename Triangulation_mesher_level_traits_3<Tr>::Zone Zone;

  typedef typename Tr::Geom_traits GT;
  typedef typename GT::Segment_3 Segment_3;
  typedef typename GT::Ray_3 Ray_3;
  typedef typename GT::Line_3 Line_3;

  typedef typename MeshDomain::Intersection Intersection;

public:
  Refine_facets_3_base(Tr& tr, Complex3InTriangulation3& c3t3,
                       const MeshDomain& oracle,
                       const Criteria& criteria,
                       std::size_t maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                       , std::atomic<bool>* stop_ptr
#endif
                       )
    : r_tr_(tr)
    , r_criteria_(criteria)
    , r_oracle_(oracle)
    , r_c3t3_(c3t3)
    , m_maximal_number_of_vertices_(maximal_number_of_vertices)
#ifndef CGAL_NO_ATOMIC
    , m_stop_ptr(stop_ptr)
#endif
  {}

  void scan_triangulation_impl_amendement() const {}

  // Tells if the refinement process of cells is currently finished
  bool no_longer_element_to_refine_impl()
  {
#ifndef CGAL_NO_ATOMIC
    if(m_stop_ptr != 0 &&
       m_stop_ptr->load(std::memory_order_acquire) == true)
    {
      return true;
    }
#endif // not defined CGAL_NO_ATOMIC
    if(m_maximal_number_of_vertices_ !=0 &&
       r_tr_.number_of_vertices() >=
       m_maximal_number_of_vertices_)
    {
      return true;
    }
    return Container_::no_longer_element_to_refine_impl();
  }

  /// Gets the point to insert from the element to refine
  Bare_point refinement_point_impl(const Facet& facet) const
  {
#ifdef CGAL_MESHES_DEBUG_REFINEMENT_POINTS
    const Cell_handle c = facet.first;
    const int i = facet.second;
    Rcpp::Rcerr << "\n Facet ("
              << r_tr_.point(c, (i+1)&3) << " , "
              << r_tr_.point(c, (i+2)&3) << " , "
              << r_tr_.point(c, (i+3)&3) << ") : refinement point is "
              << get_facet_surface_center(facet) << std::endl;
#endif

    CGAL_assertion (this->is_facet_on_surface(facet));
    this->set_last_vertex_index(get_facet_surface_center_index(facet));
    return get_facet_surface_center(facet);
  }

  Facet get_next_element_impl()
  {
    return this->extract_element_from_container_value(
      Container_::get_next_element_impl());
  }

  /// Job to do before insertion
  void before_insertion_impl(const Facet& facet,
                             const Weighted_point& point,
                             Zone& zone);

  /// Job to do after insertion
  void after_insertion_impl(const Vertex_handle& v)
  {
    restore_restricted_Delaunay(v);
  }

  /// debug info: class name
  std::string debug_info_class_name_impl() const
  {
    return "Refine_facets_3";
  }

  /// debug info
  std::string debug_info() const
  {
    std::stringstream s;
    s << Container_::size();
    return s.str();
  }

  /// debug_info_header
  std::string debug_info_header() const
  {
    return "#facets to refine";
  }

  std::string debug_info_element_impl(const Facet &facet) const
  {
    std::stringstream sstr;
    sstr.precision(17);
    sstr << "Facet { " << std::endl
    << "  " << *facet.first->vertex((facet.second+1)%4) << std::endl
    << "  " << *facet.first->vertex((facet.second+2)%4) << std::endl
    << "  " << *facet.first->vertex((facet.second+3)%4) << std::endl
    << "  4th vertex in cell: " << *facet.first->vertex(facet.second)  << std::endl
    << "}" << std::endl;

    return sstr.str();
  }

  int dimension(const Intersection& intersection) const
  {
    return std::get<2>(intersection);
  }
  const typename MeshDomain::Index& index(const Intersection& intersection) const
  {
    return std::get<1>(intersection);
  }
  const typename MeshDomain::Point_3& point(const Intersection& intersection) const
  {
    return std::get<0>(intersection);
  }

protected:

  // Functor for scan_triangulation_impl function
  template <typename Refine_facets_>
  class Scan_facet
  {
    Refine_facets_ & m_refine_facets;

    typedef typename Refine_facets_::Facet Facet;

  public:
    // Constructor
    Scan_facet(Refine_facets_ & rf)
    : m_refine_facets(rf)
    {}

    // Constructor
    Scan_facet(const Scan_facet &sf)
    : m_refine_facets(sf.m_refine_facets)
    {}

    // operator()
    // f cannot be const, see treat_new_facet signature
    void operator()( Facet f ) const
    {
      m_refine_facets.treat_new_facet(f);
    }
  };


protected:
  //-------------------------------------------------------
  // Private types
  //-------------------------------------------------------
  typedef typename Criteria::Facet_quality Quality;
  typedef typename Criteria::Is_facet_bad Is_facet_bad;
  typedef typename MeshDomain::Surface_patch_index Surface_patch_index;
  typedef typename MeshDomain::Index Index;

  struct Facet_prop
  {
    Surface_patch_index surface_patch_index;
    Index index;
    Bare_point point;
  };
  typedef typename std::optional<Facet_prop> Facet_properties;


  /// Returns canonical facet of facet
  Facet canonical_facet(const Facet& facet) const
  {
    const Facet mirror = mirror_facet(facet);
    return ( (facet < mirror)?facet:mirror );
  }

  /// Returns true if `f` has already been visited.
  bool is_facet_visited(const Facet& f) const
  {
    return f.first->is_facet_visited(f.second);
  }

  /// Sets facet `f` to visited.
  void set_facet_visited(Facet& f) const
  {
    f.first->set_facet_visited(f.second);
  }

  /// Sets the facet `f` and its mirrored facet's surface centers to `p`.
  void set_facet_surface_center(const Facet& f,
                                const Bare_point& p,
                                const Index& index) const
  {
    const Facet mirror = mirror_facet(f);

    f.first->set_facet_surface_center(f.second, p);
    mirror.first->set_facet_surface_center(mirror.second, p);

    f.first->set_facet_surface_center_index(f.second,index);
    mirror.first->set_facet_surface_center_index(mirror.second,index);
  }

  /// Returns facet surface center of `f`.
  Bare_point get_facet_surface_center(const Facet& f) const
  {
    return f.first->get_facet_surface_center(f.second);
  }

  /// Returns index of surface center of facet `f`.
  Index get_facet_surface_center_index(const Facet& f) const
  {
    return f.first->get_facet_surface_center_index(f.second);
  }

  /// Sets `f` to surface facets, with index `index`.
  void set_facet_on_surface(const Facet& f,
                            const Surface_patch_index& index)
  {
    r_c3t3_.add_to_complex(f, index);
  }

  /// Returns index of facet `f`.
  Surface_patch_index get_facet_surface_index(const Facet& f) const
  {
    return r_c3t3_.surface_patch_index(f.first, f.second);
  }

  /// Sets index and dimension of vertex `v`.
  void set_vertex_properties(Vertex_handle& v, const Index& index)
  {
    r_c3t3_.set_index(v, index);
    // Set dimension of v: v is on surface by construction, so dimension=2
    v->set_dimension(2);
  }

  /// Returns true if point encroaches facet
  bool is_facet_encroached(const Facet& facet, const Weighted_point& point) const;

  /// Returns whethere an encroached facet is refinable or not
  bool is_encroached_facet_refinable(Facet& facet) const;

  /// Insert facet into refinement queue
  void insert_bad_facet(Facet facet, const Quality& quality)
  {
#ifdef CGAL_MESH_3_VERY_VERBOSE
    std::stringstream s;
    s << "insert_bad_facet(" << debug_info_element_impl(facet) << ", ...) by thread "
      << std::this_thread::get_id() << '\n';
    Rcpp::Rcerr << s.str();
#endif
    // Insert the facet and its mirror
    this->add_bad_element(
      this->from_facet_to_refinement_queue_element(facet, mirror_facet(facet)),
      quality);
  }

  /// Insert encroached facet into refinement queue
  void insert_encroached_facet_in_queue(Facet& facet)
  {
    insert_bad_facet(facet,Quality());
  }

protected:
  /**
   * Action to perform on a facet inside the conflict zone before insertion
   * @return true if source_facet is the same as facet or mirror(facet)
   */
  bool before_insertion_handle_facet_in_conflict_zone(Facet& facet,
                                                     const Facet& source_facet);

  /**
   * Action to perform on a facet on the boundary of the conflict zone
   * before insertion
   * @return true if source_facet is the same as facet or mirror(facet)
   */
  bool before_insertion_handle_facet_on_conflict_zone(Facet& facet,
                                                      const Facet& source_facet)
  {
    // perform the same operations as for an internal facet
    return before_insertion_handle_facet_in_conflict_zone(facet, source_facet);
  }

  /// Restore restricted Delaunay ; may be call by Cells_mesher visitor
  void restore_restricted_Delaunay(const Vertex_handle& v);

  /// Action to perform on a facet incident to the new vertex
  void after_insertion_handle_incident_facet(Facet& facet);

  /// Action to perform on a facet opposite to the new vertex
  void after_insertion_handle_opposite_facet(Facet& facet)
  {
    // perform the same operations as for a facet incident to the new vertex
    after_insertion_handle_incident_facet(facet);
  }

  /// Get mirror facet
  Facet mirror_facet(const Facet& f) const { return r_tr_.mirror_facet(f); }

  /// for debugging
  std::string display_dual(Facet f) const
  {
    std::stringstream stream;
    stream.precision(17);
    Object dual = r_tr_.dual(f);

    if ( const Segment_3* p_segment = object_cast<Segment_3>(&dual) ) {
      stream << "Segment(" << p_segment->source()
             << " , " << p_segment->target() << ")";
    }
    else if ( const Ray_3* p_ray = object_cast<Ray_3>(&dual) ) {
      stream << "Ray(" << p_ray->point(0)
             << " , " << p_ray->point(1)
             << "), with vector (" << p_ray->to_vector() << ")";
    }
    else if ( const Line_3* p_line = object_cast<Line_3>(&dual) ) {
      stream << "Line(point=" << p_line->point(0)
             << " , vector=" << p_line->to_vector() << ")";
    }
    return stream.str();
  }

  /// Returns to if `f` is on surface
  bool is_facet_on_surface(const Facet& f) const
  {
    return r_c3t3_.is_in_complex(f) ;
  }

  /// Removes `f` from surface facets.
  void remove_facet_from_surface(const Facet& f)
  {
    r_c3t3_.remove_from_complex(f);
  }

  /// Removes facet from refinement queue
  // Sequential
  void remove_bad_facet(const Facet& facet, Sequential_tag)
  {
    // If sequential AND NOT lazy, remove cell from refinement queue
#if !defined(CGAL_MESH_3_USE_LAZY_SORTED_REFINEMENT_QUEUE) \
 && !defined(CGAL_MESH_3_USE_LAZY_UNSORTED_REFINEMENT_QUEUE)
    // Remove canonical facet
    Facet canonical_facet = this->canonical_facet(facet);
    this->remove_element(canonical_facet);
#endif
    CGAL_USE(facet);
  }
#ifdef CGAL_LINKED_WITH_TBB
  /// Removes facet from refinement queue
  // Parallel: it's always lazy, so do nothing
  void remove_bad_facet(const Facet&, Parallel_tag) {}
#endif // CGAL_LINKED_WITH_TBB

  /// Sets facet f to not visited
  void reset_facet_visited(Facet& f) const
  {
    f.first->reset_visited(f.second);
  }

  /// Computes facet properties and add facet to the refinement queue if needed
  void treat_new_facet(Facet& facet);

  /**
   * Computes simultaneously `is_facet_on_surface` and `facet_surface_center`.
   * @param facet The input facet
   * @return `true` if `facet` is on surface, `false` otherwise
   */
  void compute_facet_properties(const Facet& facet, Facet_properties& fp,
                                bool force_exact = false ) const;

protected:
  /// The triangulation
  Tr& r_tr_;
  /// The facet criteria
  const Criteria& r_criteria_;
  /// The oracle
  const MeshDomain& r_oracle_;
  /// The mesh result
  Complex3InTriangulation3& r_c3t3_;
  /// Maximal allowed number of vertices
  std::size_t m_maximal_number_of_vertices_;
#ifndef CGAL_NO_ATOMIC
  /// Pointer to the atomic Boolean that can stop the process
  std::atomic<bool>* const m_stop_ptr;
#endif
}; // end class template Refine_facets_3_base

/************************************************
// Class Refine_facets_3
//
// Template parameters should be models of
// Tr         : MeshTriangulation_3
// Criteria   : SurfaceMeshFacetsCriteria_3
// MeshDomain : MeshTraits_3
//
// Implements a Mesher_level for facets
************************************************/

// TODO document Container_ requirements
template<class Tr,
         class Criteria,
         class MeshDomain,
         class Complex3InTriangulation3,
         class Previous_level_,
         class Concurrency_tag,
         template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2>
            class Base_ = Refine_facets_3_base,
#ifdef CGAL_LINKED_WITH_TBB
         class Container_ = std::conditional_t // (parallel/sequential?)
         <
          std::is_convertible_v<Concurrency_tag, Parallel_tag>,
          // Parallel
# ifdef CGAL_MESH_3_USE_LAZY_UNSORTED_REFINEMENT_QUEUE
          Meshes::Filtered_deque_container
# else
          Meshes::Filtered_multimap_container
# endif
          <
            Facets_erase_counters<typename Tr::Facet>,
            typename Criteria::Facet_quality,
            Facet_to_refine_is_not_zombie<typename Tr::Facet>,
            Concurrency_tag
          >,
          // Sequential
# ifdef CGAL_MESH_3_USE_LAZY_UNSORTED_REFINEMENT_QUEUE
          Meshes::Filtered_deque_container
          <
            Facets_erase_counters<typename Tr::Facet>,
            typename Criteria::Facet_quality,
            Facet_to_refine_is_not_zombie<typename Tr::Facet>,
            Concurrency_tag
          >
# elif defined(CGAL_MESH_3_USE_LAZY_SORTED_REFINEMENT_QUEUE)
          Meshes::Filtered_multimap_container
          <
            Facets_erase_counters<typename Tr::Facet>,
            typename Criteria::Facet_quality,
            Facet_to_refine_is_not_zombie<typename Tr::Facet>,
            Concurrency_tag
          >
# else
          Meshes::Double_map_container<typename Tr::Facet,
                                       typename Criteria::Facet_quality>
# endif
         > // std::conditional (parallel/sequential)

#else // !CGAL_LINKED_WITH_TBB

         // Sequential
         class Container_ =
# ifdef CGAL_MESH_3_USE_LAZY_UNSORTED_REFINEMENT_QUEUE
          Meshes::Filtered_deque_container
          <
            Facets_erase_counters<typename Tr::Facet>,
            typename Criteria::Facet_quality,
            Facet_to_refine_is_not_zombie<typename Tr::Facet>,
            Concurrency_tag
          >
# elif defined(CGAL_MESH_3_USE_LAZY_SORTED_REFINEMENT_QUEUE)
          Meshes::Filtered_multimap_container
          <
            Facets_erase_counters<typename Tr::Facet>,
            typename Criteria::Facet_quality,
            Facet_to_refine_is_not_zombie<typename Tr::Facet>,
            Concurrency_tag
          >
# else
          Meshes::Double_map_container<typename Tr::Facet,
                                       typename Criteria::Facet_quality>
# endif
#endif // CGAL_LINKED_WITH_TBB
>
class Refine_facets_3
: public Base_<Tr,
               Criteria,
               MeshDomain,
               Complex3InTriangulation3,
               Concurrency_tag,
               Container_>
, public Mesh_3::Mesher_level<Tr,
                      Refine_facets_3<Tr,
                                      Criteria,
                                      MeshDomain,
                                      Complex3InTriangulation3,
                                      Previous_level_,
                                      Concurrency_tag,
                                      Base_,
                                      Container_>,
                      typename Tr::Facet,
                      Previous_level_,
                      Triangulation_mesher_level_traits_3<Tr>,
                      Concurrency_tag >
, public No_after_no_insertion
, public No_before_conflicts
{
  // Self
  typedef Refine_facets_3<Tr,
                          Criteria,
                          MeshDomain,
                          Complex3InTriangulation3,
                          Previous_level_,
                          Concurrency_tag,
                          Base_,
                          Container_> Self;

  typedef Base_<Tr,
                Criteria,
                MeshDomain,
                Complex3InTriangulation3,
                Concurrency_tag,
                Container_> Rf_base;

  typedef Rf_base Base;

  typedef Mesher_level<Tr,
                       Self,
                       typename Tr::Facet,
                       Previous_level_,
                       Triangulation_mesher_level_traits_3<Tr>,
                       Concurrency_tag >               Base_ML;

  typedef typename Tr::Lock_data_structure Lock_data_structure;

public:
  using Base_ML::add_to_TLS_lists;
  using Base_ML::splice_local_lists;

  typedef Container_ Container; // Because we need it in Mesher_level
  typedef typename Container::Element Container_element;
  typedef typename Tr::Weighted_point Weighted_point;
  typedef typename Tr::Bare_point Bare_point;
  typedef typename Tr::Facet Facet;
  typedef typename Tr::Vertex_handle Vertex_handle;
  typedef typename Triangulation_mesher_level_traits_3<Tr>::Zone Zone;
  typedef Complex3InTriangulation3 C3T3;

  /// Constructor
  // For sequential
  Refine_facets_3(Tr& triangulation,
                  const Criteria& criteria,
                  const MeshDomain& oracle,
                  Previous_level_& previous,
                  C3T3& c3t3,
                  int mesh_topology,
                  std::size_t maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                  , std::atomic<bool>* stop_ptr
#endif
                  );
  // For parallel
  Refine_facets_3(Tr& triangulation,
                  const Criteria& criteria,
                  const MeshDomain& oracle,
                  Previous_level_& previous,
                  C3T3& c3t3,
                  Lock_data_structure *lock_ds,
                  WorksharingDataStructureType *worksharing_ds,
                  std::size_t maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                  , std::atomic<bool>* stop_ptr
#endif
                  );

  /// Destructor
  virtual ~Refine_facets_3() { }

  /// Get a reference on triangulation
  Tr& triangulation_ref_impl() { return this->r_tr_; }
  const Tr& triangulation_ref_impl() const { return this->r_tr_; }

  /// Initialization function
  void scan_triangulation_impl();

  int number_of_bad_elements_impl();

  Bare_point circumcenter_impl(const Facet& facet) const
  {
    return get_facet_surface_center(facet);
  }

  template <typename Mesh_visitor>
  void before_next_element_refinement_in_superior_impl(Mesh_visitor visitor)
  {
    // Before refining any cell, we refine the facets in the local refinement
    // queue
    this->treat_local_refinement_queue(visitor);
  }

  void before_next_element_refinement_impl()
  {
  }

  Facet get_next_local_element_impl()
  {
    return extract_element_from_container_value(
      Container_::get_next_local_element_impl());
  }

  /// Tests if `p` encroaches facet from `zone`.
  // For sequential
  Mesher_level_conflict_status
  test_point_conflict_from_superior_impl(const Weighted_point& p, Zone& zone);

  /// Tests if `p` encroaches facet from `zone`.
  // For parallel
  template <typename Mesh_visitor>
  Mesher_level_conflict_status
  test_point_conflict_from_superior_impl(const Weighted_point& p, Zone& zone,
                                         Mesh_visitor &visitor);

  /// Useless here
  Mesher_level_conflict_status private_test_point_conflict_impl(const Weighted_point& p,
                                                                Zone& zone)
  {
    if( zone.locate_type == Tr::VERTEX )
    {
      std::stringstream sstr;
      sstr.precision(17);
      sstr << "(" << p << ") is already inserted on surface.\n";
      CGAL_error_msg(([this,str=sstr.str()] {
        dump_c3t3(this->r_c3t3_, "dump-bug");
        return str.c_str();
      }()));
      return CONFLICT_AND_ELEMENT_SHOULD_BE_DROPPED;
    }
    else
      return NO_CONFLICT;
  }

  /// Returns the conflicts zone
  Zone conflicts_zone_impl(const Weighted_point& point
                           , const Facet& facet
                           , bool &facet_is_in_its_cz);
  Zone conflicts_zone_impl(const Weighted_point& point
                           , const Facet& facet
                           , bool &facet_is_in_its_cz
                           , bool &could_lock_zone);

  /// Inserts `p` into the triangulation.
  Vertex_handle insert_impl(const Weighted_point& p, const Zone& zone);

  bool try_lock_element(const Facet &f, int lock_radius = 0) const
  {
    return this->triangulation().try_lock_facet(f, lock_radius);
  }

#ifdef CGAL_MESH_3_MESHER_STATUS_ACTIVATED
  std::size_t queue_size() const { return this->size(); }
#endif

private:
  // private types
  typedef typename Tr::Cell_handle Cell_handle;
  typedef typename MeshDomain::Surface_patch_index Surface_patch_index;
  typedef typename MeshDomain::Index Index;
  typedef typename Tr::Geom_traits GT;
  typedef typename GT::Ray_3 Ray_3;

private:
  // Disabled copy constructor
  Refine_facets_3(const Self& src);
  // Disabled assignment operator
  Self& operator=(const Self& src);
};  // end class Refine_facets_3




// For sequential
template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
Refine_facets_3(Tr& triangulation,
                const Cr& criteria,
                const MD& oracle,
                P_& previous,
                C3T3& c3t3,
                int mesh_topology,
                std::size_t maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                , std::atomic<bool>* stop_ptr
#endif
                )
  : Rf_base(triangulation, c3t3, oracle, criteria, mesh_topology,
            maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                , stop_ptr
#endif
            )
  , Mesher_level<Tr, Self, Facet, P_,
      Triangulation_mesher_level_traits_3<Tr>, Ct>(previous)
  , No_after_no_insertion()
  , No_before_conflicts()
{

}

// For parallel
template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
Refine_facets_3(Tr& triangulation,
                const Cr& criteria,
                const MD& oracle,
                P_& previous,
                C3T3& c3t3,
                Lock_data_structure *lock_ds,
                WorksharingDataStructureType *worksharing_ds,
                std::size_t maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
                , std::atomic<bool>* stop_ptr
#endif
                )
  : Rf_base(triangulation, c3t3, oracle, criteria, maximal_number_of_vertices
#ifndef CGAL_NO_ATOMIC
            , stop_ptr
#endif
            )
  , Mesher_level<Tr, Self, Facet, P_,
      Triangulation_mesher_level_traits_3<Tr>, Ct>(previous)
  , No_after_no_insertion()
  , No_before_conflicts()
{
  Base::set_lock_ds(lock_ds);
  Base::set_worksharing_ds(worksharing_ds);
}


template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
void
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
scan_triangulation_impl()
{
  typedef typename Tr::Finite_facets_iterator Finite_facet_iterator;

#ifdef CGAL_MESH_3_PROFILING
  WallClockTimer t;
#endif

#ifdef CGAL_MESH_3_VERY_VERBOSE
  Rcpp::Rcerr
    << "Vertices: " << this->r_c3t3_.triangulation().number_of_vertices() << std::endl
    << "Facets  : " << this->r_c3t3_.number_of_facets_in_complex() << std::endl
    << "Tets    : " << this->r_c3t3_.number_of_cells_in_complex() << std::endl;
#endif

#ifdef CGAL_LINKED_WITH_TBB
  // Parallel
  if (std::is_convertible<Ct, Parallel_tag>::value)
  {
# if defined(CGAL_MESH_3_VERBOSE) || defined(CGAL_MESH_3_PROFILING)
    Rcpp::Rcerr << "Scanning triangulation for bad facets (in parallel) - "
      "number of finite facets = "
      << this->r_c3t3_.triangulation().number_of_finite_facets() << "..."
      << std::endl;
# endif
    add_to_TLS_lists(true);

    // PARALLEL FOR_EACH
    tbb::parallel_for_each(
      this->r_tr_.finite_facets_begin(), this->r_tr_.finite_facets_end(),
      typename Rf_base::template Scan_facet<Self>(*this)
    );

    splice_local_lists();
    add_to_TLS_lists(false);
  }
  // Sequential
  else
#endif // CGAL_LINKED_WITH_TBB
  {
#if defined(CGAL_MESH_3_VERBOSE) || defined(CGAL_MESH_3_PROFILING)
    Rcpp::Rcerr << "Scanning triangulation for bad facets (sequential) - "
      "number of finite facets = "
      << this->r_c3t3_.triangulation().number_of_finite_facets() << "..."
      << std::endl;
#endif
    for(Finite_facet_iterator facet_it = this->r_tr_.finite_facets_begin();
        facet_it != this->r_tr_.finite_facets_end();
        ++facet_it)
    {
      // Cannot be const, see treat_new_facet signature
      Facet facet = *facet_it;
#ifdef CGAL_MESH_3_DEBUG_FACET_CRITERIA
      Rcpp::Rcerr << "TREAT FACET : " << std::endl
                 << "*" << *facet.first->vertex((facet.second+1)%4)  << std::endl
                << "  " << *facet.first->vertex((facet.second+2)%4)  << std::endl
                << "  " << *facet.first->vertex((facet.second+3)%4)  << std::endl;
#endif
      this->treat_new_facet(facet);
    }
  }

#ifdef CGAL_MESH_3_PROFILING
  double facet_scan_time = t.elapsed();
  Rcpp::Rcerr << "==== Facet scan: " << facet_scan_time << " seconds ===="
            << std::endl << std::endl;

 # ifdef CGAL_MESH_3_EXPORT_PERFORMANCE_DATA
    // If it's parallel but the refinement is forced to sequential, we don't
    // output the value
 #   ifndef CGAL_DEBUG_FORCE_SEQUENTIAL_MESH_REFINEMENT
  CGAL_MESH_3_SET_PERFORMANCE_DATA("Facets_scan_time", facet_scan_time);
 #   endif
 # endif
#endif

#if defined(CGAL_MESH_3_VERBOSE) || defined(CGAL_MESH_3_PROFILING)
  Rcpp::Rcerr << "Number of bad facets: " << C_::size() << std::endl;
#endif

#ifdef CGAL_MESH_3_PROFILING
  Rcpp::Rcerr << "Refining... ";
  Base_ML::m_timer.reset();
#endif
  Base::scan_triangulation_impl_amendement();
}



template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
int
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
number_of_bad_elements_impl()
{
  typedef typename MD::Subdomain_index        Subdomain_index;
  typedef std::optional<Subdomain_index>    Subdomain;
  typedef typename Tr::Finite_facets_iterator Finite_facet_iterator;

  int count = 0, count_num_bad_surface_facets = 0;
  int num_internal_facets_that_should_be_on_surface = 0;
#if defined(CGAL_MESH_3_VERBOSE) || defined(CGAL_MESH_3_PROFILING)
  Rcpp::Rcerr << "Scanning triangulation for bad facets - "
    "number of finite facets = "
    << this->r_c3t3_.triangulation().number_of_finite_facets() << "...";
#endif
  int num_tested_facets = 0;
  for(Finite_facet_iterator facet_it = this->r_tr_.finite_facets_begin();
      facet_it != this->r_tr_.finite_facets_end();
      ++facet_it)
  {
    Facet facet = *facet_it;
    typename Rf_base::Facet_properties properties;
    this->compute_facet_properties(facet, properties);

#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
    //facet.first->mark = 0;
#endif

    // On surface?
    if ( properties )
    {
      // This facet should be on surface...
      if (!this->is_facet_on_surface(facet))
      {
        Rcpp::Rcerr << "\n\n*** The facet f is on surface but is NOT MARKED ON SURFACE. " << std::endl;

        Cell_handle c = facet.first;
        int ind = facet.second;
        Cell_handle mc = this->mirror_facet(facet).first;
        int mind = this->mirror_facet(facet).second;

#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
        c->mark2 = ind;
#endif

        // c and mc are the cells adjacent to f
        // browse each facet ff of c and mc, and mark it if it is "on surface"
        int num_erroneous_surface_facets_in_c = 0;
        int num_erroneous_surface_facets_in_mc = 0;
        int num_real_surface_facets_in_c = 0;
        int num_real_surface_facets_in_mc = 0;
        for (int i = 0 ; i < 4 ; ++i)
        {
          if (i != ind)
          {
            const Facet f1(c, i);
            if (this->is_facet_on_surface(f1))
            {
              Rcpp::Rcerr << "*** f1 is " << (this->r_criteria_(this->r_tr_, f1) ? "bad" : "good") << std::endl;

#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
              c->mark = i;
#endif
              typename Rf_base::Facet_properties properties;
              this->compute_facet_properties(f1, properties);
              if (properties)
                ++num_real_surface_facets_in_c;
              else
                ++num_erroneous_surface_facets_in_c;
            }
          }
          if (i != mind)
          {
            const Facet f2(c, i);
            if (this->is_facet_on_surface(f2))
            {
              Rcpp::Rcerr << "*** f2 is " << (this->r_criteria_(this->r_tr_, f2) ? "bad" : "good") << std::endl;

#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
              mc->mark = i;
#endif
              typename Rf_base::Facet_properties properties;
              this->compute_facet_properties(f2, properties);
              if (properties)
                ++num_real_surface_facets_in_mc;
              else
                ++num_erroneous_surface_facets_in_mc;
            }
          }
        }

        Rcpp::Rcerr
          << "*** Num of erroneous surface facets in c: " << num_erroneous_surface_facets_in_c << std::endl
          << "*** Num of erroneous surface facets in mc: " << num_erroneous_surface_facets_in_mc << std::endl
          << "*** Num of real surface facets in c: " << num_real_surface_facets_in_c << std::endl
          << "*** Num of real surface facets in mc: " << num_real_surface_facets_in_mc << std::endl;

        const Subdomain c_subdomain = this->r_oracle_.is_in_domain_object()(this->r_tr_.dual(c));
        const Subdomain mc_subdomain = this->r_oracle_.is_in_domain_object()(this->r_tr_.dual(mc));

        Rcpp::Rcerr << "*** Is in complex? c is marked in domain: " << this->r_c3t3_.is_in_complex(c)
          << " / c is really in subdomain: " << IO::oformat(c_subdomain)
          << " / mc is marked in domain: " << this->r_c3t3_.is_in_complex(mc)
          << " / mc is really in subdomain: " << IO::oformat(mc_subdomain)
          << std::endl;


        // ... if it's not, count it
        ++num_internal_facets_that_should_be_on_surface;

      }

      //const Surface_patch_index& surface_index = std::get<0>(*properties);
      //const Index& surface_center_index = std::get<1>(*properties);
      //const Bare_point& surface_center = std::get<2>(*properties);

      // Facet is on surface: set facet properties
      //set_facet_surface_center(facet, surface_center, surface_center_index);
      //set_facet_on_surface(facet, surface_index);

      const typename Rf_base::Is_facet_bad is_facet_bad = this->r_criteria_(this->r_tr_, facet);
      if ( is_facet_bad )
      {
        ++count;
        if (this->is_facet_on_surface(facet))
          ++count_num_bad_surface_facets;

#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
        //facet.first->mark = facet.second;
#endif
      }
      ++ num_tested_facets;
    }
    // Not on surface?
    else
    {
      // Facet is not on surface
      //remove_facet_from_surface(facet);

      // Marked on surface?
      if (this->is_facet_on_surface(facet))
      {
        Rcpp::Rcerr << "************** The facet is marked on surface whereas it's not! **************" << std::endl;
#ifdef SHOW_REMAINING_BAD_ELEMENT_IN_RED
        facet.first->mark = facet.second;
#endif
      }
    }
  }

  /*Rcpp::Rcerr << "done (" << num_internal_facets_that_should_be_on_surface
    << " facets which were internal facets were added to the surface)." << std::endl;*/
  Rcpp::Rcerr << "done (" << num_internal_facets_that_should_be_on_surface
    << " facets that should be on surface are actually internal facets)." << std::endl;
  Rcpp::Rcerr << std::endl << "Num_tested_facets = " << num_tested_facets << std::endl;
  Rcpp::Rcerr << std::endl << "Num bad surface-marked facets = " << count_num_bad_surface_facets << std::endl;

  return count;
}

// For sequential
template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
Mesher_level_conflict_status
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
test_point_conflict_from_superior_impl(const Weighted_point& point, Zone& zone)
{
  typedef typename Zone::Facets_iterator Facet_iterator;

  for (Facet_iterator facet_it = zone.internal_facets.begin();
       facet_it != zone.internal_facets.end();
       ++facet_it)
  {
    // surface facets which are internal facets of the conflict zone are
    // encroached
    if( this->is_facet_on_surface(*facet_it) )
    {
      if ( this->is_encroached_facet_refinable(*facet_it) )
      {
        this->insert_encroached_facet_in_queue(*facet_it);
        return CONFLICT_BUT_ELEMENT_CAN_BE_RECONSIDERED;
      }
      else
        return CONFLICT_AND_ELEMENT_SHOULD_BE_DROPPED;
    }
  }

  for (Facet_iterator facet_it = zone.boundary_facets.begin();
       facet_it != zone.boundary_facets.end();
       ++facet_it)
  {
    if( this->is_facet_encroached(*facet_it, point) )
    {
      // Insert already existing surface facet into refinement queue
      if ( this->is_encroached_facet_refinable(*facet_it) )
      {
        this->insert_encroached_facet_in_queue(*facet_it);
        return CONFLICT_BUT_ELEMENT_CAN_BE_RECONSIDERED;
      }
      else
        return CONFLICT_AND_ELEMENT_SHOULD_BE_DROPPED;
    }
  }

  return NO_CONFLICT;
}

// For parallel
template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
template <typename Mesh_visitor>
Mesher_level_conflict_status
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
test_point_conflict_from_superior_impl(const Weighted_point& point, Zone& zone,
                                       Mesh_visitor &visitor)
{
  typedef typename Zone::Facets_iterator Facet_iterator;

  for (Facet_iterator facet_it = zone.internal_facets.begin();
       facet_it != zone.internal_facets.end();
       ++facet_it)
  {
    // surface facets which are internal facets of the conflict zone are
    // encroached
    if( this->is_facet_on_surface(*facet_it) )
    {
      if ( this->is_encroached_facet_refinable(*facet_it) )
      {
        // Even if it doesn't succeed, it will be tried again
        this->try_to_refine_element(*facet_it, visitor);
        return CONFLICT_BUT_ELEMENT_CAN_BE_RECONSIDERED;
      }
      else
        return CONFLICT_AND_ELEMENT_SHOULD_BE_DROPPED;
    }
  }

  for (Facet_iterator facet_it = zone.boundary_facets.begin();
       facet_it != zone.boundary_facets.end();
       ++facet_it)
  {
    if( this->is_facet_encroached(*facet_it, point) )
    {
      // Insert already existing surface facet into refinement queue
      if ( this->is_encroached_facet_refinable(*facet_it) )
      {
        // Even if it doesn't succeed, it will be tried again
        this->try_to_refine_element(*facet_it, visitor);
        return CONFLICT_BUT_ELEMENT_CAN_BE_RECONSIDERED;
      }
      else
        return CONFLICT_AND_ELEMENT_SHOULD_BE_DROPPED;
    }
  }

  return NO_CONFLICT;
}


template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
typename Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::Zone
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
conflicts_zone_impl(const Weighted_point& point
                    , const Facet& facet
                    , bool &facet_is_in_its_cz)
{
  Zone zone;

  // TODO may be avoid the locate here
  zone.cell = this->r_tr_.locate(point,
                                 zone.locate_type,
                                 zone.i,
                                 zone.j,
                                 facet.first);

  if(zone.locate_type != Tr::VERTEX)
  {
    const Facet *p_facet = (facet == Facet() ? 0 : &facet);

    this->r_tr_.find_conflicts(point,
                               zone.cell,
                               std::back_inserter(zone.boundary_facets),
                               std::back_inserter(zone.cells),
                               std::back_inserter(zone.internal_facets)
                               , 0
                               , p_facet
                               , &facet_is_in_its_cz);

    if (p_facet != 0 && !facet_is_in_its_cz)
    {
# ifdef CGAL_MESH_3_VERBOSE
      Rcpp::Rcerr << "Info: the facet is not in the conflict zone of (" << point
                << "). Switching to exact computation." << std::endl;
# endif

      typename Rf_base::Facet_properties properties;
      this->compute_facet_properties(facet, properties, /*force_exact=*/true);
      if ( properties )
      {
        const auto& [surface_index, surface_center_index, surface_center] = *properties;

        // Facet is on surface: set facet properties
        this->set_facet_surface_center(facet, surface_center, surface_center_index);
        this->set_facet_on_surface(facet, surface_index);
      }
      else
      {
        // Facet is not on surface
        this->remove_facet_from_surface(facet);
        this->remove_bad_facet(facet, Ct());
      }
    }
  }

  return zone;
}

template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
typename Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::Zone
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
conflicts_zone_impl(const Weighted_point& point
                    , const Facet& facet
                    , bool &facet_is_in_its_cz
                    , bool &could_lock_zone)
{
  Zone zone;

  // TODO may be avoid the locate here
  zone.cell = this->r_tr_.locate(point,
                                 zone.locate_type,
                                 zone.i,
                                 zone.j,
                                 facet.first,
                                 &could_lock_zone);

  if(could_lock_zone && zone.locate_type != Tr::VERTEX)
  {
    const Facet *p_facet = (facet == Facet() ? 0 : &facet);

    this->r_tr_.find_conflicts(point,
                               zone.cell,
                               std::back_inserter(zone.boundary_facets),
                               std::back_inserter(zone.cells),
                               std::back_inserter(zone.internal_facets)
                               , &could_lock_zone
                               , p_facet
                               , &facet_is_in_its_cz);

    if (could_lock_zone && p_facet != 0 && !facet_is_in_its_cz)
    {
#ifdef CGAL_MESH_3_VERBOSE
      Rcpp::Rcerr << "Info: the facet is not in its conflict zone. "
        "Switching to exact computation." << std::endl;
#endif

      typename Rf_base::Facet_properties properties;
      this->compute_facet_properties(facet, properties, /*force_exact=*/true);
      if ( properties )
      {
        const auto& [surface_index, surface_center_index, surface_center] = *properties;

        // Facet is on surface: set facet properties
        this->set_facet_surface_center(facet, surface_center, surface_center_index);
        this->set_facet_on_surface(facet, surface_index);
      }
      else
      {
        // Facet is not on surface
        this->remove_facet_from_surface(facet);
        this->remove_bad_facet(facet, Ct());
      }
    }
  }

  return zone;
}


template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
void
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
before_insertion_impl(const Facet& facet,
                      const Weighted_point& point,
                      Zone& zone)
{
  typedef typename Zone::Facets_iterator Facets_iterator;

  bool source_facet_is_in_conflict = false;

  // Iterate on conflict zone facets
  for (Facets_iterator facet_it = zone.internal_facets.begin();
       facet_it != zone.internal_facets.end();
       ++facet_it)
  {
    if (before_insertion_handle_facet_in_conflict_zone(*facet_it, facet) )
    {
      source_facet_is_in_conflict = true;
    }
  }

  for (Facets_iterator facet_it = zone.boundary_facets.begin() ;
       facet_it != zone.boundary_facets.end() ;
       ++facet_it)
  {
    if (before_insertion_handle_facet_on_conflict_zone(*facet_it, facet))
    {
      source_facet_is_in_conflict = true;
    }
  }

  // source_facet == Facet() when this->before_insertion_impl is
  // called from a Mesh_3 visitor.
  if ( !source_facet_is_in_conflict && facet != Facet()  )
  {
    const Facet source_other_side = mirror_facet(facet);

    using boost::io::group;
    using std::setprecision;

    std::stringstream error_msg;
    error_msg <<
      boost::format("Mesh_3 ERROR: "
                    "A facet is not in conflict with its refinement point!\n"
                    "Debugging information:\n"
                    "  Facet: (%1%, %2%) = (%6%, %7%, %8%)\n"
                    "  Dual: %3%\n"
                    "  Refinement point: %5%\n"
                    "  Cells adjacent to facet:\n"
                    "    ( %9% , %10% , %11% , %12% )\n"
                    "    ( %13% , %14% , %15% , %16% )\n")
      % group(setprecision(17), (&*facet.first))
      % group(setprecision(17), facet.second)
      % display_dual(facet)
      % 0 // dummy: %4% no longer used
      % group(setprecision(17), point)
      % group(setprecision(17), r_tr_.point(facet.first, (facet.second + 1)&3))
      % group(setprecision(17), r_tr_.point(facet.first, (facet.second + 2)&3))
      % group(setprecision(17), r_tr_.point(facet.first, (facet.second + 3)&3))
      % r_tr_.point(facet.first, 0)
      % r_tr_.point(facet.first, 1)
      % r_tr_.point(facet.first, 2)
      % r_tr_.point(facet.first, 3)
      % r_tr_.point(source_other_side.first, 0)
      % r_tr_.point(source_other_side.first, 1)
      % r_tr_.point(source_other_side.first, 2)
      % r_tr_.point(source_other_side.first, 3);

    CGAL_error_msg(error_msg.str().c_str());
  }
}



template<class Tr, class Cr, class MD, class C3T3_, class P_, class Ct, template<class Tr_, class Cr_, class MD_, class C3T3_2, class Ct_, class C_2> class B_, class C_>
typename Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::Vertex_handle
Refine_facets_3<Tr,Cr,MD,C3T3_,P_,Ct,B_,C_>::
insert_impl(const Weighted_point& point, const Zone& zone)
{
  if( zone.locate_type == Tr::VERTEX )
  {
    // TODO look at this
    Rcpp::Rcerr<<"VERTEX\n";
    return zone.cell->vertex(zone.i);
  }

  const Facet& facet = *(zone.boundary_facets.begin());

  Vertex_handle v = this->r_tr_.insert_in_hole(point,
                                               zone.cells.begin(),
                                               zone.cells.end(),
                                               facet.first,
                                               facet.second);

  // Set index and dimension of v
  this->set_vertex_properties(v, Base::get_last_vertex_index());

  return v;
}



template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
void
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
restore_restricted_Delaunay(const Vertex_handle& vertex)
{
  typedef std::vector<Cell_handle> Cell_handle_vector;
  typedef typename Cell_handle_vector::iterator Cell_handle_vector_iterator;

  // Update incident facets
  Cell_handle_vector cells;
  r_tr_.incident_cells(vertex, std::back_inserter(cells));

  for(Cell_handle_vector_iterator cell_it = cells.begin();
      cell_it != cells.end();
      ++cell_it)
  {
    // Look at all four facets of the cell, starting with the
    // facet opposite to the new vertex
    int index = (*cell_it)->index(vertex);

    Facet opposite_facet(*cell_it, index);
    after_insertion_handle_opposite_facet(opposite_facet);

    for (int i = 1; i <= 3; ++i)
    {
      Facet incident_facet(*cell_it, (index+i)&3);
      after_insertion_handle_incident_facet(incident_facet);
    }
  }
}

//-------------------------------------------------------
// Private methods
//-------------------------------------------------------
template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
void
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
treat_new_facet(Facet& facet)
{
  // Treat facet
  Facet_properties properties;
  compute_facet_properties(facet, properties);
  if ( properties )
  {
    const auto& [surface_index, surface_center_index, surface_center] = *properties;

    // Facet is on surface: set facet properties
    set_facet_surface_center(facet, surface_center, surface_center_index);
    set_facet_on_surface(facet, surface_index);

    // Insert facet into refinement queue if needed
    const Is_facet_bad is_facet_bad = r_criteria_(r_tr_, facet);

    if ( is_facet_bad )
    {
      insert_bad_facet(facet, *is_facet_bad);

#ifdef CGAL_MESH_3_DEBUG_FACET_CRITERIA
      Rcpp::Rcerr << "INSERT BAD FACET : " << std::endl
                << "* " << *facet.first->vertex((facet.second+1)%4) << std::endl
                << "  " << *facet.first->vertex((facet.second+2)%4) << std::endl
                << "  " << *facet.first->vertex((facet.second+3)%4) << std::endl
                << "  Surface center: " << get_facet_surface_center(facet) << std::endl
                << "  Quality = " << is_facet_bad->second << std::endl;
#endif
    }
  }
  else
  {
    // Facet is not on surface
    this->remove_facet_from_surface(facet);
  }

  // Set facet visited
  Facet mirror = mirror_facet(facet);
  set_facet_visited(facet);
  set_facet_visited(mirror);
}

template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
void
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
compute_facet_properties(const Facet& facet,
                         Facet_properties& fp,
                         bool force_exact) const
{
  //-------------------------------------------------------
  // Facet must be finite
  //-------------------------------------------------------
  CGAL_assertion( ! r_tr_.is_infinite(facet) );
  CGAL_assertion( r_tr_.dimension() == 3 );

  // types
  typedef std::optional<typename MD::Surface_patch_index> Surface_patch;
  typedef typename MD::Intersection Intersection;

  // Functor
  typename GT::Is_degenerate_3 is_degenerate =
      r_tr_.geom_traits().is_degenerate_3_object();
  typename GT::Compare_xyz_3 compare_xyz =
      r_tr_.geom_traits().compare_xyz_3_object();
  typename GT::Construct_segment_3 construct_segment =
      r_tr_.geom_traits().construct_segment_3_object();
#ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
  typename MD::Do_intersect_surface do_intersect_surface =
      r_oracle_.do_intersect_surface_object();
#endif // not CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3

  Cell_handle c = facet.first;
  int i = facet.second;
  Cell_handle n = c->neighbor(i);
  if ( ! r_tr_.is_infinite(c) && ! r_tr_.is_infinite(n) ){
    // the dual is a segment
    Bare_point p1, p2;
    if(force_exact){
      r_tr_.dual_segment_exact(facet, p1, p2);
    } else {
      r_tr_.dual_segment(facet, p1, p2);
    }
    if (p1 == p2) { fp = Facet_properties(); return; }

    // Trick to have canonical vector : thus, we compute always the same
    // intersection
    Segment_3 segment = ( compare_xyz(p1, p2)== CGAL::SMALLER )
                          ? construct_segment(p1, p2)
                          : construct_segment(p2, p1);

    // If facet is on surface, compute intersection point and return true
#ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
    Surface_patch surface = do_intersect_surface(segment);
    if ( surface )
#endif // not CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
    {
      typename MD::Construct_intersection construct_intersection =
          r_oracle_.construct_intersection_object();

      Intersection intersect = construct_intersection(segment);
#ifdef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
      // In the following, std::get<2>(intersect) == 0 is a way to
      // test "intersect == Intersection()" (aka empty intersection), but
      // the latter does not work.
      Surface_patch surface =
        (dimension(intersect) == 0) ? Surface_patch() :
        Surface_patch(
          r_oracle_.surface_patch_index(index(intersect)));
      if(surface)
#endif // CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
      fp =  Facet_prop{*surface, index(intersect), point(intersect)};
    }
  }
  // If the dual is a ray
  else
  {
    // If a facet is on the convex hull, and if its finite incident
    // cell has a very big Delaunay ball, then the dual of the facet is
    // a ray constructed with a point with very big coordinates, and a
    // vector with small coordinates. Its can happen than the
    // constructed ray is degenerate (the point(1) of the ray is
    // point(0) plus a vector whose coordinates are epsilon).
    Ray_3 ray;
    if(force_exact){
      r_tr_.dual_ray_exact(facet,ray);
    } else {
      r_tr_.dual_ray(facet,ray);
    }
    if (is_degenerate(ray)) { fp = Facet_properties(); return; }

#ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
    Surface_patch surface = do_intersect_surface(ray);
    if ( surface )
#endif // not CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
    {
      typename MD::Construct_intersection construct_intersection =
          r_oracle_.construct_intersection_object();

      Intersection intersect = construct_intersection(ray);
#ifdef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
      Surface_patch surface =
        (dimension(intersect) == 0) ? Surface_patch() :
        Surface_patch(
          r_oracle_.surface_patch_index(index(intersect)));
      if(surface)
#endif // CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
      {
        fp = Facet_prop{*surface, index(intersect), point(intersect)};
      }
    }
  }
}


template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
bool
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
is_facet_encroached(const Facet& facet,
                    const Weighted_point& point) const
{
  if ( r_tr_.is_infinite(facet) || ! this->is_facet_on_surface(facet) )
    return false;

  const Cell_handle& cell = facet.first;
  const int& facet_index = facet.second;

  const Bare_point& center = get_facet_surface_center(facet);
  const Weighted_point& reference_point = r_tr_.point(cell, (facet_index+1)&3);

  // the facet is encroached if the new point is closer to the center than
  // any vertex of the facet
  return r_tr_.greater_or_equal_power_distance(center, reference_point, point);
}

template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
bool
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
is_encroached_facet_refinable(Facet& facet) const
{
  typedef typename Tr::Weighted_point Weighted_point;
  typedef typename GT::FT      FT;

  typename GT::Compute_squared_radius_smallest_orthogonal_sphere_3 sq_radius =
    r_tr_.geom_traits().compute_squared_radius_smallest_orthogonal_sphere_3_object();
  typename GT::Compute_weight_3 cw =
    r_tr_.geom_traits().compute_weight_3_object();
  typename GT::Compare_weighted_squared_radius_3 compare =
    r_tr_.geom_traits().compare_weighted_squared_radius_3_object();

  const Cell_handle& c = facet.first;
  const int& k = facet.second;

  int k1 = (k+1)&3;
  int k2 = (k+2)&3;
  int k3 = (k+3)&3;

  // Get number of weighted points, and ensure that they will be accessible
  // using k1...ki, if i is the number of weighted points.
  int wp_nb = 0;
  const Weighted_point& wpk1 = r_tr_.point(c, k1);
  if(compare(wpk1, FT(0)) == CGAL::SMALLER)
  {
    ++wp_nb;
  }

  const Weighted_point& wpk2 = r_tr_.point(c, k2);
  if(compare(wpk2, FT(0)) == CGAL::SMALLER)
  {
    if ( 0 == wp_nb ) { std::swap(k1,k2); }
    ++wp_nb;
  }

  const Weighted_point& wpk3 = r_tr_.point(c, k3);
  if(compare(wpk3, FT(0)) == CGAL::SMALLER)
  {
    if ( 0 == wp_nb ) { std::swap(k1,k3); }
    if ( 1 == wp_nb ) { std::swap(k2,k3); }
    ++wp_nb;
  }

  const Weighted_point& p1 = r_tr_.point(c, k1);
  const Weighted_point& p2 = r_tr_.point(c, k2);
  const Weighted_point& p3 = r_tr_.point(c, k3);

  const FT min_ratio (0.16); // (0.2*2)^2

  // Check ratio
  switch ( wp_nb )
  {
    case 1:
    {
      FT r = (std::max)(sq_radius(p1,p2),sq_radius(p1,p3));
      if ( r < min_ratio * cw(p1) ) { return false; }
      break;
    }

    case 2:
    {
      bool do_spheres_intersect = (compare(p1,p2,FT(0)) != CGAL::LARGER);
      if ( do_spheres_intersect )
      {
        FT r13 = sq_radius(p1,p3) / cw(p1);
        FT r23 = sq_radius(p2,p3) / cw(p1);
        FT r = (std::max)(r13,r23);

        if ( r < min_ratio ) { return false; }
      }
      break;
    }

    case 3:
    {
      bool do_spheres_intersect = (compare(p1,p2,p3,FT(0)) != CGAL::LARGER);
      if ( do_spheres_intersect ) { return false; }
      break;
    }

    default: break;
  }

  return true;
}

/**
  * `facet` is an internal facet we are going to remove
  * `source_facet` is the facet we want to refine by inserting a new point
  */
template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
bool
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
before_insertion_handle_facet_in_conflict_zone(Facet& facet,
                                               const Facet& source_facet)
{
  Facet other_side = mirror_facet(facet);

  // Is the facet on the surface of the complex
  if ( this->is_facet_on_surface(facet) )
  {
    // Remove element (if needed - see remove_bad_facet implementation)
    remove_bad_facet(facet, Ct());

    // Remove facet from complex
    remove_facet_from_surface(facet);

    // Reset visited
    reset_facet_visited(facet);
    reset_facet_visited(other_side);
  }

  return ( (facet == source_facet) || (other_side == source_facet) );
}



template<class Tr, class Cr, class MD, class C3T3_, class Ct, class C_>
void
Refine_facets_3_base<Tr,Cr,MD,C3T3_,Ct,C_>::
after_insertion_handle_incident_facet(Facet& facet)
{
  // If the facet is infinite or has been already visited,
  // then there is nothing to do as for it or its edges
  // Facet other_side = mirror_facet(facet);
  if ( r_tr_.is_infinite(facet) || (is_facet_visited(facet)) ) // && is_facet_visited(other_side)) )
  {
    return;
  }

  treat_new_facet(facet);
}


}  // end namespace Mesh_3


}  // end namespace CGAL

#include <CGAL/enable_warnings.h>

#endif // CGAL_MESH_3_REFINE_FACETS_3_H

