// Copyright (c) 2016-2025 GeometryFactory (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.2-beta1/PMP_Boolean_operations/include/CGAL/Polygon_mesh_processing/clip.h $
// $Id: include/CGAL/Polygon_mesh_processing/clip.h 431cfb5357d $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Sebastien Loriot

#ifndef CGAL_POLYGON_MESH_PROCESSING_CLIP_H
#define CGAL_POLYGON_MESH_PROCESSING_CLIP_H

#include <CGAL/license/Polygon_mesh_processing/corefinement.h>

#include <CGAL/Polygon_mesh_processing/corefinement.h>
#include <CGAL/Polygon_mesh_processing/connected_components.h>
#include <CGAL/Polygon_mesh_processing/bbox.h>
#include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
#include <CGAL/Polygon_mesh_processing/orientation.h>
#include <CGAL/Polygon_mesh_processing/triangulate_hole.h>
#include <CGAL/Polygon_mesh_processing/repair.h>
#include <CGAL/Polygon_mesh_processing/internal/clip_convex.h>
#include <CGAL/Polygon_mesh_processing/internal/Corefinement/Generic_clip_output_builder.h>

#include <CGAL/AABB_triangle_primitive_3.h>
#include <CGAL/boost/graph/border.h>
#include <CGAL/boost/graph/properties.h>
#include <CGAL/boost/graph/Face_filtered_graph.h>
#include <CGAL/iterator.h>

#include <boost/property_map/property_map.hpp>

#include <array>
#include <algorithm>
#include <map>
#include <set>
#include <type_traits>
#include <unordered_map>
#include <utility>
#include <vector>
#include <bitset>

#include <CGAL/Polygon_mesh_processing/refine_with_plane.h>

#ifndef CGAL_PLANE_CLIP_DO_NOT_USE_TRIANGULATION
#include <CGAL/Triangulation_vertex_base_with_info_2.h>
#include <CGAL/Triangulation_face_base_with_info_2.h>
#include <CGAL/Constrained_Delaunay_triangulation_2.h>
#include <CGAL/Projection_traits_3.h>
#include <CGAL/mark_domain_in_triangulation.h>
#include <CGAL/Delaunay_mesh_face_base_2.h>
#include <boost/iterator/transform_iterator.hpp>
#endif

namespace CGAL {
namespace Polygon_mesh_processing {
namespace internal {

#ifndef CGAL_PLANE_CLIP_DO_NOT_USE_TRIANGULATION
template <class Traits,
          class TriangleMesh,
          class VertexPointMap,
          class Visitor>
void close_and_triangulate(TriangleMesh& tm, VertexPointMap vpm, typename Traits::Vector_3 plane_normal, Visitor& visitor)
{
  using vertex_descriptor = typename boost::graph_traits<TriangleMesh>::vertex_descriptor;
  using halfedge_descriptor = typename boost::graph_traits<TriangleMesh>::halfedge_descriptor;
  using face_descriptor = typename boost::graph_traits<TriangleMesh>::face_descriptor;
  using P_traits = Projection_traits_3<Traits>;
  using Vb = Triangulation_vertex_base_with_info_2<vertex_descriptor, P_traits>;
  using Fb = CGAL::Delaunay_mesh_face_base_2<P_traits>;
  using TDS = Triangulation_data_structure_2<Vb, Fb>;
  using Itag = No_constraint_intersection_tag;
  using CDT = Constrained_Delaunay_triangulation_2<P_traits, TDS, Itag>;

  P_traits p_traits(plane_normal);

  std::vector<std::pair<typename Traits::Point_3, vertex_descriptor>> points;
  std::vector<std::pair<vertex_descriptor, vertex_descriptor>> csts;

  halfedge_descriptor href = boost::graph_traits<TriangleMesh>::null_halfedge ();
  bool first=true;

  for (halfedge_descriptor h : halfedges(tm))
  {
    if (is_border(h, tm))
    {
      if (first)
      {
        href=h;
        first=false;
      }
      vertex_descriptor src = source(h, tm), tgt = target(h, tm);
      points.emplace_back(get(vpm, tgt), tgt);
      csts.emplace_back(src, tgt);
    }
  }

  if (points.empty()) return;

  CDT cdt(p_traits);
  cdt.insert(points.begin(), points.end());

  // TODO: in case of degenerate edges, we don't triangulate but it's kind of an issue on our side
  if (cdt.number_of_vertices()!=points.size()) return;


  typedef CGAL::dynamic_vertex_property_t<typename CDT::Vertex_handle> V_tag;
  typename boost::property_map<TriangleMesh, V_tag>::type v2v = get(V_tag(), tm);
  for (auto vh : cdt.finite_vertex_handles())
    put(v2v, vh->info(), vh);

  for (auto vv : csts)
    cdt.insert_constraint(get(v2v, vv.first), get(v2v, vv.second));

  mark_domain_in_triangulation(cdt);

  typename CDT::Edge edge_ref;
  CGAL_assertion_code(bool OK =)
  cdt.is_edge(get(v2v, csts[0].first), get(v2v, csts[0].second), edge_ref.first, edge_ref.second);
  CGAL_assertion(OK);

  if (!edge_ref.first->is_in_domain()) edge_ref = cdt.mirror_edge(edge_ref);
  CGAL_assertion(edge_ref.first->is_in_domain());

  bool flip_ori = ( edge_ref.first->vertex( (edge_ref.second+1)%3 )->info() != source(href, tm) );

  CGAL_assertion(
    ( !flip_ori &&
      edge_ref.first->vertex( (edge_ref.second+1)%3 )->info() == source(href, tm) &&
      edge_ref.first->vertex( (edge_ref.second+2)%3 )->info() == target(href, tm) )
    ||
    ( flip_ori &&
      edge_ref.first->vertex( (edge_ref.second+2)%3 )->info() == source(href, tm) &&
      edge_ref.first->vertex( (edge_ref.second+1)%3 )->info() == target(href, tm) )
  );

  for (auto fh : cdt.finite_face_handles())
  {
    if (!fh->is_in_domain()) continue;

    std::array<vertex_descriptor,3> vrts = make_array(fh->vertex(0)->info(),
                                                      fh->vertex(1)->info(),
                                                      fh->vertex(2)->info());
    if (flip_ori) std::swap(vrts[0], vrts[1]);

    CGAL_assertion(Euler::can_add_face(vrts, tm));
    visitor.before_face_copy(boost::graph_traits<TriangleMesh>::null_face(), tm, tm);
    face_descriptor f = Euler::add_face(vrts, tm);
    visitor.after_face_copy(boost::graph_traits<TriangleMesh>::null_face(), tm, f, tm);
  }
}

template <class Traits,
          class PolygonMesh,
          class VertexPointMap,
          class Visitor>
bool close(PolygonMesh& pm, VertexPointMap vpm, typename Traits::Vector_3 plane_normal, Visitor& visitor)
{
  //using vertex_descriptor = typename boost::graph_traits<PolygonMesh>::vertex_descriptor;
  using halfedge_descriptor = typename boost::graph_traits<PolygonMesh>::halfedge_descriptor;
  // using face_descriptor = typename boost::graph_traits<PolygonMesh>::face_descriptor;
  using Point_3 = typename Traits::Point_3;
  using P_traits = Projection_traits_3<Traits>;

  std::vector< std::vector<Point_3> > polygons;
  std::vector< halfedge_descriptor > border_cycles;
  std::vector< Bbox_3 > bboxes;

  typedef CGAL::dynamic_halfedge_property_t<bool> H_tag;
  typename boost::property_map<PolygonMesh, H_tag>::type
    is_hedge_selected = get(H_tag(), pm, false);

  for (halfedge_descriptor h : halfedges(pm))
  {
    if (is_border(h, pm) && get(is_hedge_selected, h)==false)
    {
      border_cycles.push_back(h);
      polygons.emplace_back();
      bboxes.emplace_back();
      for (halfedge_descriptor he : CGAL::halfedges_around_face(h, pm))
      {
        put(is_hedge_selected, he, true);
        polygons.back().push_back(get(vpm, target(he, pm)));
        bboxes.back()+=polygons.back().back().bbox();
      }
    }
  }

  if (bboxes.empty()) return true;

  Bbox_3 gbox;
  for (const Bbox_3& bb : bboxes)
    gbox+=bb;

  // arrange polygons
  int axis = 0;
  if ((gbox.ymax()-gbox.ymin()) > (gbox.xmax()-gbox.xmin())) axis=1;
  if ((gbox.zmax()-gbox.zmin()) > ((gbox.max)(axis)-(gbox.min)(axis))) axis=2;

  std::vector<std::size_t> poly_ids(polygons.size());
  std::iota(poly_ids.begin(), poly_ids.end(), 0);

  std::sort(poly_ids.begin(), poly_ids.end(),
            [&bboxes, axis](std::size_t i, std::size_t j)
            {
              return (bboxes[i].min)(axis) < (bboxes[j].min)(axis);
            });


  std::vector<std::size_t> simply_connected_faces;
  std::vector<bool> handled(poly_ids.size(), false);

  P_traits ptraits(plane_normal);


  for (std::size_t pid=0; pid<poly_ids.size()-1; ++pid)
  {
    std::size_t curr_poly_id = poly_ids[pid];

    if (handled[curr_poly_id]) continue;

    std::vector<std::size_t> nested;
    for (std::size_t npid=pid+1; npid<poly_ids.size(); ++npid)
    {
      std::size_t next_poly_id = poly_ids[npid];

      if (do_overlap(bboxes[curr_poly_id], bboxes[next_poly_id]))
      {
        //TODO: what about tanjencies?
        //TODO: check orientation for predicate
        if (bounded_side_2(polygons[curr_poly_id].begin(), polygons[curr_poly_id].end(),
                           polygons[next_poly_id].front(), ptraits) == ON_BOUNDED_SIDE)
        {
          nested.push_back(next_poly_id);
          handled[next_poly_id]=true;
        }
      }
      else
        break; // no further overlaps
    }

    handled[curr_poly_id] = true;

    if (nested.empty())
      simply_connected_faces.push_back(curr_poly_id);
  }

  if (!handled[poly_ids.back()])
    simply_connected_faces.push_back(poly_ids.back());

  for (std::size_t id : simply_connected_faces)
  {
    halfedge_descriptor h = border_cycles[id];
    visitor.before_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, pm);
    Euler::fill_hole(h, pm);
    visitor.after_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, face(h, pm), pm);
  }

  return simply_connected_faces.size()==poly_ids.size();
}

#endif

template <class PolygonMesh,
          class Visitor>
void naive_close(PolygonMesh& pm, Visitor& visitor)
{
  using halfedge_descriptor = typename boost::graph_traits<PolygonMesh>::halfedge_descriptor;

  std::vector< halfedge_descriptor > border_cycles;
  extract_boundary_cycles(pm, std::back_inserter(border_cycles));
  std::vector< Bbox_3 > bboxes;

  for (halfedge_descriptor h : border_cycles)
  {
    visitor.before_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, pm);
    Euler::fill_hole(h, pm);
    visitor.after_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, face(h, pm), pm);
  }
}


template <class Plane_3,
          class TriangleMesh,
          class NamedParameters>
Oriented_side
clip_to_bbox(const Plane_3& plane,
             const Bbox_3& bbox,
                   TriangleMesh& tm_out,
             const NamedParameters& np)
{
  typedef typename GetGeomTraits<TriangleMesh, NamedParameters>::type Geom_traits;
  typedef typename Geom_traits::Point_3 Point_3;
  typedef typename GetVertexPointMap<TriangleMesh,
                                     NamedParameters>::type Vpm;

  Vpm vpm_out = parameters::choose_parameter(parameters::get_parameter(np, internal_np::vertex_point),
                                             get_property_map(boost::vertex_point, tm_out));


  std::vector<Point_3> corners(8);
  corners[0] = Point_3(bbox.xmin(),bbox.ymin(),bbox.zmin());
  corners[1] = Point_3(bbox.xmin(),bbox.ymax(),bbox.zmin());
  corners[2] = Point_3(bbox.xmax(),bbox.ymax(),bbox.zmin());
  corners[3] = Point_3(bbox.xmax(),bbox.ymin(),bbox.zmin());
  corners[4] = Point_3(bbox.xmin(),bbox.ymin(),bbox.zmax());
  corners[5] = Point_3(bbox.xmin(),bbox.ymax(),bbox.zmax());
  corners[6] = Point_3(bbox.xmax(),bbox.ymax(),bbox.zmax());
  corners[7] = Point_3(bbox.xmax(),bbox.ymin(),bbox.zmax());

  std::array<CGAL::Oriented_side,8> orientations = {{
    plane.oriented_side(corners[0]),
    plane.oriented_side(corners[1]),
    plane.oriented_side(corners[2]),
    plane.oriented_side(corners[3]),
    plane.oriented_side(corners[4]),
    plane.oriented_side(corners[5]),
    plane.oriented_side(corners[6]),
    plane.oriented_side(corners[7])
  }};

  // description of faces of the bbox
  static constexpr std::array<int, 24> face_indices
    { { 0, 1, 2, 3,
        2, 1, 5, 6,
        3, 2, 6, 7,
        1, 0, 4, 5,
        4, 0, 3, 7,
        6, 5, 4, 7 } };

  static constexpr std::array<int, 24> edge_indices
    { { 0,  1,  2, 3,
        1,  4,  5, 6,
        2,  6,  7, 8,
        0,  9, 10, 4,
        9,  3,  8, 11,
        5, 10, 11, 7 } };

  std::array<int, 12> edge_ipt_id;
  edge_ipt_id.fill(-1);

  auto inter_pt_index =
    [&plane, &corners, &edge_ipt_id](int i, int j, int edge_id)
  {
    if (edge_ipt_id[edge_id]==-1)
    {
      edge_ipt_id[edge_id] = static_cast<int> (corners.size());
      corners.push_back(typename Geom_traits::Construct_plane_line_intersection_point_3()
                      (plane, corners[i], corners[j]));
    }

    return edge_ipt_id[edge_id];
  };

  std::vector< std::vector<int> > output_faces(6);
  bool all_in = true;
  bool all_out = true;
  std::bitset<14> in_point_bits; // to collect the set of points in the clipped bbox

  // for each face of the bbox, we look for intersection of the plane with its edges
  for(int i=0; i<6; ++i)
  {
    for(int k=0; k< 4; ++k)
    {
      int current_id = face_indices[4*i + k];
      int next_id = face_indices[4*i + (k+1)%4];
      int edge_id = edge_indices[4 * i + k];

      switch(orientations[ current_id ])
      {
        case ON_NEGATIVE_SIDE:
        {
          all_out=false;
          // point on or on the negative side
          output_faces[i].push_back(current_id);
          in_point_bits.set(output_faces[i].back());
          // check for intersection of the edge
          if(orientations[ next_id ] == ON_POSITIVE_SIDE)
          {
            output_faces[i].push_back(
              inter_pt_index(current_id, next_id, edge_id));
            in_point_bits.set(output_faces[i].back());
          }
          break;
        }
        case ON_POSITIVE_SIDE:
        {
          all_in = false;
          // check for intersection of the edge
          if(orientations[ next_id ] == ON_NEGATIVE_SIDE)
          {
            output_faces[i].push_back(
              inter_pt_index(current_id, next_id, edge_id));
            in_point_bits.set(output_faces[i].back());
          }
          break;
        }
        case ON_ORIENTED_BOUNDARY:
        {
          output_faces[i].push_back(current_id);
          in_point_bits.set(output_faces[i].back());
        }
      }
    }
    if(output_faces[i].size() < 3){
      CGAL_assertion(output_faces[i].empty() ||
                     (output_faces[i].front()<8 && output_faces[i].back()<8));
      output_faces[i].clear(); // edge of the bbox included in the plane
    }
  }

  // the intersection is the full bbox
  if(all_in) return ON_NEGATIVE_SIDE;
  if(all_out) return ON_POSITIVE_SIDE;

  // build the clipped bbox
  typedef boost::graph_traits<TriangleMesh> graph_traits;
  typedef typename graph_traits::vertex_descriptor vertex_descriptor;
  typedef typename graph_traits::halfedge_descriptor halfedge_descriptor;
  typedef typename graph_traits::face_descriptor face_descriptor;

  std::map<int, vertex_descriptor> out_vertices;
  for(int i=0; i<14;++i)
  {
    if (in_point_bits.test(i))
    {
      vertex_descriptor v = add_vertex(tm_out);
      out_vertices.insert(std::make_pair(i, v));
      put(vpm_out, v, corners[i]);
    }
  }

  std::map< std::pair<int,int>, halfedge_descriptor> hedge_map;
  const halfedge_descriptor null_hedge = graph_traits::null_halfedge();
  const face_descriptor null_fd = graph_traits::null_face();
  for(const std::vector<int>& findices : output_faces)
  {
    if(findices.empty()) continue;
    const face_descriptor fd=add_face(tm_out);
    int prev_id = findices.back();

    // create of recover face boundary halfedges
    std::vector<halfedge_descriptor> hedges;
    hedges.reserve(findices.size());
    for(int current_id : findices)
    {
      vertex_descriptor src = out_vertices[prev_id], tgt = out_vertices[current_id];

      std::pair<typename std::map< std::pair<int,int>,
                halfedge_descriptor>::iterator, bool> res =
        hedge_map.insert(std::make_pair(std::make_pair(prev_id, current_id), null_hedge));
      if(res.second)
      {
        res.first->second = halfedge(add_edge(tm_out), tm_out);
        hedge_map.insert(std::make_pair(std::make_pair(current_id, prev_id),
                            opposite(res.first->second, tm_out)));
        set_face(opposite(res.first->second, tm_out), null_fd, tm_out);

      }
      hedges.push_back(res.first->second);
      // set edge source and target
      set_target(hedges.back(), tgt, tm_out);
      set_target(opposite(hedges.back(), tm_out), src, tm_out);
      // set face pointer of halfedges
      set_face(hedges.back(), fd, tm_out);
      // set vertex halfedge
      set_halfedge(src, opposite(hedges.back(), tm_out), tm_out);
      set_halfedge(tgt, hedges.back(), tm_out);

      if(current_id==findices.front())
        set_halfedge(fd, hedges.back(), tm_out);

      prev_id = current_id;
    }
    CGAL_assertion(hedges.size() == findices.size());

    // set next/prev relationship
    halfedge_descriptor prev_h=hedges.back();
    for(halfedge_descriptor h : hedges)
    {
      set_next(prev_h, h, tm_out);
      prev_h = h;
    }
  }

  // handle the face of the plane:
  // look for a border halfedge and reconstruct the face of the plane
  // by turning around vertices inside the mesh constructed above
  // until we reach another border halfedge
  for(halfedge_descriptor h : halfedges(tm_out))
  {
    if(face(h, tm_out) == null_fd)
    {
      face_descriptor fd = add_face(tm_out);
      set_halfedge(fd, h, tm_out);

      halfedge_descriptor h_prev=h;
      halfedge_descriptor h_curr=h;
      do{
        h_curr=opposite(h_curr, tm_out);
        do{
          h_curr=opposite(prev(h_curr, tm_out), tm_out);
        } while(face(h_curr, tm_out) != null_fd && h_curr!=h);
        set_face(h_prev, fd, tm_out);
        set_next(h_prev, h_curr, tm_out);
        if(h_curr==h)
          break;
        h_prev=h_curr;
      } while(true);
      break;
    }
  }
  CGAL_assertion(is_valid_polygon_mesh(tm_out));

  // triangulate the faces
  CGAL::Polygon_mesh_processing::triangulate_faces(tm_out, np);

  return ON_ORIENTED_BOUNDARY;
}

template <class TriangleMesh, class Ecm, class VPM, class UserVisitor>
void split_along_edges(TriangleMesh& tm,
                       Ecm ecm,
                       VPM vpm,
                       UserVisitor& user_visitor)
{
  typedef boost::graph_traits<TriangleMesh> GT;
  typedef typename GT::face_descriptor face_descriptor;
  typedef typename GT::edge_descriptor edge_descriptor;
  typedef typename GT::vertex_descriptor vertex_descriptor;
  typedef typename GT::halfedge_descriptor halfedge_descriptor;

  std::vector<edge_descriptor> shared_edges;
  for(edge_descriptor e : edges(tm))
    if(get(ecm, e))
      shared_edges.push_back(e);

  std::size_t nb_shared_edges = shared_edges.size();
  std::vector<halfedge_descriptor> hedges_to_update;

  typedef CGAL::dynamic_halfedge_property_t<bool> H_tag;
  typename boost::property_map<TriangleMesh, H_tag>::type
    no_target_update = get(H_tag(), tm);

  std::vector< std::pair<halfedge_descriptor, vertex_descriptor> > vertices_to_duplicate;

  //collect border halfedges having as target one of the edge endpoints
  std::set<halfedge_descriptor> extra_border_hedges;
  for(std::size_t k=0; k<nb_shared_edges; ++k)
  {
    if (is_border(shared_edges[k], tm)) continue;
    for(halfedge_descriptor h : halfedges_around_target(target(shared_edges[k], tm), tm))
      if(is_border(h, tm))
        extra_border_hedges.insert(h);
    for(halfedge_descriptor h : halfedges_around_target(source(shared_edges[k], tm), tm))
      if(is_border(h, tm))
        extra_border_hedges.insert(h);
  }

  for(halfedge_descriptor h : extra_border_hedges)
  {
    put(no_target_update, h, true);
    set_halfedge(target(h, tm), h, tm);
    hedges_to_update.push_back(h);
  }

  // now duplicate the edge and set its pointers
  for(std::size_t k=0; k<nb_shared_edges; ++k)
  {
    if (is_border(shared_edges[k], tm)) continue;
    halfedge_descriptor h    = halfedge(shared_edges[k], tm);
    face_descriptor fh = face(h, tm);
    //add edge
    user_visitor.before_edge_duplicated(h, tm);
    halfedge_descriptor new_hedge = halfedge(add_edge(tm), tm),
                        new_opp   = opposite(new_hedge,tm);
    user_visitor.after_edge_duplicated(h, new_hedge, tm);

    vertex_descriptor vt = target(h, tm);
    vertex_descriptor vs = source(h, tm);

    //replace h with new_hedge
    set_next(new_hedge, next(h, tm), tm);
    set_next(prev(h, tm), new_hedge, tm);
    set_face(new_hedge, fh, tm);
    set_halfedge(fh, new_hedge, tm);

    set_target(new_hedge, vt, tm);
    set_target(new_opp, vs, tm);

    set_face(new_opp, GT::null_face(), tm);
    set_face(h, GT::null_face(), tm);

    // handle vertices to duplicate
    halfedge_descriptor h_vt = halfedge(vt, tm);
    if(get(no_target_update, h_vt))
      vertices_to_duplicate.push_back(std::make_pair(h, vt));
    else
      set_halfedge(vt, h, tm);
    halfedge_descriptor h_vs = halfedge(vs, tm);
    if(get(no_target_update, h_vs))
      vertices_to_duplicate.push_back(std::make_pair(new_opp, vs));
    else
      set_halfedge(vs, new_opp, tm);

    hedges_to_update.push_back(h);
    put(no_target_update, h, true);
    hedges_to_update.push_back(new_opp);
    put(no_target_update, new_opp, true);

    CGAL_assertion(next(prev(new_hedge, tm), tm) == new_hedge);
    CGAL_assertion(prev(next(new_hedge, tm), tm) == new_hedge);
  }

  // update next/prev relationship
  for(halfedge_descriptor h : hedges_to_update)
  {
    CGAL_assertion(is_border(h, tm));
    halfedge_descriptor h_opp = opposite(h, tm);

    // set next pointer of h, visiting faces inside the patch we consider
    halfedge_descriptor candidate = opposite(prev(h_opp, tm), tm);
    while (!is_border(candidate, tm))
      candidate = opposite(prev(candidate, tm), tm);
    set_next(h, candidate, tm);
    CGAL_assertion(prev(next(h_opp, tm), tm)==h_opp);

    CGAL_assertion(prev(next(h, tm), tm) == h);
    CGAL_assertion(is_border(next(h, tm), tm));
  }

  for(const std::pair<halfedge_descriptor, vertex_descriptor>& p : vertices_to_duplicate)
  {
    user_visitor.before_vertex_copy(p.second, tm, tm);
    vertex_descriptor nv = add_vertex(tm);
    put(vpm, nv, get(vpm, p.second));
    user_visitor.after_vertex_copy(p.second, tm, nv, tm);

    for(halfedge_descriptor h : halfedges_around_target(p.first, tm))
      set_target(h, nv, tm);
    set_halfedge(nv, p.first, tm);
   }

  CGAL_assertion_code(for(halfedge_descriptor h : hedges_to_update))
  {
    CGAL_assertion(next(prev(h, tm), tm) == h);
    CGAL_assertion(prev(next(h, tm), tm) == h);
  }

  for(halfedge_descriptor h : hedges_to_update)
  {
    for(halfedge_descriptor hh : halfedges_around_target(h, tm))
        if(h!=hh)
          set_target(hh, target(h, tm), tm);
  }

  CGAL_assertion(is_valid_polygon_mesh(tm));
}

template <class TriangleMesh,
          class NamedParameters1,
          class NamedParameters2>
void
generic_clip_impl(
        TriangleMesh& tm1,
        TriangleMesh& tm2,
  const NamedParameters1& np1,
  const NamedParameters2& np2)
{
  using parameters::choose_parameter;
  using parameters::get_parameter;

// Vertex point maps
  //for input meshes
  typedef typename GetVertexPointMap<TriangleMesh,
                                     NamedParameters1>::type Vpm;
  typedef typename GetVertexPointMap<TriangleMesh,
                                     NamedParameters2>::type Vpm2;

  static_assert(std::is_same<typename boost::property_traits<Vpm>::value_type,
                             typename boost::property_traits<Vpm>::value_type>::value);

  Vpm vpm1 = choose_parameter(get_parameter(np1, internal_np::vertex_point),
                              get_property_map(boost::vertex_point, tm1));

  Vpm2 vpm2 = choose_parameter(get_parameter(np2, internal_np::vertex_point),
                               get_property_map(boost::vertex_point, tm2));

  if (&tm1==&tm2)
  {
    // TODO mark all edges
    return;
  }

  // handle case of empty meshes (isolated vertices are ignored)
  if (faces(tm1).empty())
    return;

// Edge is-constrained maps
  //for input meshes
  typedef typename internal_np::Lookup_named_param_def <
    internal_np::edge_is_constrained_t,
    NamedParameters1,
    Corefinement::No_mark<TriangleMesh>//default
  > ::type User_ecm1;

  // User and internal edge is-constrained map
  typedef typename boost::template property_map<TriangleMesh, CGAL::dynamic_edge_property_t<bool> >::type Algo_ecm1;
  typedef Corefinement::No_mark<TriangleMesh> Ecm2;
  typedef OR_property_map<Algo_ecm1, User_ecm1> Ecm1;
  typedef Corefinement::Ecm_bind<TriangleMesh, Ecm1, Ecm2> Ecm_in;

  Algo_ecm1 algo_ecm1  = get(CGAL::dynamic_edge_property_t<bool>(), tm1);
  Ecm1 ecm1 = Ecm1(algo_ecm1, choose_parameter<User_ecm1>(get_parameter(np1, internal_np::edge_is_constrained)));
  Ecm2 ecm2;

  // Face index point maps
  typedef typename CGAL::GetInitializedFaceIndexMap<TriangleMesh, NamedParameters1>::type FaceIndexMap1;
  FaceIndexMap1 fid_map1 = get_initialized_face_index_map(tm1, np1);

  const bool use_compact_clipper =
    choose_parameter(get_parameter(np1, internal_np::use_compact_clipper), true);


  // User visitor
  typedef typename internal_np::Lookup_named_param_def <
    internal_np::visitor_t,
    NamedParameters1,
    Corefinement::Default_visitor<TriangleMesh>//default
  > ::type User_visitor;
  User_visitor uv(choose_parameter<User_visitor>(get_parameter(np1, internal_np::visitor)));

  // surface intersection algorithm call
  typedef Corefinement::Generic_clip_output_builder<TriangleMesh,
                                                    Vpm, Vpm2,
                                                    Algo_ecm1,
                                                    FaceIndexMap1,
                                                    Default> Ob;

  typedef Corefinement::Surface_intersection_visitor_for_corefinement<
    TriangleMesh, Vpm, Vpm2, Ob, Ecm_in, User_visitor> Algo_visitor;
  Ecm_in ecm_in(tm1,tm2,ecm1,ecm2);
  Ob ob(tm1, tm2, vpm1, vpm2, algo_ecm1, fid_map1, use_compact_clipper);

  Corefinement::Intersection_of_triangle_meshes<TriangleMesh, Vpm, Vpm2, Algo_visitor >
    functor(tm1, tm2, vpm1, vpm2, Algo_visitor(uv,ob,ecm_in,&tm2), &tm2);
  functor(CGAL::Emptyset_iterator(), false, true);
}




#ifndef CGAL_PLANE_CLIP_DO_NOT_USE_TRIANGULATION
template <class PolygonMesh, class Clip_visitor>
struct Visitor_wrapper_for_triangulate_face
  : public ::CGAL::Polygon_mesh_processing::Hole_filling::Default_visitor
//TODO: @afabri --> I shouldn't be the one doing the inheritance...
//TODO: @afabri --> nothing on edge?
{
  using face_descriptor = typename boost::graph_traits<PolygonMesh>::face_descriptor;

  Clip_visitor& clip_visitor;
  const PolygonMesh& pm;
  std::vector<face_descriptor> triangulation_faces;

  Visitor_wrapper_for_triangulate_face(const PolygonMesh& pm, Clip_visitor& clip_visitor)
    : clip_visitor(clip_visitor)
    , pm(pm)
  {}

  void before_subface_creations(face_descriptor f_split)
  {
    CGAL_assertion(triangulation_faces.empty());
    triangulation_faces.push_back(f_split);
  }
  void after_subface_creations()
  {
    for (face_descriptor f : triangulation_faces)
    {
      clip_visitor.before_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, pm);
      clip_visitor.after_face_copy(boost::graph_traits<PolygonMesh>::null_face(), pm, f, pm);
    }
    triangulation_faces.clear();
  }

  void after_subface_created(face_descriptor f_new)
  {
    triangulation_faces.push_back(f_new);
  }
};
#endif

} // end of internal namespace

/**
  * \ingroup PMP_clip_grp
  *
  * \brief clips `tm` by keeping the part that is inside the volume \link coref_def_subsec bounded \endlink by `clipper`.
  *
  * If `tm` is closed, the clipped part can be kept closed by setting the named parameter `clip_volume` to `true`.
  * See Subsection \ref coref_clip for more details.
  *
  * \attention In the current implementation, `clipper` will be modified (refined with the intersection with `tm`) unless the named parameter `do_not_modify` is set to `true`.
  *
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(clipper)` \endlink
  * \pre \link CGAL::Polygon_mesh_processing::does_bound_a_volume() `CGAL::Polygon_mesh_processing::does_bound_a_volume(clipper)` \endlink
  *
  * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
  * @tparam NamedParameters1 a sequence of \ref bgl_namedparameters "Named Parameters"
  * @tparam NamedParameters2 a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param tm input triangulated surface mesh
  * @param clipper triangulated surface mesh used to clip `tm`
  * @param np_tm an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  * @param np_c an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `tm` (resp. `clipper`)}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, tm (resp. clipper))`}
  *     \cgalParamExtra{If this parameter is omitted, an internal property map for `CGAL::vertex_point_t`
  *                     must be available in `TriangleMesh`.}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{face_index_map}
  *     \cgalParamDescription{a property map associating to each face of `tm` (`clipper`) a unique index between `0` and `num_faces(tm (resp. clipper)) - 1`}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%face_descriptor`
  *                    as key type and `std::size_t` as value type}
  *     \cgalParamDefault{an automatically indexed internal map}
  *     \cgalParamExtra{if the property map is writable, the indices of the faces of `tm` and `clipper`
  *                     will be set after refining `tm` with the intersection with `clipper`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{a visitor used to track the creation of new faces}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<TriangleMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles close to the intersection of `tm` and `clipper` will be
  *                           checked for self-intersections and `Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{clip_volume}
  *     \cgalParamDescription{If `true`, and `tm` is closed, the clipping will be done on the volume
  *                           \link coref_def_subsec bounded \endlink by `tm` rather than on its surface
  *                           (i.e., `tm` will be kept closed).}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{use_compact_clipper}
  *     \cgalParamDescription{if `false`, the parts of `tm` coplanar with `clipper` will not be part of the output.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`true`}
  *     \cgalParamExtra{This option has an effect only if a surface and not a volume is clipped,
  *                     (i.e., if `clip_volume` is `false` or if `tm` is open).}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{do_not_modify}
  *     \cgalParamDescription{(`np_c` only) if `true`, `clipper` will not be modified.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *     \cgalParamExtra{If this option is set to `true`, `tm` is no longer required to be without self-intersection.
  *                     Setting this option to `true` will automatically set `throw_on_self_intersection` to `false`
  *                     and `clip_volume` to `false`.}
  *   \cgalParamNEnd
  * \cgalNamedParamsEnd
  *
  * @return `true` if the output surface mesh is manifold.
  *         If `false` is returned `tm` and `clipper` are only corefined.
  *
  * @see `split()`
  */
template <class TriangleMesh,
          class NamedParameters1 = parameters::Default_named_parameters,
          class NamedParameters2 = parameters::Default_named_parameters>
bool
clip(TriangleMesh& tm,
     TriangleMesh& clipper,
     const NamedParameters1& np_tm = parameters::default_values(),
     const NamedParameters2& np_c = parameters::default_values())
{
  if (parameters::choose_parameter(parameters::get_parameter(np_c, internal_np::do_not_modify), false))
  {
    CGAL_assertion(is_closed(clipper));

    internal::generic_clip_impl(tm, clipper, np_tm, np_c);
    return true;
  }

  const bool clip_volume =
    parameters::choose_parameter(parameters::get_parameter(np_tm, internal_np::clip_volume), false);

  if(clip_volume && is_closed(tm))
    return corefine_and_compute_intersection(tm, clipper, tm, np_tm, np_c);
  return corefine_and_compute_intersection(tm, clipper, tm,
                                           np_tm.use_bool_op_to_clip_surface(true),
                                           np_c);
}

/**
  * \ingroup PMP_clip_grp
  *
  * \brief clips `pm` by keeping the part that is on the negative side of `plane` (the side opposite to its normal vector).
  *
  * If `pm` is closed, the clipped part can be kept closed by setting the named parameter `clip_volume`to `true`.
  * See Subsection \ref coref_clip for more details.
  *
  * @tparam PolygonMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
  *                      An internal property map for `CGAL::vertex_point_t` must be available.
  *
  * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param pm input surface mesh
  * @param plane plane whose negative side defines the halfspace to intersect `pm` with.
  *              `Plane_3` is the plane type for the same CGAL kernel as the point of the vertex point map of `pm`.
  * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
  *
  *   \cgalParamNBegin{concurrency_tag}
  *     \cgalParamDescription{a tag indicating if the task should be performed using one or several threads.}
  *     \cgalParamType{Either `CGAL::Sequential_tag`, or `CGAL::Parallel_tag`, or `CGAL::Parallel_if_available_tag`}
  *     \cgalParamDefault{`CGAL::Sequential_tag`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `pm`}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, pm)`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{a visitor used to track the creation of new faces, edges, and faces.
  *                           Note that as there are no mesh associated with `plane`,
  *                           `boost::graph_traits<PolygonMesh>::null_halfedge()` and `boost::graph_traits<PolygonMesh>::null_face()` will be used when calling
  *                           functions of the visitor expecting a halfedge or a face from `plane`. Similarly, `pm` will be used as the mesh of `plane`.}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<PolygonMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles close to the intersection of `pm`
  *                           and `plane` will be checked for self-intersections
  *                           and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.
  *                           This option is only taken into account if `pm` is a triangle mesh.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{allow_self_intersections}
  *     \cgalParamDescription{If `true`, self-intersections in `pm` are accepted.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *     \cgalParamExtra{If this option is set to `true`, `pm` is no longer required to be without self-intersection.
  *                     Setting this option to `true` will automatically set `throw_on_self_intersection` to `false`
  *                     and `clip_volume` to `false` (overwriting any value provided)}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{clip_volume}
  *     \cgalParamDescription{If `true`, and if `pm` is closed, the clipping will be done on
  *                           the volume \link coref_def_subsec bounded \endlink by `pm`
  *                           rather than on its surface (i.e., `pm` will remain closed).}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{use_compact_clipper}
  *     \cgalParamDescription{If `false`, the parts of `pm` coplanar with `plane` will not be part of the output.
  *                           Always `true` if `clip_volume` is `true`.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`true`}
  *   \cgalParamNEnd
  *
  *    \cgalParamNBegin{use_convex_specialization}
  *      \cgalParamDescription{If set to `true`, a faster implementation specialized for convex meshes is used. The input mesh must be convex to guarantee a correct execution and results.}
  *      \cgalParamType{Boolean}
  *      \cgalParamDefault{`false`}
  *    \cgalParamNEnd
  *
  *   \cgalParamNBegin{do_not_triangulate_faces}
  *      \cgalParamDescription{If the input mesh is triangulated and this parameter is set to `false`, the mesh will be kept triangulated.
  *                            Always `true` if `pm` is not a triangle mesh.}
  *      \cgalParamType{Boolean}
  *      \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{geom_traits}
  *     \cgalParamDescription{an instance of a geometric traits class}
  *     \cgalParamType{a class model of `Kernel`}
  *     \cgalParamDefault{a \cgal kernel deduced from the point type, using `CGAL::Kernel_traits`}
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
  * \cgalNamedParamsEnd
  *
  * @return `true`
  *
  * @see `split()`
  */
template <class PolygonMesh,
          class NamedParameters = parameters::Default_named_parameters>
bool clip(PolygonMesh& pm,
#ifdef DOXYGEN_RUNNING
          const Plane_3& plane,
#else
          const typename GetGeomTraits<PolygonMesh, NamedParameters>::type::Plane_3& plane,
#endif
          const NamedParameters& np = parameters::default_values())
{
  using parameters::choose_parameter;
  using parameters::get_parameter;
  using parameters::get_parameter_reference;

  bool use_convex_specialization = choose_parameter(get_parameter(np, internal_np::use_convex_specialization), false);
  if(use_convex_specialization){
    internal::clip_convex(pm, plane, np);
    return true;
  }

  using halfedge_descriptor = typename boost::graph_traits<PolygonMesh>::halfedge_descriptor;

  using GT = typename GetGeomTraits<PolygonMesh, NamedParameters>::type;
  GT traits = choose_parameter<GT>(get_parameter(np, internal_np::geom_traits));
  auto vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
                              get_property_map(vertex_point, pm));


  using Default_visitor = Corefinement::Default_visitor<PolygonMesh>;
  Default_visitor default_visitor;
  using Visitor_ref = typename internal_np::Lookup_named_param_def<internal_np::visitor_t, NamedParameters, Default_visitor>::reference;
  Visitor_ref visitor = choose_parameter(get_parameter_reference(np, internal_np::visitor), default_visitor);
  // constexpr bool has_visitor = !std::is_same_v<Default_visitor, std::remove_cv_t<std::remove_reference_t<Visitor_ref>>>;

  typedef typename internal_np::Lookup_named_param_def <
    internal_np::concurrency_tag_t,
    NamedParameters,
    Sequential_tag
  > ::type Concurrency_tag;

  // config flags
  bool clip_volume =
    choose_parameter(get_parameter(np, internal_np::clip_volume), false);
  bool use_compact_clipper =
    choose_parameter(get_parameter(np, internal_np::use_compact_clipper), true);
  const bool throw_on_self_intersection =
    choose_parameter(get_parameter(np, internal_np::throw_on_self_intersection), false);
  const bool allow_self_intersections =
    choose_parameter(get_parameter(np, internal_np::allow_self_intersections), false);
  bool triangulate = !choose_parameter(get_parameter(np, internal_np::do_not_triangulate_faces), false);
  constexpr bool traits_supports_cdt2 = !internal::Has_member_Does_not_support_CDT2<GT>::value;
  auto vos = get(dynamic_vertex_property_t<Oriented_side>(), pm);
  auto ecm = get(dynamic_edge_property_t<bool>(), pm, false);
  auto construct_orthogonal_vector = traits.construct_orthogonal_vector_3_object();

  if (traits_supports_cdt2 && triangulate && !is_triangle_mesh(pm))
    triangulate = false;

  refine_with_plane(pm, plane, parameters::vertex_oriented_side_map(vos)
                                          .edge_is_marked_map(ecm)
                                          .vertex_point_map(vpm)
                                          .geom_traits(traits)
                                          .do_not_triangulate_faces(!triangulate)
                                          .throw_on_self_intersection(!allow_self_intersections &&
                                                                      throw_on_self_intersection)
                                          .visitor(std::ref(visitor))
                                          .concurrency_tag(Concurrency_tag()));

  CGAL_assertion(is_valid_polygon_mesh(pm));

  if (allow_self_intersections)
    clip_volume=false;

  if (clip_volume && !is_closed(pm)) clip_volume=false;
  if (clip_volume && use_compact_clipper) use_compact_clipper=false;

  CGAL_precondition(!clip_volume || !triangulate || does_bound_a_volume(pm));

  auto fcc = get(dynamic_face_property_t<std::size_t>(), pm);

  std::size_t nbcc = connected_components(pm, fcc, CGAL::parameters::edge_is_constrained_map(ecm));

  std::vector<bool> classified(nbcc, false);
  std::vector<std::size_t> ccs_to_remove;

  for (auto f : faces(pm))
  {
    std::size_t ccid = get(fcc, f);
    if (classified[ccid]) continue;
    halfedge_descriptor hf = halfedge(f, pm);
    for(halfedge_descriptor h : CGAL::halfedges_around_face(hf, pm))
    {
      CGAL::Oriented_side os = get(vos, target(h,pm));
      if (os==CGAL::ON_ORIENTED_BOUNDARY) continue;
      classified[ccid]=true;
      if (os==CGAL::ON_POSITIVE_SIDE) ccs_to_remove.push_back(ccid);
    }

    if (!classified[ccid])
    {
      if (!use_compact_clipper) ccs_to_remove.push_back(ccid);
      classified[ccid]=true;
    }
  }

  remove_connected_components(pm, ccs_to_remove, fcc);

  if constexpr (traits_supports_cdt2)
  {
    if (clip_volume)
    {
      if (triangulate)
        internal::close_and_triangulate<GT>(pm, vpm, construct_orthogonal_vector(plane), visitor);
      else if (!internal::close<GT>(pm, vpm, plane.orthogonal_vector(), visitor))
        internal::close_and_triangulate<GT>(pm, vpm, construct_orthogonal_vector(plane), visitor);
    }
  }
  else
    if (clip_volume)
      internal::naive_close(pm, visitor);

  return true;
}

/**
  * \ingroup PMP_clip_grp
  *
  * \brief clips `tm` by keeping the part that is inside `iso_cuboid`.
  *
  * If `tm` is closed, the clipped part can be kept closed by setting the named parameter `clip_volume` to `true`.
  * See Subsection \ref coref_clip for more details.
  *
  * \note `Iso_cuboid_3` must be from the same kernel as the point of the internal vertex point map of `TriangleMesh`.
  * \note `Iso_cuboid_3` must be from the same kernel as the point of the vertex point map of `tm`.
  *
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
  *
  * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph` and `FaceListGraph`.
  *                      An internal property map for `CGAL::vertex_point_t` must be available.
  *
  * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param tm input triangulated surface mesh
  * @param iso_cuboid iso-cuboid used to clip `tm`.
  * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `tm`}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<PolygonMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{a visitor used to track the creation of new faces}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<TriangleMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{clip_volume}
  *     \cgalParamDescription{If `true`, and `tm` is closed, the clipping will be done on
  *                           the volume \link coref_def_subsec bounded \endlink by `tm`
  *                           rather than on its surface (i.e., `tm` will be kept closed).}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{use_compact_clipper}
  *     \cgalParamDescription{if `false` the parts of `tm` coplanar with `iso_cuboid` will not be part of the output}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`true`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles close to the intersection of `tm`
  *                           and `iso_cuboid` will be checked for self-intersections
  *                           and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{allow_self_intersections}
  *     \cgalParamDescription{If `true`, self-intersections in `tm` are accepted.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *     \cgalParamExtra{If this option is set to `true`, `tm` is no longer required to be without self-intersection.
  *                     Setting this option to `true` will automatically set `throw_on_self_intersection` to `false`
  *                     and `clip_volume` to `false`.}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{geom_traits}
  *     \cgalParamDescription{an instance of a geometric traits class}
  *     \cgalParamType{a class model of `Kernel`}
  *     \cgalParamDefault{a \cgal kernel deduced from the point type, using `CGAL::Kernel_traits`}
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
  * \cgalNamedParamsEnd
  *
  * @return `true` if the output surface mesh is manifold.
  *         If `false` is returned `tm` is only refined by the intersection with `iso_cuboid`.
  *
  * @see `split()`
  */
template <class TriangleMesh,
          class NamedParameters = parameters::Default_named_parameters>
bool clip(TriangleMesh& tm,
#ifdef DOXYGEN_RUNNING
          const Iso_cuboid_3& iso_cuboid,
#else
          const typename GetGeomTraits<TriangleMesh, NamedParameters>::type::Iso_cuboid_3& iso_cuboid,
#endif
          const NamedParameters& np = parameters::default_values())
{
  namespace PMP = CGAL::Polygon_mesh_processing;
  namespace params = CGAL::parameters;

  using params::get_parameter;
  using params::choose_parameter;

  if(std::begin(faces(tm))==std::end(faces(tm))) return true;
  TriangleMesh clipper;

  make_hexahedron(iso_cuboid[0], iso_cuboid[1], iso_cuboid[2], iso_cuboid[3],
                  iso_cuboid[4], iso_cuboid[5], iso_cuboid[6], iso_cuboid[7],
                  clipper);
  triangulate_faces(clipper);

  const bool do_not_modify = choose_parameter(get_parameter(np, internal_np::allow_self_intersections), false);
  return clip(tm, clipper, np, params::do_not_modify(do_not_modify));
}

/*!
  * \ingroup PMP_clip_grp
  *
  * corefines `tm` and `splitter` and duplicates edges in `tm` that are on the intersection with `splitter`.
  *
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(splitter)` \endlink
  *
  * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph`, and `FaceListGraph`.
  *
  * @tparam NamedParameters1 a sequence of \ref bgl_namedparameters "Named Parameters"
  * @tparam NamedParameters2 a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param tm input triangulated surface mesh
  * @param splitter triangulated surface mesh used to split `tm`
  * @param np_tm an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  * @param np_s an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `tm` (`splitter`)}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
  *     \cgalParamDefault{If this parameter is omitted, an internal property map for
  *                       `CGAL::vertex_point_t` must be available in `TriangleMesh`.}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{(`np_tm` only) a visitor used to track a series of events such as the creation
  *                           of new faces, edges... in both `tm` and `splitter`.}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<TriangleMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles closed to the intersection of `tm`
  *                           and `splitter` will be checked for self-intersections
  *                           and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{do_not_modify}
  *     \cgalParamDescription{(`np_s` only) if `true`, `splitter` will not be modified.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *     \cgalParamExtra{If this option is set to `true`, `tm` is no longer required to be without self-intersection.
  *                     Setting this option to `true` will automatically set `throw_on_self_intersection` to `false`
  *                     and `clip_volume` to `false`.}
  *   \cgalParamNEnd
  *
  * \cgalNamedParamsEnd
  *
  * @see `clip()`
*/
template <class TriangleMesh,
          class NamedParameters1 = parameters::Default_named_parameters,
          class NamedParameters2 = parameters::Default_named_parameters>
void split(TriangleMesh& tm,
           TriangleMesh& splitter,
           const NamedParameters1& np_tm = parameters::default_values(),
           const NamedParameters2& np_s = parameters::default_values())
{
  namespace PMP = CGAL::Polygon_mesh_processing;

  using parameters::get_parameter;
  using parameters::choose_parameter;

  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters1>::type VPM1;
  typedef typename GetVertexPointMap<TriangleMesh, NamedParameters2>::type VPM2;

  typedef typename boost::template property_map<TriangleMesh, CGAL::dynamic_edge_property_t<bool> >::type Ecm;

  VPM1 vpm_tm = choose_parameter(get_parameter(np_tm, internal_np::vertex_point),
                                 get_property_map(vertex_point, tm));
  VPM2 vpm_s = choose_parameter(get_parameter(np_s, internal_np::vertex_point),
                                get_property_map(vertex_point, splitter));

  Ecm ecm  = get(CGAL::dynamic_edge_property_t<bool>(), tm);

  typedef typename internal_np::Lookup_named_param_def <
    internal_np::visitor_t,
    NamedParameters1,
    Corefinement::Default_visitor<TriangleMesh>//default
  > ::type User_visitor;
  User_visitor uv(choose_parameter<User_visitor>(get_parameter(np_tm, internal_np::visitor)));


  // create a constrained edge map and corefine input mesh with the splitter,
  // and mark edges

  const bool do_not_modify_splitter = choose_parameter(get_parameter(np_s, internal_np::do_not_modify), false);

  PMP::corefine(tm, splitter,
                CGAL::parameters::vertex_point_map(vpm_tm).edge_is_constrained_map(ecm).visitor(uv),
                CGAL::parameters::vertex_point_map(vpm_s).do_not_modify(do_not_modify_splitter));

  //split mesh along marked edges
  internal::split_along_edges(tm, ecm, vpm_tm, uv);
}

/**
  * \ingroup PMP_clip_grp
  *
  * splits a polygon mesh with a plane.
  *
  * The polygon mesh is refined with the intersection edges, and those edges are duplicated as to create a boundary,
  * and thus separate connected components on either side of the plane.
  *
  * @tparam PolygonMesh a model of `MutableFaceGraph`, `HalfedgeListGraph`, and `FaceListGraph`.
  *                      An internal property map for `CGAL::vertex_point_t` must be available.
  * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param pm input surface mesh
  * @param plane the plane that will be used to split `pm`.
  *              `Plane_3` is the plane type for the same CGAL kernel as the point of the vertex point map of `pm`.
  * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `pm`}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, pm)`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{a visitor used to track the creation of new faces, edges, and vertices.
  *                           Note that as there are no mesh associated with `plane`,
  *                           `boost::graph_traits<PolygonMesh>::null_halfedge()` and `boost::graph_traits<PolygonMesh>::null_face()` will be used when calling
  *                           functions of the visitor expecting a halfedge or a face from `plane`. Similarly, `pm` will be used as the mesh of `plane`.}}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<TriangleMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles close to the intersection of `pm`
  *                           and `plane` will be checked for self-intersections
  *                           and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.
  *                           This option is only taken into account if `pm` is a triangle mesh.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *    \cgalParamNBegin{do_not_triangulate_faces}
  *      \cgalParamDescription{If the input mesh is triangulated and this parameter is set to `false`, the mesh will be kept triangulated.
  *                            Always `true` if `pm` is not a triangle mesh.}
  *      \cgalParamType{Boolean}
  *      \cgalParamDefault{`false`}
  *    \cgalParamNEnd
  *
  *   \cgalParamNBegin{geom_traits}
  *     \cgalParamDescription{an instance of a geometric traits class}
  *     \cgalParamType{a class model of `Kernel`}
  *     \cgalParamDefault{a \cgal kernel deduced from the point type, using `CGAL::Kernel_traits`}
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
  * \cgalNamedParamsEnd
  *
  * @see `clip()`
  */
template <class PolygonMesh,
          class NamedParameters = parameters::Default_named_parameters>
void split(PolygonMesh& pm,
#ifdef DOXYGEN_RUNNING
          const Plane_3& plane,
#else
          const typename GetGeomTraits<PolygonMesh, NamedParameters>::type::Plane_3& plane,
#endif
          const NamedParameters& np = parameters::default_values())
{
  using parameters::choose_parameter;
  using parameters::get_parameter;
  using parameters::get_parameter_reference;

  using GT = typename GetGeomTraits<PolygonMesh, NamedParameters>::type;
  GT traits = choose_parameter<GT>(get_parameter(np, internal_np::geom_traits));
  auto vpm = choose_parameter(get_parameter(np, internal_np::vertex_point),
                              get_property_map(vertex_point, pm));

  typedef typename internal_np::Lookup_named_param_def <
    internal_np::concurrency_tag_t,
    NamedParameters,
    Sequential_tag
  > ::type Concurrency_tag;

  // config flags
  const bool throw_on_self_intersection =
    choose_parameter(get_parameter(np, internal_np::throw_on_self_intersection), false);
  bool triangulate = !choose_parameter(get_parameter(np, internal_np::do_not_triangulate_faces), false);

  auto vos = get(dynamic_vertex_property_t<Oriented_side>(), pm);
  auto ecm = get(dynamic_edge_property_t<bool>(), pm, false);

  if (triangulate && !is_triangle_mesh(pm))
    triangulate = false;

  using Default_visitor = Corefinement::Default_visitor<PolygonMesh>;
  Default_visitor default_visitor;
  using Visitor_ref = typename internal_np::Lookup_named_param_def<internal_np::visitor_t, NamedParameters, Default_visitor>::reference;
  Visitor_ref visitor = choose_parameter(get_parameter_reference(np, internal_np::visitor), default_visitor);

  refine_with_plane(pm, plane, parameters::vertex_oriented_side_map(vos)
                                          .edge_is_marked_map(ecm)
                                          .vertex_point_map(vpm)
                                          .geom_traits(traits)
                                          .do_not_triangulate_faces(!triangulate)
                                          .throw_on_self_intersection(throw_on_self_intersection)
                                          .concurrency_tag(Concurrency_tag())
                                          .visitor(std::ref(visitor)));

  //split mesh along marked edges
  internal::split_along_edges(pm, ecm, vpm, visitor);
}


/**
  * \ingroup PMP_clip_grp
  *
  * adds intersection edges of `iso_cuboid` and `tm` in `tm` and duplicates those edges.
  *
  * \note `Iso_cuboid_3` must be from the same kernel as the point of the internal vertex point map of `TriangleMesh`.
  * \note `Iso_cuboid_3` must be from the same kernel as the point of the vertex point map of `tm`.
  *
  * \pre \link CGAL::Polygon_mesh_processing::does_self_intersect() `!CGAL::Polygon_mesh_processing::does_self_intersect(tm)` \endlink
  *
  * @tparam TriangleMesh a model of `MutableFaceGraph`, `HalfedgeListGraph`, and `FaceListGraph`.
  *                      An internal property map for `CGAL::vertex_point_t` must be available.
  * @tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
  *
  * @param tm input triangulated surface mesh
  * @param iso_cuboid iso-cuboid used to split `tm`.
  * @param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below
  *
  * \cgalNamedParamsBegin
  *   \cgalParamNBegin{vertex_point_map}
  *     \cgalParamDescription{a property map associating points to the vertices of `tm`}
  *     \cgalParamType{a class model of `ReadWritePropertyMap` with `boost::graph_traits<TriangleMesh>::%vertex_descriptor`
  *                    as key type and `%Point_3` as value type}
  *     \cgalParamDefault{`boost::get(CGAL::vertex_point, tm)`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{visitor}
  *     \cgalParamDescription{a visitor used to track the creation of new faces}
  *     \cgalParamType{a class model of `PMPCorefinementVisitor`}
  *     \cgalParamDefault{`Corefinement::Default_visitor<TriangleMesh>`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{clip_volume}
  *     \cgalParamDescription{If `true`, and `tm` is closed, the clipping will be done on
  *                           the volume \link coref_def_subsec bounded \endlink by `tm`
  *                           rather than on its surface (i.e., `tm` will be kept closed).}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{use_compact_clipper}
  *     \cgalParamDescription{if `false`, the parts of `tm` coplanar with `iso_cuboid` will not be part of the output.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`true`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{throw_on_self_intersection}
  *     \cgalParamDescription{If `true`, the set of triangles close to the intersection of `tm`
  *                           and `iso_cuboid` will be checked for self-intersections
  *                           and `CGAL::Polygon_mesh_processing::Corefinement::Self_intersection_exception`
  *                           will be thrown if at least one self-intersection is found.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{allow_self_intersections}
  *     \cgalParamDescription{If `true`, self-intersections in `tm` are accepted.}
  *     \cgalParamType{Boolean}
  *     \cgalParamDefault{`false`}
  *     \cgalParamExtra{If this option is set to `true`, `tm` is no longer required to be without self-intersection.
  *                     Setting this option to `true` will automatically set `throw_on_self_intersection` to `false`
  *                     and `clip_volume` to `false`.}
  *   \cgalParamNEnd
  *
  *   \cgalParamNBegin{geom_traits}
  *     \cgalParamDescription{an instance of a geometric traits class}
  *     \cgalParamType{a class model of `Kernel`}
  *     \cgalParamDefault{a \cgal kernel deduced from the point type, using `CGAL::Kernel_traits`}
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
  * \cgalNamedParamsEnd
  *
  * @see `clip()`
  */
template <class TriangleMesh,
          class NamedParameters = parameters::Default_named_parameters>
void split(TriangleMesh& tm,
#ifdef DOXYGEN_RUNNING
           const Iso_cuboid_3& iso_cuboid,
#else
           const typename GetGeomTraits<TriangleMesh, NamedParameters>::type::Iso_cuboid_3& iso_cuboid,
#endif
           const NamedParameters& np = parameters::default_values())
{
  namespace PMP = CGAL::Polygon_mesh_processing;
  namespace params = CGAL::parameters;

  using params::get_parameter;
  using params::choose_parameter;

  TriangleMesh splitter;

  make_hexahedron(iso_cuboid[0], iso_cuboid[1], iso_cuboid[2], iso_cuboid[3],
                  iso_cuboid[4], iso_cuboid[5], iso_cuboid[6], iso_cuboid[7],
                  splitter);
  triangulate_faces(splitter);
  const bool do_not_modify = choose_parameter(get_parameter(np, internal_np::allow_self_intersections), false);
  return split(tm, splitter, np, params::do_not_modify(do_not_modify));
}

} } //end of namespace CGAL::Polygon_mesh_processing

#endif // CGAL_POLYGON_MESH_PROCESSING_CLIP_H
