// Copyright (c) 2019 GeometryFactory SARL (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL$
// $Id$
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Simon Giraudot, Dmitry Anisimov

#ifndef CGAL_KSR_3_DATA_STRUCTURE_H
#define CGAL_KSR_3_DATA_STRUCTURE_H

// #include <CGAL/license/Kinetic_shape_reconstruction.h>

// CGAL includes.
// #include <CGAL/Delaunay_triangulation_2.h>

#include <boost/iterator/transform_iterator.hpp>
#include <boost/bind.hpp>
#include <boost/function.hpp>

// Internal includes.
#include <CGAL/KSR/enum.h>
#include <CGAL/KSR/utils.h>
#include <CGAL/KSR/debug.h>
#include <CGAL/KSR/parameters.h>
#include <CGAL/KSR/conversions.h>

#include <CGAL/KSR_3/Support_plane.h>
#include <CGAL/KSR_3/Intersection_graph.h>

namespace CGAL {
namespace KSR_3 {

template<typename GeomTraits>
class Data_structure {

public:
  using Kernel = GeomTraits;
  using IK = CGAL::Exact_predicates_inexact_constructions_kernel;
  using EK = CGAL::Exact_predicates_exact_constructions_kernel;
  using IK_to_EK = CGAL::Cartesian_converter<IK, EK>;
  using EK_to_IK = CGAL::Cartesian_converter<EK, IK>;

private:
  using FT          = typename Kernel::FT;
  using Point_2     = typename Kernel::Point_2;
  using Point_3     = typename Kernel::Point_3;
  using Segment_2   = typename Kernel::Segment_2;
  using Segment_3   = typename Kernel::Segment_3;
  using Vector_2    = typename Kernel::Vector_2;
  using Direction_2 = typename Kernel::Direction_2;
  using Triangle_2  = typename Kernel::Triangle_2;
  using Line_2      = typename Kernel::Line_2;
  using Plane_3     = typename Kernel::Plane_3;

  using Polygon_2  = CGAL::Polygon_2<Kernel>;
  using Parameters = KSR::Parameters_3<FT>;

public:
  using Support_plane      = KSR_3::Support_plane<Kernel>;
  using Intersection_graph = KSR_3::Intersection_graph<Kernel>;
  using FaceEvent          = typename Support_plane::FaceEvent;

  using Mesh           = typename Support_plane::Mesh;
  using Vertex_index   = typename Mesh::Vertex_index;
  using Face_index     = typename Mesh::Face_index;
  using Edge_index     = typename Mesh::Edge_index;
  using Halfedge_index = typename Mesh::Halfedge_index;

  using PVertex = std::pair<std::size_t, Vertex_index>;
  using PFace   = std::pair<std::size_t, Face_index>;
  using PEdge   = std::pair<std::size_t, Edge_index>;

  template<typename PSimplex>
  struct Make_PSimplex {
    using argument_type = typename PSimplex::second_type;
    using result_type   = PSimplex;

    const std::size_t support_plane_idx;
    Make_PSimplex(const std::size_t sp_idx) :
    support_plane_idx(sp_idx)
    { }

    const result_type operator()(const argument_type& arg) const {
      return result_type(support_plane_idx, arg);
    }
  };

  using PVertex_iterator =
    boost::transform_iterator<Make_PSimplex<PVertex>, typename Mesh::Vertex_range::iterator>;
  using PVertices = CGAL::Iterator_range<PVertex_iterator>;

  using PFace_iterator =
    boost::transform_iterator<Make_PSimplex<PFace>, typename Mesh::Face_range::iterator>;
  using PFaces = CGAL::Iterator_range<PFace_iterator>;

  using PEdge_iterator =
    boost::transform_iterator<Make_PSimplex<PEdge>, typename Mesh::Edge_range::iterator>;
  using PEdges = CGAL::Iterator_range<PEdge_iterator>;

  struct Halfedge_to_pvertex {
    using argument_type = Halfedge_index;
    using result_type   = PVertex;

    const std::size_t support_plane_idx;
    const Mesh& mesh;

    Halfedge_to_pvertex(const std::size_t sp_idx, const Mesh& m) :
    support_plane_idx(sp_idx),
    mesh(m)
    { }

    const result_type operator()(const argument_type& arg) const {
      return result_type(support_plane_idx, mesh.target(arg));
    }
  };

  using PVertex_of_pface_iterator =
    boost::transform_iterator<Halfedge_to_pvertex, CGAL::Halfedge_around_face_iterator<Mesh> >;
  using PVertices_of_pface = CGAL::Iterator_range<PVertex_of_pface_iterator>;

  struct Halfedge_to_pedge {
    using argument_type = Halfedge_index;
    using result_type = PEdge;

    const std::size_t support_plane_idx;
    const Mesh& mesh;

    Halfedge_to_pedge(const std::size_t sp_idx, const Mesh& m) :
    support_plane_idx(sp_idx),
    mesh(m)
    { }

    const result_type operator()(const argument_type& arg) const {
      return result_type(support_plane_idx, mesh.edge(arg));
    }
  };

  struct Halfedge_to_pface {
    using argument_type = Halfedge_index;
    using result_type = PFace;

    const std::size_t support_plane_idx;
    const Mesh& mesh;

    Halfedge_to_pface(const std::size_t sp_idx, const Mesh& m) :
    support_plane_idx(sp_idx),
    mesh(m)
    { }

    const result_type operator()(const argument_type& arg) const {
      return result_type(support_plane_idx, mesh.face(arg));
    }
  };

  using PEdge_around_pvertex_iterator =
    boost::transform_iterator<Halfedge_to_pedge, CGAL::Halfedge_around_target_iterator<Mesh> >;
  using PEdges_around_pvertex = CGAL::Iterator_range<PEdge_around_pvertex_iterator>;

  using PEdge_of_pface_iterator =
    boost::transform_iterator<Halfedge_to_pedge, CGAL::Halfedge_around_face_iterator<Mesh> >;
  using PEdges_of_pface = CGAL::Iterator_range<PEdge_of_pface_iterator>;

  using PFace_around_pvertex_iterator =
    boost::transform_iterator<Halfedge_to_pface, CGAL::Halfedge_around_target_iterator<Mesh> >;
  using PFaces_around_pvertex = CGAL::Iterator_range<PFace_around_pvertex_iterator>;

  using IVertex = typename Intersection_graph::Vertex_descriptor;
  using IEdge   = typename Intersection_graph::Edge_descriptor;
  using IFace   = typename Intersection_graph::Face_descriptor;

  using Visibility_label = KSR::Visibility_label;

  struct Volume_cell {
    std::vector<PFace> pfaces;
    std::vector<int> neighbors;
    std::set<PVertex> pvertices;
    std::size_t index = std::size_t(-1);
    Point_3 centroid;

    Visibility_label visibility = Visibility_label::INSIDE;
    FT inside  = FT(1);
    FT outside = FT(0);
    FT weight  = FT(0);

    void add_pface(const PFace& pface, const int neighbor) {
      pfaces.push_back(pface);
      neighbors.push_back(neighbor);
    }
    void set_index(const std::size_t idx) {
      index = idx;
    }
    void set_centroid(const Point_3& point) {
      centroid = point;
    }
  };

  struct Reconstructed_model {
    std::vector<PFace> pfaces;
    void clear() {
      pfaces.clear();
    }
  };

  using Kinetic_traits = KSR::Kinetic_traits_3<Kernel>;

private:
  std::map< std::pair<std::size_t, IEdge>, Point_2>  m_points;
  std::map< std::pair<std::size_t, IEdge>, Vector_2> m_directions;
  std::vector<Support_plane> m_support_planes;
  Intersection_graph m_intersection_graph;

  const Parameters& m_parameters;
  FT m_previous_time;
  FT m_current_time;
  Kinetic_traits m_kinetic_traits;

  std::vector<Volume_cell> m_volumes;
  std::map<int, std::size_t> m_volume_level_map;
  std::map<PFace, std::pair<int, int> > m_map_volumes;
  std::map<std::size_t, std::size_t> m_input_polygon_map;
  Reconstructed_model m_reconstructed_model;

public:
  Data_structure(const Parameters& parameters) :
  m_parameters(parameters),
  m_previous_time(FT(0)),
  m_current_time(FT(0)),
  m_kinetic_traits(parameters.use_hybrid_mode)
  { }

  /*******************************
  **      INITIALIZATION        **
  ********************************/

  void clear() {
    m_points.clear();
    m_directions.clear();
    m_support_planes.clear();
    m_intersection_graph.clear();

    m_previous_time = FT(0);
    m_current_time  = FT(0);

    m_volumes.clear();
    m_volume_level_map.clear();
    m_map_volumes.clear();
    m_input_polygon_map.clear();
    m_reconstructed_model.clear();
  }

  void precompute_iedge_data() {

    for (std::size_t i = 0; i < number_of_support_planes(); ++i) {
      auto& unique_iedges = support_plane(i).unique_iedges();
      CGAL_assertion(unique_iedges.size() > 0);

      auto& iedges    = this->iedges(i);
      auto& ibboxes   = this->ibboxes(i);
      auto& isegments = this->isegments(i);

      iedges.clear();
      iedges.reserve(unique_iedges.size());
      std::copy(unique_iedges.begin(), unique_iedges.end(), std::back_inserter(iedges));
      unique_iedges.clear();

      ibboxes.clear();
      isegments.clear();

      ibboxes.reserve(iedges.size());
      isegments.reserve(iedges.size());

      for (const auto& iedge : iedges) {
        isegments.push_back(segment_2(i, iedge));
        ibboxes.push_back(isegments.back().bbox());
      }
    }
  }

  /*******************************
  **           ACCESS           **
  ********************************/

  void set_input_polygon_map(
    const std::map<std::size_t, std::size_t>& input_polygon_map) {
    m_input_polygon_map = input_polygon_map;
  }

  int support_plane_index(const std::size_t polygon_index) const {

    CGAL_assertion(m_input_polygon_map.find(polygon_index) != m_input_polygon_map.end());
    const std::size_t sp_idx = m_input_polygon_map.at(polygon_index);
    return static_cast<int>(sp_idx);
  }

  int number_of_volume_levels() const {
    return static_cast<int>(m_volume_level_map.size());
  }

  std::size_t number_of_volumes(const int volume_level) const {

    CGAL_assertion(volume_level < number_of_volume_levels());
    if (volume_level >= number_of_volume_levels()) return std::size_t(-1);
    if (volume_level < 0) {
      return m_volumes.size();
    }

    CGAL_assertion(volume_level >= 0);
    CGAL_assertion(m_volume_level_map.find(volume_level) != m_volume_level_map.end());
    return m_volume_level_map.at(volume_level);
  }

  /*******************************
  **          GENERAL           **
  ********************************/

  std::map<PFace, std::pair<int, int> >& pface_neighbors() { return m_map_volumes; }
  const std::map<PFace, std::pair<int, int> >& pface_neighbors() const { return m_map_volumes; }

  std::map<int, std::size_t>& volume_level_map() { return m_volume_level_map; }
  const std::map<int, std::size_t>& volume_level_map() const { return m_volume_level_map; }

  const std::vector<Support_plane>& support_planes() const { return m_support_planes; }
  std::vector<Support_plane>& support_planes() { return m_support_planes; }

  const Intersection_graph& igraph() const { return m_intersection_graph; }
  Intersection_graph& igraph() { return m_intersection_graph; }

  void resize(const std::size_t number_of_items) {
    m_support_planes.resize(number_of_items);
  }

  void reserve(const std::size_t number_of_polygons) {
    m_support_planes.reserve(number_of_polygons + 6);
  }

  const FT current_time() const { return m_current_time; }
  const FT previous_time() const { return m_previous_time; }

  void update_positions(const FT time) {
    m_previous_time = m_current_time;
    m_current_time = time;
  }

  void set_last_event_time(const PVertex& pvertex, const FT time) {
    support_plane(pvertex).set_last_event_time(pvertex.second, time);
  }

  const FT last_event_time(const PVertex& pvertex) {
    return support_plane(pvertex).last_event_time(pvertex.second, current_time());
  }

  FT calculate_edge_intersection_time(std::size_t sp_idx, IEdge edge, FaceEvent &event) {
    // Not need to calculate for border edges.
    if (m_intersection_graph.iedge_is_on_bbox(edge))
      return 0;

    IK_to_EK to_exact;
    EK_to_IK to_inexact;
    Support_plane& sp = m_support_planes[sp_idx];

    Point_2 centroid = sp.data().centroid;

    Intersection_graph::Kinetic_interval& kinetic_interval = m_intersection_graph.kinetic_interval(edge, sp_idx);

    //std::cout << "kinetic segments on intersection line" << std::endl;

    //std::cout << edge << std::endl;
    //std::cout << point_3(m_intersection_graph.source(edge)) << " ";
    //std::cout << point_3(m_intersection_graph.target(edge)) << std::endl;
    //std::cout << std::endl;

    //std::cout << "centroid source" << std::endl;
    //std::cout << point_3(m_intersection_graph.source(edge)) << " " << sp.to_3d(sp.data().centroid) << std::endl;
    //std::cout << "centroid target" << std::endl;
    //std::cout << point_3(m_intersection_graph.target(edge)) << " " << sp.to_3d(sp.data().centroid) << std::endl;
    //std::cout << std::endl;

    // Just intersect all vertex rays with the line of the edge and interpolate? accurate? It is linear, so it should be accurate.
    Point_2 s = sp.to_2d(point_3(m_intersection_graph.source(edge)));
    Point_2 t = sp.to_2d(point_3(m_intersection_graph.target(edge)));
    Vector_2 segment = t - s;
    FT segment_length = sqrt(segment * segment);
    CGAL_assertion(segment_length > 0);
    segment = segment / segment_length;
    Direction_2 to_source(s - centroid);
    Direction_2 to_target(t - centroid);

    std::size_t source_idx = -1;
    std::size_t target_idx = -1;

    event.crossed_edge = edge;
    event.support_plane = sp_idx;

    std::pair<IFace, IFace> faces;
    m_intersection_graph.get_faces(sp_idx, edge, faces);

    if (m_intersection_graph.face(faces.first).part_of_partition)
      event.face = faces.second;
    else
      event.face = faces.first;

    for (std::size_t i = 0; i < sp.data().original_directions.size(); i++) {
      Vector_2 tmp = sp.data().original_directions[i].vector();
      //std::cout << "2 " << sp.to_3d(centroid + tmp) << " " << sp.to_3d(centroid) <<  std::endl;
      //std::cout << sp.to_3d(sp.data().original_vertices[i]) << " " << sp.data().centroid << std::endl;
      if (source_idx == -1 && sp.data().original_directions[i] > to_source)
        source_idx = i;

      if (target_idx == -1 && sp.data().original_directions[i] > to_target)
        target_idx = i;
    }

    source_idx = (source_idx == -1) ? 0 : source_idx;
    target_idx = (target_idx == -1) ? 0 : target_idx;

    std::size_t lower = ((std::min<std::size_t>)(source_idx, target_idx) + sp.data().original_directions.size() - 1) % sp.data().original_directions.size();
    std::size_t upper = (std::max<std::size_t>)(source_idx, target_idx);

    std::size_t num = ((upper - lower + sp.data().original_directions.size()) % sp.data().original_directions.size()) + 1;
    std::vector<FT> time(num);
    std::vector<Point_2> intersections(num);
    std::vector<FT> intersections_bary(num);

    // Shooting rays to find intersection with line of IEdge
    Line_2 ln = sp.to_2d(m_intersection_graph.line_3(edge));
    //std::cout << sp.to_3d(ln.point(0)) << " " << sp.to_3d(ln.point(5)) << std::endl;
    EK::Line_2 l = to_exact(sp.to_2d(m_intersection_graph.line_3(edge)));
    for (std::size_t i = 0; i < num; i++) {
      std::size_t idx = (i + lower) % sp.data().original_directions.size();
      const auto result = CGAL::intersection(l, sp.data().original_rays[idx]);
      if (!result) {
        time[i] = std::numeric_limits<double>::max();
        continue;
      }
      const EK::Point_2* p = nullptr;
      if (p = boost::get<EK::Point_2>(&*result)) {
        FT l = CGAL::sqrt(sp.data().original_vectors[idx].squared_length());
        //std::cout << "i " << sp.to_3d(to_inexact(sp.data().original_rays[idx].point(0))) << " " << sp.to_3d(to_inexact(*p)) << std::endl;
        double l2 = CGAL::to_double((*p - sp.data().original_rays[idx].point(0)).squared_length());
        time[i] = l2 / l;
        CGAL_assertion(0 <= time[i]);
        intersections[i] = to_inexact(*p);
        intersections_bary[i] = ((to_inexact(*p) - s) * segment) / segment_length;
        //std::cout << "intersection t:" << time[i] << " at " << intersections_bary[i] << " p: " << sp.to_3d(intersections[i]) << std::endl;
      }
      // If the intersection is a segment, it can be safely ignored as there are also two intersections with the adjacent edges.
    }

    // Calculate pedge vs ivertex collision
    FT edge_time[2];

    // Select endpoints of iedge for distance calculation and direction of pedges
    if (source_idx == upper) {
      // Moving direction of pedges is orthogonal to their direction
      // Direction of pedge 1
      //std::cout << "lower for source_idx == upper:" << std::endl;
      //std::cout << sp.to_3d(sp.data().original_vertices[lower]) << " ";
      //std::cout << sp.to_3d(sp.data().original_vertices[(lower + 1) % sp.data().original_vertices.size()]) << std::endl;
      //std::cout << "target: " << point_3(m_intersection_graph.target(edge)) << " ";
      Vector_2 dir = sp.data().original_vertices[lower] - sp.data().original_vertices[(lower + 1) % sp.data().original_vertices.size()];
      // Normalize
      dir = dir / CGAL::sqrt(dir * dir);
      // Orthogonal direction matching the direction of the adjacent vertices
      dir = Vector_2(-dir.y(), dir.x());
      dir = (dir * sp.data().original_vectors[lower] < 0) ? -dir : dir;

      // Moving speed matches the speed of adjacent vertices
      FT speed = (dir * sp.data().original_vectors[lower]);
      CGAL_assertion(speed > 0);

      // Distance from edge to endpoint of iedge
      FT dist = (t - sp.data().original_vertices[lower]) * dir;
      Point_3 vis = sp.to_3d(t - (dist * dir));
      //std::cout << vis << std::endl;
      edge_time[0] = dist / speed;
      CGAL_assertion(0 <= edge_time[0]);
      //std::cout << "time: " << edge_time[0] << std::endl;

      // Same for the upper boundary edge.
      //std::cout << "upper for source_idx == upper:" << std::endl;
      //std::cout << sp.to_3d(sp.data().original_vertices[(upper + sp.data().original_vertices.size() - 1) % sp.data().original_vertices.size()]) << " ";
      //std::cout << sp.to_3d(sp.data().original_vertices[upper]) << std::endl;
      //std::cout << "source: " << point_3(m_intersection_graph.source(edge)) << " ";
      dir = sp.data().original_vertices[(upper + sp.data().original_vertices.size() - 1) % sp.data().original_vertices.size()] - sp.data().original_vertices[upper];
      // Normalize
      dir = dir / CGAL::sqrt(dir * dir);
      // Orthogonal direction matching the direction of the adjacent vertices
      dir = Vector_2(-dir.y(), dir.x());
      dir = (dir * sp.data().original_vectors[upper] < 0) ? -dir : dir;

      // Moving speed matches the speed of adjacent vertices
      speed = (dir * sp.data().original_vectors[upper]);
      CGAL_assertion(speed > 0);

      // Distance from edge to endpoint of iedge
      dist = (s - sp.data().original_vertices[upper]) * dir;
      vis = sp.to_3d(s - (dist * dir));
      //std::cout << vis << std::endl;
      edge_time[1] = dist / speed;
      CGAL_assertion(0 <= edge_time[1]);
      //std::cout << "time: " << edge_time[1] << std::endl;

      event.time = edge_time[1];
      event.intersection_bary = 0;

      kinetic_interval.push_back(std::pair<FT, FT>(0, edge_time[1]));
      for (std::size_t i = upper; i >= lower && i <= upper; i--) {
        if (0 <= intersections_bary[i - lower] && intersections_bary[i - lower] <= 1) {
          kinetic_interval.push_back(std::pair<FT, FT>(intersections_bary[i - lower], time[i - lower]));
          if (event.time > time[i - lower]) {
            event.time = time[i - lower];
            event.intersection_bary = intersections_bary[i - lower];
          }
        }
      }

      kinetic_interval.push_back(std::pair<FT, FT>(1, edge_time[0]));
      if (event.time > edge_time[0]) {
        event.time = edge_time[0];
        event.intersection_bary = 1;
      }
    }
    else {
      // Moving direction of pedges is orthogonal to their direction
      //std::cout << "lower for source_idx == lower:" << std::endl;
      //std::cout << sp.to_3d(sp.data().original_vertices[lower]) << " ";
      //std::cout << sp.to_3d(sp.data().original_vertices[(lower + 1) % sp.data().original_vertices.size()]) << std::endl;
      //std::cout << "source: " << point_3(m_intersection_graph.source(edge)) << " ";
      Vector_2 dir = sp.data().original_vertices[lower] - sp.data().original_vertices[(lower + 1) % sp.data().original_directions.size()];
      // Normalize
      dir = dir / CGAL::sqrt(dir * dir);
      // Orthogonal direction matching the direction of the adjacent vertices
      dir = Vector_2(-dir.y(), dir.x());
      dir = (dir * sp.data().original_vectors[lower] < 0) ? -dir : dir;

      // Moving speed matches the speed of adjacent vertices
      FT speed = (dir * sp.data().original_vectors[lower]);
      CGAL_assertion(speed > 0);

      // Distance from edge to endpoint of iedge
      FT dist = (s - sp.data().original_vertices[lower]) * dir;
      Point_3 vis = sp.to_3d(s - (dist * dir));
      //std::cout << vis << std::endl;
      edge_time[0] = dist / speed;
      CGAL_assertion(0 <= edge_time[0]);
      //std::cout << "time: " << edge_time[0] << std::endl;

      // Same for the upper boundary edge.
      //std::cout << "upper for source_idx == lower:" << std::endl;
      //std::cout << sp.to_3d(sp.data().original_vertices[(upper + sp.data().original_vertices.size() - 1) % sp.data().original_vertices.size()]) << " ";
      //std::cout << sp.to_3d(sp.data().original_vertices[upper]) << std::endl;
      //std::cout << "target: " << point_3(m_intersection_graph.target(edge)) << " ";
      dir = sp.data().original_vertices[(upper + sp.data().original_directions.size() - 1) % sp.data().original_directions.size()] - sp.data().original_vertices[upper];
      // Normalize
      dir = dir / CGAL::sqrt(dir * dir);
      // Orthogonal direction matching the direction of the adjacent vertices
      dir = Vector_2(-dir.y(), dir.x());
      dir = (dir * sp.data().original_vectors[upper] < 0) ? -dir : dir;

      // Moving speed matches the speed of adjacent vertices
      speed = (dir * sp.data().original_vectors[upper]);
      CGAL_assertion(speed > 0);

      // Distance from edge to endpoint of iedge
      dist = (t - sp.data().original_vertices[upper]) * dir;
      vis = sp.to_3d(t - (dist * dir));
      //std::cout << vis << std::endl;
      edge_time[1] = dist / speed;
      CGAL_assertion(0 <= edge_time[1]);
      //std::cout << "time: " << edge_time[1] << std::endl;

      event.time = edge_time[0];
      event.intersection_bary = 0;

      kinetic_interval.push_back(std::pair<FT, FT>(0, edge_time[0]));
      for (std::size_t i = lower; i <= upper; i++) {
        if (0 <= intersections_bary[i - lower] && intersections_bary[i - lower] <= 1) {
          kinetic_interval.push_back(std::pair<FT, FT>(intersections_bary[i - lower], time[i - lower]));
          if (event.time > time[i - lower] && 0 <= intersections_bary[i - lower] && intersections_bary[i - lower] <= 1) {
            event.time = time[i - lower];
            event.intersection_bary = intersections_bary[i - lower];
          }
        }
      }

      kinetic_interval.push_back(std::pair<FT, FT>(1, edge_time[1]));
      if (event.time > edge_time[1]) {
        event.time = edge_time[1];
        event.intersection_bary = 1;
      }
    }

    //std::cout << "new event: sp " << event.support_plane << " f " << event.face << " edge " << event.crossed_edge << " t " << event.time << std::endl;

    CGAL_assertion(0 <= event.intersection_bary && event.intersection_bary <= 1);

    return event.time;
  }

  template<typename Queue>
  void fill_event_queue(Queue& queue) {
    for (std::size_t sp_idx = 6; sp_idx < m_support_planes.size(); sp_idx++) {
      std::vector<IEdge> border;
      m_support_planes[sp_idx].get_border(m_intersection_graph, border);

      for (IEdge edge : border) {
        if (m_intersection_graph.has_crossed(edge, sp_idx))
          continue;

        FaceEvent fe;
        FT t = calculate_edge_intersection_time(sp_idx, edge, fe);
        if (t > 0)
          queue.push(fe);
      }
    }
  }

  std::vector<Volume_cell>& volumes() { return m_volumes; }
  const std::vector<Volume_cell>& volumes() const { return m_volumes; }

  Reconstructed_model& reconstructed_model() { return m_reconstructed_model; }
  const Reconstructed_model& reconstructed_model() const { return m_reconstructed_model; }

  /*******************************
  **      SUPPORT PLANES        **
  ********************************/

  template<typename PSimplex>
  const Support_plane& support_plane(const PSimplex& psimplex) const { return support_plane(psimplex.first); }
  const Support_plane& support_plane(const std::size_t idx) const { return m_support_planes[idx]; }

  template<typename PSimplex>
  Support_plane& support_plane(const PSimplex& psimplex) { return support_plane(psimplex.first); }
  Support_plane& support_plane(const std::size_t idx) { return m_support_planes[idx]; }

  template<typename PSimplex>
  const Mesh& mesh(const PSimplex& psimplex) const { return mesh(psimplex.first); }
  const Mesh& mesh(const std::size_t support_plane_idx) const { return support_plane(support_plane_idx).mesh(); }

  template<typename PSimplex>
  Mesh& mesh(const PSimplex& psimplex) { return mesh(psimplex.first); }
  Mesh& mesh(const std::size_t support_plane_idx) { return support_plane(support_plane_idx).mesh(); }

  std::size_t number_of_support_planes() const {
    return m_support_planes.size();
  }

  bool is_bbox_support_plane(const std::size_t support_plane_idx) const {
    return (support_plane_idx < 6); // Shouldn't it rather use the bbox flag inside Support_plane?
  }

  template<typename PointRange>
  std::pair<std::size_t, bool> add_support_plane(
    const PointRange& polygon, const bool is_bbox) {

    const Support_plane new_support_plane(
      polygon, is_bbox, m_parameters.distance_tolerance, number_of_support_planes());
    std::size_t support_plane_idx = KSR::no_element();
    bool found_coplanar_polygons = false;
    bool is_added = false;
    for (std::size_t i = 0; i < number_of_support_planes(); ++i) {
      if (new_support_plane == support_plane(i)) {
        found_coplanar_polygons = true;
        support_plane_idx = i;
        return std::make_pair(support_plane_idx, is_added);
      }
    }
    CGAL_assertion_msg(!found_coplanar_polygons,
    "ERROR: NO COPLANAR POLYGONS HERE!");

    is_added = !is_added;
    if (support_plane_idx == KSR::no_element()) {
      support_plane_idx = number_of_support_planes();
      m_support_planes.push_back(new_support_plane);
    }

    intersect_with_bbox(support_plane_idx);
    return std::make_pair(support_plane_idx, is_added);
  }

  void intersect_with_bbox(const std::size_t sp_idx) {
    if (is_bbox_support_plane(sp_idx)) return;

    // std::cout << "input graph: " << std::endl;
    // for (const auto iedge : m_intersection_graph.edges())
    //   std::cout << "2 " << segment_3(iedge) << std::endl;

    // Intersect current plane with all bbox iedges.
    Point_3 point;
    const auto& sp = support_plane(sp_idx);
    const auto& plane = sp.plane();

    using IEdge_vec = std::vector<IEdge>;
    using IPair = std::pair<IVertex, IEdge_vec>;
    using Pair = std::pair<Point_3, IPair>;

    std::vector<Pair> polygon;
    polygon.reserve(3);
    const FT ptol = KSR::point_tolerance<FT>();
    const auto all_iedges = m_intersection_graph.edges();
    for (const auto iedge : all_iedges) {
      const auto segment = segment_3(iedge);
      if (!m_kinetic_traits.intersection(plane, segment, point)) {
        continue;
      }

      const auto isource = source(iedge);
      const auto itarget = target(iedge);
      const FT dist1 = KSR::distance(point, point_3(isource));
      const FT dist2 = KSR::distance(point, point_3(itarget));
      const bool is_isource = (dist1 < ptol);
      const bool is_itarget = (dist2 < ptol);

      std::vector<IEdge> iedges;
      if (is_isource) {
        CGAL_assertion(!is_itarget);
        const auto inc_edges = m_intersection_graph.incident_edges(isource);
        CGAL_assertion(iedges.size() == 0);
        iedges.reserve(inc_edges.size());
        std::copy(inc_edges.begin(), inc_edges.end(), std::back_inserter(iedges));
        CGAL_assertion(iedges.size() == inc_edges.size());
        polygon.push_back(std::make_pair(point, std::make_pair(isource, iedges)));
      }

      if (is_itarget) {
        CGAL_assertion(!is_isource);
        const auto inc_edges = m_intersection_graph.incident_edges(itarget);
        CGAL_assertion(iedges.size() == 0);
        iedges.reserve(inc_edges.size());
        std::copy(inc_edges.begin(), inc_edges.end(), std::back_inserter(iedges));
        CGAL_assertion(iedges.size() == inc_edges.size());
        polygon.push_back(std::make_pair(point, std::make_pair(itarget, iedges)));
      }

      if (!is_isource && !is_itarget) {
        CGAL_assertion(iedges.size() == 0);
        iedges.push_back(iedge);
        polygon.push_back(std::make_pair(point, std::make_pair(null_ivertex(), iedges)));
      }
    }
    // std::cout << "num intersections: " << polygon.size() << std::endl;

    // Sort the points to get an oriented polygon.
    boost::function<Point_3(Pair&)> f = boost::bind(&Pair::first, _1);
    Point_2 mid = sp.to_2d(CGAL::centroid(boost::make_transform_iterator(polygon.begin(), f), boost::make_transform_iterator(polygon.end(), f), CGAL::Dimension_tag<0>()));
    std::sort(polygon.begin(), polygon.end(),
    [&](const Pair& a, const Pair& b) {
      const auto a2 = sp.to_2d(a.first);
      const auto b2 = sp.to_2d(b.first);
      const Segment_2 sega(mid, a2);
      const Segment_2 segb(mid, b2);
      return (Direction_2(sega) < Direction_2(segb));
    });

    // std::cout << "oriented polygon: " << std::endl;
    // for (const auto& pair : polygon) {
    //   const auto& item = pair.second;
    //   std::cout << item.second.size() << " : " << pair.first << std::endl;
    // }

    remove_equal_points(polygon, ptol);
    // std::cout << "clean polygon: " << std::endl;
    // for (const auto& pair : polygon) {
    //   const auto& item = pair.second;
    //   std::cout << item.second.size() << " : " << pair.first << std::endl;
    // }
    CGAL_assertion(is_valid_polygon(sp_idx, polygon));

    // Find common planes.
    std::vector<IVertex> vertices;
    std::vector<std::size_t> common_planes_idx;
    std::map<std::size_t, std::size_t> map_lines_idx;

    const std::size_t n = polygon.size();
    common_planes_idx.reserve(n);
    vertices.reserve(n);

    std::vector< std::set<std::size_t> > all_iplanes;
    all_iplanes.reserve(n);
    for (std::size_t i = 0; i < n; ++i) {
      const auto& item = polygon[i].second;
      const auto& iedges = item.second;

      std::set<std::size_t> iplanes;
      for (const auto& iedge : iedges) {
        const auto& planes = m_intersection_graph.intersected_planes(iedge);
        iplanes.insert(planes.begin(), planes.end());
      }
      // std::cout << "num iplanes: " << iplanes.size() << std::endl;
      CGAL_assertion(iplanes.size() >= 2);
      all_iplanes.push_back(iplanes);
    }
    CGAL_assertion(all_iplanes.size() == n);

    for (std::size_t i = 0; i < n; ++i) {
      const std::size_t ip = (i + 1) % n;
      const auto& item = polygon[i].second;

      const auto& iplanes0 = all_iplanes[i];
      const auto& iplanes1 = all_iplanes[ip];

      std::size_t common_plane_idx = KSR::no_element();
      const std::function<void(const std::size_t& idx)> lambda =
        [&](const std::size_t& idx) {
          if (idx < 6) {
            CGAL_assertion(common_plane_idx == KSR::no_element());
            common_plane_idx = idx;
          }
        };

      std::set_intersection(
        iplanes0.begin(), iplanes0.end(),
        iplanes1.begin(), iplanes1.end(),
        boost::make_function_output_iterator(lambda)
      );

      // std::cout << "cpi: " << common_plane_idx << std::endl;
      CGAL_assertion(common_plane_idx != KSR::no_element());
      common_planes_idx.push_back(common_plane_idx);

      const auto pair = map_lines_idx.insert(
        std::make_pair(common_plane_idx, KSR::no_element()));
      const bool is_inserted = pair.second;
      if (is_inserted) {
        pair.first->second = m_intersection_graph.add_line();
      }

      if (item.first != null_ivertex()) {
        vertices.push_back(item.first);
      } else {
        CGAL_assertion(item.first == null_ivertex());
        vertices.push_back(
          m_intersection_graph.add_vertex(polygon[i].first).first);
      }
    }
    CGAL_assertion(common_planes_idx.size() == n);
    CGAL_assertion(vertices.size() == n);

    // std::cout << "vertices: " << std::endl;
    // for (const auto& vertex : vertices) {
    //   std::cout << point_3(vertex) << std::endl;
    // }

    // Insert, split iedges.
    CGAL_assertion(common_planes_idx.size() == n);
    for (std::size_t i = 0; i < n; ++i) {
      const std::size_t ip = (i + 1) % n;
      const auto& item = polygon[i].second;

      const std::size_t common_plane_idx = common_planes_idx[i];
      const auto new_iedge = m_intersection_graph.add_edge(vertices[i], vertices[ip], sp_idx).first;
      m_intersection_graph.intersected_planes(new_iedge).insert(common_plane_idx);
      CGAL_assertion(map_lines_idx.find(common_plane_idx) != map_lines_idx.end());
      m_intersection_graph.set_line(new_iedge, map_lines_idx.at(common_plane_idx));
      support_plane(sp_idx).unique_iedges().insert(new_iedge);
      support_plane(common_plane_idx).unique_iedges().insert(new_iedge);

      if (item.first == null_ivertex()) { // edge case, split
        const auto& iplanes = all_iplanes[i];
        CGAL_assertion(iplanes.size() >= 2);
        CGAL_assertion(item.second.size() == 1);
        const auto& iedge = item.second[0];
        for (const std::size_t plane_idx : iplanes) {
          support_plane(plane_idx).unique_iedges().erase(iedge);
        }
        const auto edges = m_intersection_graph.split_edge(iedge, vertices[i]);

        const auto& iplanes0 = m_intersection_graph.intersected_planes(edges.first);
        for (const std::size_t plane_idx : iplanes0) {
          support_plane(plane_idx).unique_iedges().insert(edges.first);
        }

        const auto& iplanes1 = m_intersection_graph.intersected_planes(edges.second);
        for (const std::size_t plane_idx : iplanes1) {
          support_plane(plane_idx).unique_iedges().insert(edges.second);
        }
      }
    }

    // std::cout << "output graph: " << std::endl;
    // for (const auto iedge : m_intersection_graph.edges())
    //   std::cout << "2 " << segment_3(iedge) << std::endl;

    // exit(EXIT_SUCCESS);
  }

  template<typename PointRange>
  void add_bbox_polygon(const PointRange& polygon) {

    bool is_added = true;
    std::size_t support_plane_idx = KSR::no_element();
    std::tie(support_plane_idx, is_added) = add_support_plane(polygon, true);
    CGAL_assertion(is_added);
    CGAL_assertion(support_plane_idx != KSR::no_element());

    std::array<IVertex, 4> ivertices;
    std::array<Point_2, 4> points;
    for (std::size_t i = 0; i < 4; ++i) {
      points[i] = support_plane(support_plane_idx).to_2d(polygon[i]);
      ivertices[i] = m_intersection_graph.add_vertex(polygon[i]).first;
    }

    const auto vertices =
      support_plane(support_plane_idx).add_bbox_polygon(points, ivertices);

    for (std::size_t i = 0; i < 4; ++i) {
      const auto pair = m_intersection_graph.add_edge(ivertices[i], ivertices[(i+1)%4], support_plane_idx);
      const auto& iedge = pair.first;
      const bool is_inserted = pair.second;
      if (is_inserted) {
        m_intersection_graph.set_line(iedge, m_intersection_graph.add_line());
      }

      support_plane(support_plane_idx).set_iedge(vertices[i], vertices[(i + 1) % 4], iedge);
      support_plane(support_plane_idx).unique_iedges().insert(iedge);
    }
  }

  void add_input_polygon(
    const std::size_t support_plane_idx,
    const std::vector<std::size_t>& input_indices,
    const std::vector<Point_2>& polygon) {

    std::vector< std::pair<Point_2, bool> > points;
    points.reserve(polygon.size());
    for (const auto& point : polygon) {
      points.push_back(std::make_pair(point, true));
    }
    CGAL_assertion(points.size() == polygon.size());

    preprocess(points);
    sort_points_by_direction(points);
    support_plane(support_plane_idx).
      add_input_polygon(points, input_indices, support_plane_idx);
    for (const std::size_t input_index : input_indices) {
      m_input_polygon_map[input_index] = support_plane_idx;
    }
  }

  template<typename Pair>
  void preprocess(
    std::vector<Pair>& points,
    const FT min_dist = KSR::tolerance<FT>(),
    const FT min_angle = FT(10)) const {

    // std::vector< std::pair<Point_2, true> > points;
    // points.push_back(std::make_pair(Point_2(0.0, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.1, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.2, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.3, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.6, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.7, 0.0)));
    // points.push_back(std::make_pair(Point_2(0.9, 0.0)));
    // points.push_back(std::make_pair(Point_2(1.0, 0.0)));
    // points.push_back(std::make_pair(Point_2(1.0, 0.1)));
    // points.push_back(std::make_pair(Point_2(1.0, 0.2)));
    // points.push_back(std::make_pair(Point_2(1.0, 0.5)));
    // points.push_back(std::make_pair(Point_2(1.0, 1.0)));
    // points.push_back(std::make_pair(Point_2(0.9, 1.0)));
    // points.push_back(std::make_pair(Point_2(0.5, 1.0)));
    // points.push_back(std::make_pair(Point_2(0.2, 1.0)));
    // points.push_back(std::make_pair(Point_2(0.0, 1.0)));
    // points.push_back(std::make_pair(Point_2(0.0, 0.9)));
    // points.push_back(std::make_pair(Point_2(0.0, 0.8)));
    // points.push_back(std::make_pair(Point_2(0.0, 0.5)));
    // points.push_back(std::make_pair(Point_2(0.0, 0.2)));
    // points.push_back(std::make_pair(Point_2(0.0, 0.1)));
    // const FT min_dist = FT(15) / FT(100);

    // std::cout << "before: " << points.size() << std::endl;
    // for (const auto& pair : points) {
    //   std::cout << pair.first << " 0 " << std::endl;
    // }

    remove_equal_points(points, min_dist);

    // std::cout << "after 1: " << points.size() << std::endl;
    // for (const auto& pair : points) {
    //   std::cout << pair.first << " 0 " << std::endl;
    // }

    remove_collinear_points(points, min_angle);

    // std::cout << "after 2: " << points.size() << std::endl;
    // for (const auto& pair : points) {
    //   std::cout << pair.first << " 0 " << std::endl;
    // }
    // exit(EXIT_SUCCESS);
  }

  template<typename Pair>
  void remove_equal_points(std::vector<Pair>& points, const FT min_dist) const {

    // std::cout << std::endl;
    std::vector<Pair> polygon;
    const std::size_t n = points.size();
    for (std::size_t i = 0; i < n; ++i) {
      const auto& first = points[i];
      polygon.push_back(first);

      while (true) {
        const auto& p = points[i].first;
        const std::size_t ip = (i + 1) % n;
        const auto& q = points[ip].first;
        const FT distance = KSR::distance(p, q);
        const bool is_small = (distance < min_dist);
        if (ip == 0 && is_small) break;
        if (is_small) {
          CGAL_assertion(ip != 0);
          i = ip; continue;
        }
        CGAL_assertion(!is_small);
        break;
      };
    }
    CGAL_assertion(polygon.size() >= 3);
    points = polygon;
    // CGAL_assertion_msg(false, "TODO: REMOVE EQUAL POINTS!");
  }

  template<typename Pair>
  void remove_collinear_points(std::vector<Pair>& points, const FT min_angle) const {

    // std::cout << std::endl;
    std::vector<Pair> polygon;
    const std::size_t n = points.size();
    for (std::size_t i = 0; i < n; ++i) {
      const std::size_t im = (i + n - 1) % n;
      const std::size_t ip = (i + 1) % n;

      const auto& p = points[im].first;
      const auto& q = points[i].first;
      const auto& r = points[ip].first;

      Vector_2 vec1(q, r);
      Vector_2 vec2(q, p);
      vec1 = KSR::normalize(vec1);
      vec2 = KSR::normalize(vec2);

      const Direction_2 dir1(vec1);
      const Direction_2 dir2(vec2);
      const FT angle = KSR::angle_2(dir1, dir2);

      // std::cout << "- angle: " << angle << " : " << min_angle << std::endl;
      if (angle > min_angle) polygon.push_back(points[i]);
    }
    if (polygon.size() >= 3) points = polygon;
    else remove_collinear_points(points, min_angle / FT(2));
    // CGAL_assertion_msg(false, "TODO: REMOVE COLLINEAR POINTS!");
  }

  template<typename Pair>
  void sort_points_by_direction(std::vector<Pair>& points) const {
    FT x = FT(0), y = FT(0);
    for (const auto& pair : points) {
      const auto& point = pair.first;
      x += point.x();
      y += point.y();
    }
    x /= static_cast<FT>(points.size());
    y /= static_cast<FT>(points.size());
    const Point_2 mid(x, y);

    std::sort(points.begin(), points.end(),
    [&](const Pair& a, const Pair& b) -> bool {
      const Segment_2 sega(mid, a.first);
      const Segment_2 segb(mid, b.first);
      return ( Direction_2(sega) < Direction_2(segb) );
    });
  }

  /*******************************
  **        PSimplices          **
  ********************************/

  static PVertex null_pvertex() { return PVertex(KSR::no_element(), Vertex_index()); }
  static PEdge   null_pedge()   { return   PEdge(KSR::no_element(),   Edge_index()); }
  static PFace   null_pface()   { return   PFace(KSR::no_element(),   Face_index()); }

  const PVertices pvertices(const std::size_t support_plane_idx) const {
    return PVertices(
      boost::make_transform_iterator(
        mesh(support_plane_idx).vertices().begin(),
        Make_PSimplex<PVertex>(support_plane_idx)),
      boost::make_transform_iterator(
        mesh(support_plane_idx).vertices().end(),
        Make_PSimplex<PVertex>(support_plane_idx)));
  }

  const PEdges pedges(const std::size_t support_plane_idx) const {
    return PEdges(
      boost::make_transform_iterator(
        mesh(support_plane_idx).edges().begin(),
        Make_PSimplex<PEdge>(support_plane_idx)),
      boost::make_transform_iterator(
        mesh(support_plane_idx).edges().end(),
        Make_PSimplex<PEdge>(support_plane_idx)));
  }

  const PFaces pfaces(const std::size_t support_plane_idx) const {
    return PFaces(
      boost::make_transform_iterator(
        mesh(support_plane_idx).faces().begin(),
        Make_PSimplex<PFace>(support_plane_idx)),
      boost::make_transform_iterator(
        mesh(support_plane_idx).faces().end(),
        Make_PSimplex<PFace>(support_plane_idx)));
  }

  // Get prev and next pvertices of the free pvertex.
  const PVertex prev(const PVertex& pvertex) const {
    return PVertex(pvertex.first, support_plane(pvertex).prev(pvertex.second));
  }
  const PVertex next(const PVertex& pvertex) const {
    return PVertex(pvertex.first, support_plane(pvertex).next(pvertex.second));
  }

  void get_and_sort_all_connected_iedges(
    const std::size_t sp_idx, const IVertex& ivertex,
    std::vector< std::pair<IEdge, Direction_2> >& iedges) const {

    auto inc_iedges = incident_iedges(ivertex);
    const std::function<void(const IEdge& inc_iedge)> lambda =
      [&](const IEdge& inc_iedge) {
        const auto iplanes = intersected_planes(inc_iedge);
        if (iplanes.find(sp_idx) == iplanes.end()) {
          return;
        }
        const Direction_2 direction(
          point_2(sp_idx, opposite(inc_iedge, ivertex)) -
          point_2(sp_idx, ivertex));
        iedges.push_back(std::make_pair(inc_iedge, direction));
      };

    std::copy(
      inc_iedges.begin(), inc_iedges.end(),
      boost::make_function_output_iterator(lambda)
    );

    std::sort(iedges.begin(), iedges.end(),
      [&](const std::pair<IEdge, Direction_2>& a,
          const std::pair<IEdge, Direction_2>& b) -> bool {
        return a.second < b.second;
      }
    );
    CGAL_assertion(iedges.size() > 0);
  }

  const PVertex add_pvertex(const std::size_t support_plane_idx, const Point_2& point) {

    CGAL_assertion(support_plane_idx != KSR::uninitialized());
    CGAL_assertion(support_plane_idx != KSR::no_element());

    auto& m = mesh(support_plane_idx);
    const auto vi = m.add_vertex(point);
    CGAL_assertion(vi != typename Support_plane::Mesh::Vertex_index());
    return PVertex(support_plane_idx, vi);
  }

  template<typename VertexRange>
  const PFace add_pface(const VertexRange& pvertices) {

    const auto support_plane_idx = pvertices.front().first;
    CGAL_assertion(support_plane_idx != KSR::uninitialized());
    CGAL_assertion(support_plane_idx != KSR::no_element());

    auto& m = mesh(support_plane_idx);
    const auto range = CGAL::make_range(
      boost::make_transform_iterator(pvertices.begin(),
      CGAL::Property_map_to_unary_function<CGAL::Second_of_pair_property_map<PVertex> >()),
      boost::make_transform_iterator(pvertices.end(),
      CGAL::Property_map_to_unary_function<CGAL::Second_of_pair_property_map<PVertex> >()));
    const auto fi = m.add_face(range);
    CGAL_assertion(fi != Support_plane::Mesh::null_face());
    return PFace(support_plane_idx, fi);
  }

  const IFace add_iface(std::size_t support_plane) {
    return m_intersection_graph.add_face(support_plane);;
  }

  const PFace add_iface_to_mesh(std::size_t support_plane, IFace f_idx) {
    typename Intersection_graph::Face_property &f = m_intersection_graph.face(f_idx);
    std::vector<Vertex_index> vertices;
    vertices.reserve(f.vertices.size());
    Support_plane& sp = m_support_planes[support_plane];

    for (auto v : f.vertices) {
      auto& m = sp.ivertex2pvertex();
      std::pair<int, int> x(1, 2);
      std::pair<IVertex, Vertex_index> p(v, std::size_t(-1));
      auto& pair = m.insert(p);
      if (pair.second) {
        pair.first->second = sp.mesh().add_vertex(point_2(support_plane, v));
      }
      sp.set_ivertex(pair.first->second, v);
      vertices.push_back(pair.first->second);
    }

    Face_index fi = sp.mesh().add_face(vertices);
    if (fi == Support_plane::Mesh::null_face()) {
      std::cout << "ERROR: invalid face created!" << std::endl;
      for (std::size_t i = 0; i < f.vertices.size(); i++) {
        std::cout << "2 " << point_3(f.vertices[i]) << " " << point_3(f.vertices[(i + 1) % f.vertices.size()]) << std::endl;
      }
      std::cout << "ERROR: end of invalid face" << std::endl;
    }

    // Link pedges to iedges
    auto h = sp.mesh().halfedge(fi);
    auto first = h;
    do {
      Edge_index e = sp.mesh().edge(h);
      PVertex t = PVertex(support_plane, sp.mesh().target(h));
      PVertex s = PVertex(support_plane, sp.mesh().source(h));
      IVertex it = ivertex(t);
      IVertex is = ivertex(s);
      sp.set_iedge(e, m_intersection_graph.edge(is, it));
      h = sp.mesh().next(h);
    } while (h != first);

    f.part_of_partition = true;

    return PFace(support_plane, fi);
  }

  void clear_pfaces(const std::size_t support_plane_idx) {
    support_plane(support_plane_idx).clear_pfaces();
  }

  void clear_polygon_faces(const std::size_t support_plane_idx) {
    Mesh& m = mesh(support_plane_idx);
    for (const auto& fi : m.faces()) {
      m.remove_face(fi);
    }
    for (const auto& ei : m.edges()) {
      m.remove_edge(ei);
    }
    for (const auto& vi : m.vertices()) {
      m.set_halfedge(vi, Halfedge_index());
    }
  }

  PVertex source(const PEdge& pedge) const {
    return PVertex(pedge.first, mesh(pedge).source(mesh(pedge).halfedge(pedge.second)));
  }
  PVertex target(const PEdge& pedge) const {
    return PVertex(pedge.first, mesh(pedge).target(mesh(pedge).halfedge(pedge.second)));
  }
  PVertex opposite(const PEdge& pedge, const PVertex& pvertex) const {

    if (mesh(pedge).target(mesh(pedge).halfedge(pedge.second)) == pvertex.second) {
      return PVertex(pedge.first, mesh(pedge).source(mesh(pedge).halfedge(pedge.second)));
    }
    CGAL_assertion(mesh(pedge).source(mesh(pedge).halfedge(pedge.second)) == pvertex.second);
    return PVertex(pedge.first, mesh(pedge).target(mesh(pedge).halfedge(pedge.second)));
  }

  Point_3 centroid_of_pface(const PFace& pface) const {

    const std::function<Point_3(PVertex)> unary_f =
    [&](const PVertex& pvertex) -> Point_3 {
      return point_3(pvertex);
    };
    const std::vector<Point_3> polygon(
      boost::make_transform_iterator(pvertices_of_pface(pface).begin(), unary_f),
      boost::make_transform_iterator(pvertices_of_pface(pface).end()  , unary_f));
    CGAL_assertion(polygon.size() >= 3);
    return CGAL::centroid(polygon.begin(), polygon.end());
  }

  Plane_3 plane_of_pface(const PFace& pface) const {

    const std::function<Point_3(PVertex)> unary_f =
    [&](const PVertex& pvertex) -> Point_3 {
      return point_3(pvertex);
    };
    const std::vector<Point_3> polygon(
      boost::make_transform_iterator(pvertices_of_pface(pface).begin(), unary_f),
      boost::make_transform_iterator(pvertices_of_pface(pface).end()  , unary_f));
    CGAL_assertion(polygon.size() >= 3);
    return Plane_3(polygon[0], polygon[1], polygon[2]);
  }

  PFace pface_of_pvertex(const PVertex& pvertex) const {
    return PFace(pvertex.first, support_plane(pvertex).face(pvertex.second));
  }

  std::pair<PFace, PFace> pfaces_of_pvertex(const PVertex& pvertex) const {

    std::pair<PFace, PFace> out(null_pface(), null_pface());
    std::tie(out.first.second, out.second.second) =
      support_plane(pvertex).faces(pvertex.second);
    if (out.first.second != Face_index()) {
      out.first.first = pvertex.first;
    }
    if (out.second.second != Face_index()) {
      out.second.first = pvertex.first;
    }
    return out;
  }

  PFaces_around_pvertex pfaces_around_pvertex(const PVertex& pvertex) const {

    const auto pfaces = PFaces_around_pvertex(
      boost::make_transform_iterator(
        halfedges_around_target(halfedge(pvertex.second, mesh(pvertex)), mesh(pvertex)).begin(),
        Halfedge_to_pface(pvertex.first, mesh(pvertex))),
      boost::make_transform_iterator(
        halfedges_around_target(halfedge(pvertex.second, mesh(pvertex)), mesh(pvertex)).end(),
        Halfedge_to_pface(pvertex.first, mesh(pvertex))));
    CGAL_assertion(pfaces.size() >= 1);
    return pfaces;
  }

  void non_null_pfaces_around_pvertex(
    const PVertex& pvertex, std::vector<PFace>& pfaces) const {

    pfaces.clear();
    const auto nfaces = pfaces_around_pvertex(pvertex);
    for (const auto pface : nfaces) {
      if (pface.second == Support_plane::Mesh::null_face()) continue;
      pfaces.push_back(pface);
    }
  }

  PVertices_of_pface pvertices_of_pface(const PFace& pface) const {

    const auto pvertices = PVertices_of_pface(
      boost::make_transform_iterator(
        halfedges_around_face(halfedge(pface.second, mesh(pface)), mesh(pface)).begin(),
        Halfedge_to_pvertex(pface.first, mesh(pface))),
      boost::make_transform_iterator(
        halfedges_around_face(halfedge(pface.second, mesh(pface)), mesh(pface)).end(),
        Halfedge_to_pvertex(pface.first, mesh(pface))));
    CGAL_assertion(pvertices.size() >= 3);
    return pvertices;
  }

  PEdges_of_pface pedges_of_pface(const PFace& pface) const {

    const auto pedges = PEdges_of_pface(
      boost::make_transform_iterator(
        halfedges_around_face(halfedge(pface.second, mesh(pface)), mesh(pface)).begin(),
        Halfedge_to_pedge(pface.first, mesh(pface))),
      boost::make_transform_iterator(
        halfedges_around_face(halfedge(pface.second, mesh(pface)), mesh(pface)).end(),
        Halfedge_to_pedge(pface.first, mesh(pface))));
    CGAL_assertion(pedges.size() >= 3);
    return pedges;
  }

  PEdges_around_pvertex pedges_around_pvertex(const PVertex& pvertex) const {

    const auto pedges = PEdges_around_pvertex(
      boost::make_transform_iterator(
        halfedges_around_target(halfedge(pvertex.second, mesh(pvertex)), mesh(pvertex)).begin(),
        Halfedge_to_pedge(pvertex.first, mesh(pvertex))),
      boost::make_transform_iterator(
        halfedges_around_target(halfedge(pvertex.second, mesh(pvertex)), mesh(pvertex)).end(),
        Halfedge_to_pedge(pvertex.first, mesh(pvertex))));
    CGAL_assertion(pedges.size() >= 2);
    return pedges;
  }

  std::vector<Volume_cell> incident_volumes(const PFace& query_pface) const {

    std::vector<Volume_cell> nvolumes;
    for (const auto& volume : m_volumes) {
      for (const auto& pface : volume.pfaces) {
        if (pface == query_pface) nvolumes.push_back(volume);
      }
    }
    return nvolumes;
  }

  void incident_faces(const IEdge& query_iedge, std::vector<PFace>& nfaces) const {

    nfaces.clear();
    for (const auto plane_idx : intersected_planes(query_iedge)) {
      for (const auto pedge : pedges(plane_idx)) {
        if (iedge(pedge) == query_iedge) {
          const auto& m = mesh(plane_idx);
          const auto he = m.halfedge(pedge.second);
          const auto op = m.opposite(he);
          const auto face1 = m.face(he);
          const auto face2 = m.face(op);
          if (face1 != Support_plane::Mesh::null_face()) {
            nfaces.push_back(PFace(plane_idx, face1));
          }
          if (face2 != Support_plane::Mesh::null_face()) {
            nfaces.push_back(PFace(plane_idx, face2));
          }
        }
      }
    }
  }

  const std::vector<std::size_t>& input(const PFace& pface) const{ return support_plane(pface).input(pface.second); }
  std::vector<std::size_t>& input(const PFace& pface) { return support_plane(pface).input(pface.second); }

  const unsigned int& k(const std::size_t support_plane_idx) const { return support_plane(support_plane_idx).k(); }
  unsigned int& k(const std::size_t support_plane_idx) { return support_plane(support_plane_idx).k(); }

  const unsigned int& k(const PFace& pface) const { return support_plane(pface).k(pface.second); }
  unsigned int& k(const PFace& pface) { return support_plane(pface).k(pface.second); }

  bool is_frozen(const PVertex& pvertex) const { return support_plane(pvertex).is_frozen(pvertex.second); }

  const Vector_2& direction(const PVertex& pvertex) const { return support_plane(pvertex).direction(pvertex.second); }
  Vector_2& direction(const PVertex& pvertex) { return support_plane(pvertex).direction(pvertex.second); }

  const FT speed(const PVertex& pvertex) { return support_plane(pvertex).speed(pvertex.second); }

  bool is_active(const PVertex& pvertex) const { return support_plane(pvertex).is_active(pvertex.second); }

  void deactivate(const PVertex& pvertex) {

    support_plane(pvertex).set_active(pvertex.second, false);
    if (iedge(pvertex) != null_iedge()) {
      m_intersection_graph.is_active(iedge(pvertex)) = false;
    }
    // std::cout << str(pvertex) << " ";
    if (ivertex(pvertex) != null_ivertex()) {
      // std::cout << " ivertex: " << point_3(ivertex(pvertex));
      m_intersection_graph.is_active(ivertex(pvertex)) = false;
    }
    // std::cout << std::endl;
  }

  void activate(const PVertex& pvertex) {

    support_plane(pvertex).set_active(pvertex.second, true);
    if (iedge(pvertex) != null_iedge()) {
      m_intersection_graph.is_active(iedge(pvertex)) = true;
    }
    if (ivertex(pvertex) != null_ivertex()) {
      m_intersection_graph.is_active(ivertex(pvertex)) = true;
    }
  }

  /*******************************
  **          ISimplices        **
  ********************************/

  static IVertex null_ivertex() { return Intersection_graph::null_ivertex(); }
  static IEdge null_iedge() { return Intersection_graph::null_iedge(); }

  decltype(auto) ivertices() const { return m_intersection_graph.vertices(); }
  decltype(auto) iedges() const { return m_intersection_graph.edges(); }

  std::size_t nb_intersection_lines() const { return m_intersection_graph.nb_lines(); }
  std::size_t line_idx(const IEdge& iedge) const { return m_intersection_graph.line(iedge); }
  std::size_t line_idx(const PVertex& pvertex) const { return line_idx(iedge(pvertex)); }

  const IVertex add_ivertex(const Point_3& point, const std::set<std::size_t>& support_planes_idx) {

    std::vector<std::size_t> vec_planes;
    std::copy(
      support_planes_idx.begin(),
      support_planes_idx.end(),
      std::back_inserter(vec_planes));
    const auto pair = m_intersection_graph.add_vertex(point, vec_planes);
    const auto ivertex = pair.first;
    return ivertex;
  }

  void add_iedge(const std::set<std::size_t>& support_planes_idx, std::vector<IVertex>& vertices) {

    const auto source = m_intersection_graph.point_3(vertices.front());
    std::sort(vertices.begin(), vertices.end(),
      [&](const IVertex& a, const IVertex& b) -> bool {
        const auto ap = m_intersection_graph.point_3(a);
        const auto bp = m_intersection_graph.point_3(b);
        const auto sq_dist_a = CGAL::squared_distance(source, ap);
        const auto sq_dist_b = CGAL::squared_distance(source, bp);
        return (sq_dist_a < sq_dist_b);
      }
    );

    std::size_t line_idx = m_intersection_graph.add_line();
    for (std::size_t i = 0; i < vertices.size() - 1; ++i) {

      CGAL_assertion(!is_zero_length_iedge(vertices[i], vertices[i + 1]));
      const auto pair = m_intersection_graph.add_edge(
        vertices[i], vertices[i + 1], support_planes_idx);
      const auto iedge = pair.first;
      const auto is_inserted = pair.second;
      CGAL_assertion(is_inserted);
      m_intersection_graph.set_line(iedge, line_idx);

      for (const auto support_plane_idx : support_planes_idx) {
        support_plane(support_plane_idx).unique_iedges().insert(iedge);
      }
    }
  }

  const IVertex source(const IEdge& edge) const { return m_intersection_graph.source(edge); }
  const IVertex target(const IEdge& edge) const { return m_intersection_graph.target(edge); }

  const IVertex opposite(const IEdge& edge, const IVertex& ivertex) const {
    const auto out = source(edge);
    if (out == ivertex) {
      return target(edge);
    }
    CGAL_assertion(target(edge) == ivertex);
    return out;
  }

  decltype(auto) incident_iedges(const IVertex& ivertex) const {
    return m_intersection_graph.incident_edges(ivertex);
  }

  const std::vector<IEdge>& iedges(const std::size_t support_plane_idx) const {
    return support_plane(support_plane_idx).iedges();
  }
  std::vector<IEdge>& iedges(const std::size_t support_plane_idx) {
    return support_plane(support_plane_idx).iedges();
  }

  const std::vector<Segment_2>& isegments(const std::size_t support_plane_idx) const {
    return support_plane(support_plane_idx).isegments();
  }
  std::vector<Segment_2>& isegments(const std::size_t support_plane_idx) {
    return support_plane(support_plane_idx).isegments();
  }

  const std::vector<Bbox_2>& ibboxes(const std::size_t support_plane_idx) const {
    return support_plane(support_plane_idx).ibboxes();
  }
  std::vector<Bbox_2>& ibboxes(const std::size_t support_plane_idx) {
    return support_plane(support_plane_idx).ibboxes();
  }

  const std::set<std::size_t>& intersected_planes(const IEdge& iedge) const {
    return m_intersection_graph.intersected_planes(iedge);
  }

  const std::set<std::size_t> intersected_planes(
    const IVertex& ivertex, const bool keep_bbox = true) const {

    std::set<std::size_t> out;
    for (const auto incident_iedge : incident_iedges(ivertex)) {
      for (const auto support_plane_idx : intersected_planes(incident_iedge)) {
        if (!keep_bbox && support_plane_idx < 6) {
          continue;
        }
        out.insert(support_plane_idx);
      }
    }
    return out;
  }

  bool is_zero_length_iedge(const IVertex& a, const IVertex& b) const {
    const auto& p = m_intersection_graph.point_3(a);
    const auto& q = m_intersection_graph.point_3(b);
    const FT distance = KSR::distance(p, q);
    const FT ptol = KSR::point_tolerance<FT>();
    return distance < ptol;
  }

  bool is_iedge(const IVertex& source, const IVertex& target) const {
    return m_intersection_graph.is_edge(source, target);
  }

  bool is_active(const IEdge& iedge) const {
    return m_intersection_graph.is_active(iedge);
  }
  bool is_active(const IVertex& ivertex) const {
    return m_intersection_graph.is_active(ivertex);
  }

  bool is_bbox_iedge(const IEdge& edge) const {

    for (const auto support_plane_idx : m_intersection_graph.intersected_planes(edge)) {
      if (support_plane_idx < 6) {
        return true;
      }
    }
    return false;
  }

  /*******************************
  **          STRINGS           **
  ********************************/

  void dump_loop(std::size_t sp) const {
    auto pl = support_plane(sp);
    auto m = pl.mesh();
    auto data = pl.data();

    Vertex_index s = Mesh::null_vertex();

    for (auto v : m.vertices()) {
      if (pl.is_active(v)) {
        s = v;
        break;
      }
    }

    if (s == Mesh::null_vertex()) {
      std::cout << "Support plane " << sp << " does not have active vertices" << std::endl;
      return;
    }

    auto h = m.halfedge(s);
    auto n = m.next(h);
    std::cout << "Support plane " << sp << ": " << s;
    while (n != h && n != Mesh::null_halfedge()) {
      std::cout << ", " << m.target(n);

      if (pl.is_frozen(m.target(n)))
        std::cout << "f";

      n = m.next(n);
    }

    if (n == Mesh::null_halfedge()) {
      std::cout << " NULL_HALFEDGE!";
    }
    std::cout << std::endl;

    m.collect_garbage();

    h = m.halfedge(s);
    n = m.next(h);
    std::cout << "after gc      " << sp << ": " << s;
    while (n != h && n != Mesh::null_halfedge()) {
      std::cout << ", " << m.target(n);

      if (pl.is_frozen(m.target(n)))
        std::cout << "f";

      n = m.next(n);
    }

    if (n == Mesh::null_halfedge()) {
      std::cout << " NULL_HALFEDGE!";
    }
    std::cout << std::endl;
  }

  inline const std::string str(const PVertex& pvertex) const {
    auto sp = support_plane(pvertex.first);
    std::string res = "PVertex(" + std::to_string(pvertex.first) + ":v" + std::to_string(pvertex.second);
    if (sp.is_frozen(pvertex.second)) res += "f";

    if (sp.has_iedge(pvertex.second)) res += " " + this->str(sp.iedge(pvertex.second));

    auto m = support_plane(pvertex.first).mesh();
    auto h = m.halfedge(pvertex.second);
    if (h != Mesh::null_halfedge()) {
      res += " p:" + std::to_string(m.source(h));
      if (support_plane(pvertex.first).is_frozen(m.source(h))) res += "f";
      if ((h = m.next(h)) != Mesh::null_halfedge()) {
        auto n = m.target(h);
        res += " n:" + std::to_string(n);
        if (support_plane(pvertex.first).is_frozen(n)) res += "f";
      }
    }
    else res += " isolated";
    return res + ")";
  }
  inline const std::string str(const PEdge& pedge) const {
    return "PEdge(" + std::to_string(pedge.first) + ":e" + std::to_string(pedge.second) + ")";
  }
  inline const std::string str(const PFace& pface) const {
    return "PFace(" + std::to_string(pface.first) + ":f" + std::to_string(pface.second) + ")";
  }
  inline const std::string str(const IVertex& ivertex) const {
    return "IVertex(" + std::to_string(ivertex) + ")";
  }
  inline const std::string str(const IEdge& iedge) const {
    std::ostringstream oss; oss << "IEdge" << iedge; return oss.str();
  }

  inline const std::string lstr(const PFace& pface) const {

    if (pface == null_pface()) {
      return "PFace(null)";
    }
    std::string out = "PFace(" + std::to_string(pface.first) + ":f" + std::to_string(pface.second) + ")[";
    for (const auto pvertex : pvertices_of_pface(pface)) {
      out += "v" + std::to_string(pvertex.second);
    }
    out += "]";
    return out;
  }

  inline const std::string lstr(const PEdge& pedge) const {
    return "PEdge(" + std::to_string(pedge.first) + ":e" + std::to_string(pedge.second)
      + ")[v" + std::to_string(source(pedge).second) + "->v" + std::to_string(target(pedge).second) + "]";
  }

  /*******************************
  **        CONNECTIVITY        **
  ********************************/

  bool has_ivertex(const PVertex& pvertex) const { return support_plane(pvertex).has_ivertex(pvertex.second); }
  IVertex ivertex(const PVertex& pvertex) const { return support_plane(pvertex).ivertex(pvertex.second); }

  bool has_iedge(const PVertex& pvertex) const { return support_plane(pvertex).has_iedge(pvertex.second); }
  IEdge iedge(const PVertex& pvertex) const { return support_plane(pvertex).iedge(pvertex.second); }

  bool has_iedge(const PEdge& pedge) const { return support_plane(pedge).has_iedge(pedge.second); }
  IEdge iedge(const PEdge& pedge) const { return support_plane(pedge).iedge(pedge.second); }

  bool has_pedge(
    const std::size_t sp_idx, const IEdge& iedge) const {

    for (const auto pedge : this->pedges(sp_idx)) {
      if (this->iedge(pedge) == iedge) {
        return true;
      }
    }
    return false;
  }

  void connect(const PVertex& pvertex, const IVertex& ivertex) { support_plane(pvertex).set_ivertex(pvertex.second, ivertex); }
  void connect(const PVertex& pvertex, const IEdge& iedge) { support_plane(pvertex).set_iedge(pvertex.second, iedge); }
  void connect(const PVertex& pvertex, const PVertex& pother, const IEdge& iedge) { support_plane(pvertex).set_iedge(pvertex.second, pother.second, iedge); }
  void connect(const PEdge& pedge, const IEdge& iedge) { support_plane(pedge).set_iedge(pedge.second, iedge); }

  void connect_pedge(
    const PVertex& pvertex, const PVertex& pother, const IEdge& iedge) {

    const PEdge pedge(pvertex.first,
      support_plane(pvertex).edge(pvertex.second, pother.second));
    connect(pedge, iedge);
    connect(pother, iedge);
  }

  /*******************************
  **        CONVERSIONS         **
  ********************************/

  Point_2 to_2d(const std::size_t support_plane_idx, const IVertex& ivertex) const {
    return support_plane(support_plane_idx).to_2d(point_3(ivertex));
  }
  Segment_2 to_2d(const std::size_t support_plane_idx, const Segment_3& segment_3) const {
    return support_plane(support_plane_idx).to_2d(segment_3);
  }
  Point_2 to_2d(const std::size_t support_plane_idx, const Point_3& point_3) const {
    return support_plane(support_plane_idx).to_2d(point_3);
  }

  Point_2 point_2(const PVertex& pvertex, const FT time) const {
    return support_plane(pvertex).point_2(pvertex.second, time);
  }
  Point_2 point_2(const PVertex& pvertex) const {
    return point_2(pvertex, m_current_time);
  }
  Point_2 point_2(const std::size_t support_plane_idx, const IVertex& ivertex) const {
    return support_plane(support_plane_idx).to_2d(point_3(ivertex));
  }

  Segment_2 segment_2(const std::size_t support_plane_idx, const IEdge& iedge) const {
    return support_plane(support_plane_idx).to_2d(segment_3(iedge));
  }

  Point_3 to_3d(const std::size_t support_plane_idx, const Point_2& point_2) const {
    return support_plane(support_plane_idx).to_3d(point_2);
  }

  Point_3 point_3(const PVertex& pvertex, const FT time) const {
    return support_plane(pvertex).point_3(pvertex.second, time);
  }
  Point_3 point_3(const PVertex& pvertex) const {
    return point_3(pvertex, m_current_time);
  }
  Point_3 point_3(const IVertex& vertex) const {
    return m_intersection_graph.point_3(vertex);
  }

  Segment_3 segment_3(const PEdge& pedge, const FT time) const {
    return support_plane(pedge).segment_3(pedge.second, time);
  }
  Segment_3 segment_3(const PEdge& pedge) const {
    return segment_3 (pedge, m_current_time);
  }
  Segment_3 segment_3(const IEdge& edge) const {
    return m_intersection_graph.segment_3(edge);
  }

  /*******************************
  **          PREDICATES        **
  ********************************/

  // TODO: ADD FUNCTION HAS_PEDGES() OR NUM_PEDGES() THAT RETURNS THE NUMBER OF PEDGES
  // CONNECTED TO THE IEDGE. THAT WILL BE FASTER THAN CURRENT COMPUTATIONS!

  std::pair<bool, bool> is_occupied(
    const PVertex& pvertex, const IVertex& ivertex, const IEdge& query_iedge) const {

    const auto pair = is_occupied(pvertex, query_iedge);
    const bool has_polygon = pair.first;
    const bool is_bbox_reached = pair.second;

    if (is_bbox_reached) return std::make_pair(true, true);
    CGAL_assertion(!is_bbox_reached);
    if (!has_polygon) {
      // std::cout << "NO POLYGON DETECTED" << std::endl;
      return std::make_pair(false, false);
    }
    CGAL_assertion(has_polygon);

    CGAL_assertion(ivertex != null_ivertex());
    std::set<PEdge> pedges;
    get_occupied_pedges(pvertex, query_iedge, pedges);
    for (const auto& pedge : pedges) {
      CGAL_assertion(pedge != null_pedge());
      // std::cout << "PEDGE: " << segment_3(pedge) << std::endl;

      const auto source = this->source(pedge);
      const auto target = this->target(pedge);
      if (this->ivertex(source) == ivertex || this->ivertex(target) == ivertex) {
        return std::make_pair(true, false);
      }
    }
    return std::make_pair(false, false);
  }

  void get_occupied_pedges(
    const PVertex& pvertex, const IEdge& query_iedge, std::set<PEdge>& pedges) const {

    for (const auto plane_idx : intersected_planes(query_iedge)) {
      if (plane_idx == pvertex.first) continue; // current plane
      if (plane_idx < 6) continue; // bbox plane

      for (const auto pedge : this->pedges(plane_idx)) {
        if (iedge(pedge) == query_iedge) {
          pedges.insert(pedge);
        }
      }
    }
  }

  std::pair<bool, bool> is_occupied(
    const PVertex& pvertex, const IEdge& query_iedge) const {

    CGAL_assertion(query_iedge != null_iedge());
    // std::cout << str(query_iedge) << ": " << segment_3(query_iedge) << std::endl;
    std::size_t num_adjacent_faces = 0;
    for (const auto plane_idx : intersected_planes(query_iedge)) {
      if (plane_idx == pvertex.first) continue; // current plane
      if (plane_idx < 6) return std::make_pair(true, true); // bbox plane

      for (const auto pedge : pedges(plane_idx)) {
        if (!has_iedge(pedge)) continue;

        // std::cout << str(iedge(pedge)) << std::endl;
        if (iedge(pedge) == query_iedge) {
          const auto& m = mesh(plane_idx);
          const auto he = m.halfedge(pedge.second);
          const auto op = m.opposite(he);
          const auto face1 = m.face(he);
          const auto face2 = m.face(op);
          if (face1 != Support_plane::Mesh::null_face()) ++num_adjacent_faces;
          if (face2 != Support_plane::Mesh::null_face()) ++num_adjacent_faces;
        }
      }
    }

    // std::cout << "num adjacent faces: " << num_adjacent_faces << std::endl;
    if (num_adjacent_faces <= 1)
      return std::make_pair(false, false);
    return std::make_pair(true, false);
  }

  /*******************************
  **    CHECKING PROPERTIES     **
  ********************************/

  template<typename Pair>
  bool is_valid_polygon(
    const std::size_t sp_idx,
    const std::vector<Pair>& points) const {

    std::vector< std::pair<Point_2, bool> > polygon;
    polygon.reserve(points.size());
    for (const auto& pair : points) {
      const auto& p = pair.first;
      const auto q = to_2d(sp_idx, p);
      polygon.push_back(std::make_pair(q, true));
    }
    CGAL_assertion(polygon.size() == points.size());

    // const bool is_simple = support_plane(sp_idx).is_simple_polygon(polygon);
    // const bool is_convex = support_plane(sp_idx).is_convex_polygon(polygon);
    const bool is_valid = support_plane(sp_idx).is_valid_polygon(polygon);

    if (!is_valid) {
      for (const auto& pair : polygon) {
        std::cout << to_3d(sp_idx, pair.first) << std::endl;
      }
    }

    // CGAL_assertion_msg(is_simple, "ERROR: POLYGON IS NOT SIMPLE!");
    // CGAL_assertion_msg(is_convex, "ERROR: POLYGON IS NOT CONVEX!");
    CGAL_assertion_msg(is_valid, "ERROR: POLYGON IS NOT VALID!");
    return is_valid;
  }

  bool check_bbox() const {

    for (std::size_t i = 0; i < 6; ++i) {
      const auto pfaces = this->pfaces(i);
      for (const auto pface : pfaces) {
        for (const auto pvertex : pvertices_of_pface(pface)) {
          if (!has_ivertex(pvertex)) {
            std::cout << "debug pvertex: " << str(pvertex) << ", " << point_3(pvertex) << std::endl;
            CGAL_assertion_msg(has_ivertex(pvertex), "ERROR: BBOX VERTEX IS MISSING AN IVERTEX!");
            return false;
          }
        }
        for (const auto pedge : pedges_of_pface(pface)) {
          if (!has_iedge(pedge)) {
            std::cout << "debug pedge: " << str(pedge) << ", " << segment_3(pedge) << std::endl;
            CGAL_assertion_msg(has_iedge(pedge), "ERROR: BBOX EDGE IS MISSING AN IEDGE!");
            return false;
          }
        }
      }
    }
    return true;
  }

  bool check_interior() const {

    for (std::size_t i = 6; i < number_of_support_planes(); ++i) {
      const auto pfaces = this->pfaces(i);
      for (const auto pface : pfaces) {
        for (const auto pvertex : pvertices_of_pface(pface)) {
          if (!has_ivertex(pvertex)) {
            std::cout << "debug pvertex: " << str(pvertex) << ", " << point_3(pvertex) << std::endl;
            CGAL_assertion_msg(has_ivertex(pvertex), "ERROR: INTERIOR VERTEX IS MISSING AN IVERTEX!");
            return false;
          }
        }
        for (const auto pedge : pedges_of_pface(pface)) {
          if (!has_iedge(pedge)) {
            std::cout << "debug pedge: " << str(pedge) << ", " << segment_3(pedge) << std::endl;
            CGAL_assertion_msg(has_iedge(pedge), "ERROR: INTERIOR EDGE IS MISSING AN IEDGE!");
            return false;
          }
        }
      }
    }
    return true;
  }

  bool check_vertices() const {

    for (const auto vertex : m_intersection_graph.vertices()) {
      const auto nedges = m_intersection_graph.incident_edges(vertex);
      if (nedges.size() <= 2) {
        std::cout << "ERROR: CURRENT NUMBER OF EDGES = " << nedges.size() << std::endl;
        CGAL_assertion_msg(nedges.size() > 2,
        "ERROR: VERTEX MUST HAVE AT LEAST 3 NEIGHBORS!");
        return false;
      }
    }
    return true;
  }

  bool check_edges() const {

    std::vector<PFace> nfaces;
    for (const auto edge : m_intersection_graph.edges()) {
      incident_faces(edge, nfaces);
      if (nfaces.size() == 1) {
        std::cout << "ERROR: CURRENT NUMBER OF FACES = " << nfaces.size() << std::endl;
        CGAL_assertion_msg(nfaces.size() != 1,
        "ERROR: EDGE MUST HAVE 0 OR AT LEAST 2 NEIGHBORS!");
        return false;
      }
    }
    return true;
  }

  bool check_faces() const {

    for (std::size_t i = 0; i < number_of_support_planes(); ++i) {
      const auto pfaces = this->pfaces(i);
      for (const auto pface : pfaces) {
        const auto nvolumes = incident_volumes(pface);
        if (nvolumes.size() == 0 || nvolumes.size() > 2) {
          std::cout << "ERROR: CURRENT NUMBER OF VOLUMES = " << nvolumes.size() << std::endl;
          CGAL_assertion_msg(nvolumes.size() == 1 || nvolumes.size() == 2,
          "ERROR: FACE MUST HAVE 1 OR 2 NEIGHBORS!");
          return false;
        }
      }
    }
    return true;
  }

  bool check_intersection_graph() const {

    std::cout.precision(20);
    const FT ptol = KSR::point_tolerance<FT>();
    const auto iedges = m_intersection_graph.edges();
    for (const auto iedge : iedges) {
      const auto isource = source(iedge);
      const auto itarget = target(iedge);
      const auto source_p = point_3(isource);
      const auto target_p = point_3(itarget);
      const FT distance = KSR::distance(source_p, target_p);
      if (distance < ptol) {
        std::cout << "ERROR: FOUND ZERO-LENGTH IEDGE: "
        << str(iedge) << ", " << distance << ", " << segment_3(iedge) << std::endl;
        CGAL_assertion_msg(distance >= ptol,
        "ERROR: INTERSECTION GRAPH HAS ZERO-LENGTH IEDGES!");
        return false;
      }
    }
    return true;
  }

  bool is_mesh_valid(
    const bool check_simplicity,
    const bool check_convexity,
    const std::size_t support_plane_idx) const {

    const bool is_valid = mesh(support_plane_idx).is_valid();
    if (!is_valid) {
      return false;
    }

    // Note: bbox faces may have multiple equal points after converting from exact to inexact!
    if (support_plane_idx < 6) {
      return true;
    }

    const auto pfaces = this->pfaces(support_plane_idx);
    for (const auto pface : pfaces) {
      std::function<Point_2(PVertex)> unary_f =
      [&](const PVertex& pvertex) -> Point_2 {
        return point_2(pvertex);
      };

      const auto pvertices = pvertices_of_pface(pface);
      const Polygon_2 polygon(
        boost::make_transform_iterator(pvertices.begin(), unary_f),
        boost::make_transform_iterator(pvertices.end(), unary_f));

      // Use only with an exact kernel!
      if (check_simplicity && !polygon.is_simple()) {
        dump_polygon(*this, support_plane_idx, polygon, "non-simple-polygon");
        const std::string msg = "ERROR: PFACE " + str(pface) + " IS NOT SIMPLE!";
        CGAL_assertion_msg(false, msg.c_str());
        return false;
      }

      // Use only with an exact kernel!
      if (check_convexity && !polygon.is_convex()) {
        dump_polygon(*this, support_plane_idx, polygon, "non-convex-polygon");
        const std::string msg = "ERROR: PFACE " + str(pface) + " IS NOT CONVEX!";
        CGAL_assertion_msg(false, msg.c_str());
        return false;
      }

      auto prev = null_pvertex();
      for (const auto pvertex : pvertices) {
        if (prev == null_pvertex()) {
          prev = pvertex;
          continue;
        }

        if (point_2(prev) == point_2(pvertex) &&
          direction(prev) == direction(pvertex)) {

          const std::string msg = "ERROR: PFACE " + str(pface) +
          " HAS TWO CONSEQUENT IDENTICAL VERTICES "
          + str(prev) + " AND " + str(pvertex) + "!";
          CGAL_assertion_msg(false, msg.c_str());
          return false;
        }
        prev = pvertex;
      }
    }
    return true;
  }

  bool check_integrity(
    const bool is_initialized   = true,
    const bool check_simplicity = true,
    const bool check_convexity  = true) const {

    for (std::size_t i = 0; i < number_of_support_planes(); ++i) {
      if (!is_mesh_valid(check_simplicity, check_convexity, i)) {
        const std::string msg = "ERROR: MESH " + std::to_string(i) + " IS NOT VALID!";
        CGAL_assertion_msg(false, msg.c_str());
        return false;
      }

      continue;

      if (is_initialized) {
        const auto& iedges = this->iedges(i);
        CGAL_assertion(iedges.size() > 0);
        for (const auto& iedge : iedges) {
          const auto& iplanes = this->intersected_planes(iedge);
          if (iplanes.find(i) == iplanes.end()) {

            const std::string msg = "ERROR: SUPPORT PLANE " + std::to_string(i) +
            " IS INTERSECTED BY " + str(iedge) +
            " BUT IT CLAIMS IT DOES NOT INTERSECT IT!";
            CGAL_assertion_msg(false, msg.c_str());
            return false;
          }
        }
      } else {
        const auto& iedges = support_plane(i).unique_iedges();
        CGAL_assertion(iedges.size() > 0);
        for (const auto& iedge : iedges) {
          const auto& iplanes = this->intersected_planes(iedge);
          if (iplanes.find(i) == iplanes.end()) {

            const std::string msg = "ERROR: SUPPORT PLANE " + std::to_string(i) +
            " IS INTERSECTED BY " + str(iedge) +
            " BUT IT CLAIMS IT DOES NOT INTERSECT IT!";
            CGAL_assertion_msg(false, msg.c_str());
            return false;
          }
        }
      }
    }

    for (const auto iedge : this->iedges()) {
      const auto& iplanes = this->intersected_planes(iedge);
      for (const auto support_plane_idx : iplanes) {

        if (is_initialized) {
          const auto& sp_iedges = this->iedges(support_plane_idx);
          CGAL_assertion(sp_iedges.size() > 0);
          if (std::find(sp_iedges.begin(), sp_iedges.end(), iedge) == sp_iedges.end()) {

            const std::string msg = "ERROR: IEDGE " + str(iedge) +
            " INTERSECTS SUPPORT PLANE " + std::to_string(support_plane_idx) +
            " BUT IT CLAIMS IT IS NOT INTERSECTED BY IT!";
            CGAL_assertion_msg(false, msg.c_str());
            return false;
          }
        } else {
          const auto& sp_iedges = support_plane(support_plane_idx).unique_iedges();
          CGAL_assertion(sp_iedges.size() > 0);
          if (sp_iedges.find(iedge) == sp_iedges.end()) {

            const std::string msg = "ERROR: IEDGE " + str(iedge) +
            " INTERSECTS SUPPORT PLANE " + std::to_string(support_plane_idx) +
            " BUT IT CLAIMS IT IS NOT INTERSECTED BY IT!";
            CGAL_assertion_msg(false, msg.c_str());
            return false;
          }
        }
      }
    }
    return true;
  }

  bool check_volume(
    const int volume_index,
    const std::size_t volume_size,
    const std::map<PFace, std::pair<int, int> >& map_volumes) const {

    std::vector<PFace> pfaces;
    for (const auto& item : map_volumes) {
      const auto& pface = item.first;
      const auto& pair  = item.second;
      if (pair.first == volume_index || pair.second == volume_index) {
        pfaces.push_back(pface);
      }
    }

    const bool is_broken_volume = is_volume_degenerate(pfaces);
    if (is_broken_volume) {
      dump_volume(*this, pfaces, "volumes/degenerate");
    }
    CGAL_assertion(!is_broken_volume);
    if (is_broken_volume) return false;
    CGAL_assertion(pfaces.size() == volume_size);
    if (pfaces.size() != volume_size) return false;
    return true;
  }

  bool is_volume_degenerate(
    const std::vector<PFace>& pfaces) const {

    for (const auto& pface : pfaces) {
      const auto pedges = pedges_of_pface(pface);
      const std::size_t n = pedges.size();

      std::size_t count = 0;
      for (const auto pedge : pedges) {
        CGAL_assertion(has_iedge(pedge));
        const auto iedge = this->iedge(pedge);
        const std::size_t num_found = find_adjacent_pfaces(pface, iedge, pfaces);
        if (num_found == 1) ++count;
      }
      if (count != n) {
        std::cout << "- current number of neighbors " << count << " != " << n << std::endl;
        dump_info(*this, pface, *pedges.begin(), pfaces);
        return true;
      }
    }
    return false;
  }

  std::size_t find_adjacent_pfaces(
    const PFace& current,
    const IEdge& query,
    const std::vector<PFace>& pfaces) const {

    std::size_t num_found = 0;
    for (const auto& pface : pfaces) {
      if (pface == current) continue;
      const auto pedges = pedges_of_pface(pface);
      for (const auto pedge : pedges) {
        CGAL_assertion(has_iedge(pedge));
        const auto iedge = this->iedge(pedge);
        if (iedge == query) ++num_found;
      }
    }
    return num_found;
  }

};

} // namespace KSR_3
} // namespace CGAL

#endif // CGAL_KSR_3_DATA_STRUCTURE_H