// Copyright (c) 2006,2007,2008,2009,2010,2011,2012,2013 Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
//
// $URL: https://github.com/CGAL/cgal/blob/v6.1/Arrangement_on_surface_2/include/CGAL/Arr_topology_traits/Arr_planar_topology_traits_base_2.h $
// $Id: include/CGAL/Arr_topology_traits/Arr_planar_topology_traits_base_2.h b26b07a1242 $
// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
//
//
// Author(s)     : Ron Wein <wein@post.tau.ac.il>
//                 Efi Fogel <efif@post.tau.ac.il>

#ifndef CGAL_ARR_PLANAR_TOPOLOGY_TRAITS_BASE_2_H
#define CGAL_ARR_PLANAR_TOPOLOGY_TRAITS_BASE_2_H

#include <CGAL/license/Arrangement_on_surface_2.h>

/*! \file
 *
 * Definition of the Arr_planar_topology_traits_base_2<GeomTraits> class.
 */

#include <CGAL/Arr_enums.h>
#include <CGAL/Arr_default_dcel.h>
#include <CGAL/Arr_walk_along_line_point_location.h>
#include <CGAL/Arrangement_2/Arr_traits_adaptor_2.h>
#include <CGAL/Surface_sweep_2/Arr_basic_insertion_traits_2.h>
#include <CGAL/Surface_sweep_2/Arr_insertion_traits_2.h>
#include <CGAL/Surface_sweep_2/Arr_overlay_traits_2.h>
#include <CGAL/Arr_point_location/Arr_batched_point_location_traits_2.h>

namespace CGAL {

/*! \class Arr_planar_topology_traits_base_2
 *
 * A base topology-traits class that encapsulates the embedding of 2D
 * arrangements of bounded or unbounded curves on the plane.
 */
template <typename GeomTraits_,
          typename Dcel_ = Arr_default_dcel<GeomTraits_> >
class Arr_planar_topology_traits_base_2
{
public:
  ///! \name The geometry-traits types.
  //@{
  typedef GeomTraits_                                     Geometry_traits_2;
  typedef typename Geometry_traits_2::Point_2             Point_2;
  typedef typename Geometry_traits_2::X_monotone_curve_2  X_monotone_curve_2;
  //@}

  ///! \name The DCEL types.
  //@{
  typedef Dcel_                                           Dcel;
  typedef typename Dcel::Size                             Size;
  typedef typename Dcel::Vertex                           Vertex;
  typedef typename Dcel::Halfedge                         Halfedge;
  typedef typename Dcel::Face                             Face;
  typedef typename Dcel::Outer_ccb                        Outer_ccb;
  typedef typename Dcel::Inner_ccb                        Inner_ccb;
  typedef typename Dcel::Isolated_vertex                  Isolated_vertex;
  //@}

  typedef Arr_planar_topology_traits_base_2<Geometry_traits_2, Dcel>
                                                          Self;

protected:
  typedef Arr_traits_basic_adaptor_2<Geometry_traits_2>   Traits_adaptor_2;

  // Data members:
  Dcel m_dcel;                           // The DCEL.

  const Traits_adaptor_2* m_geom_traits; // The geometry-traits adaptor.
  bool m_own_geom_traits;                // Indicate whether we should
                                         // eventually free the traits object.

  // Copy constructor and assignment operator - not supported.
  Arr_planar_topology_traits_base_2(const Self&);
  Self& operator=(const Self&);

public:
  ///! \name Construction methods.
  //@{

  /*! constructs defaults. */
  Arr_planar_topology_traits_base_2() :
    m_own_geom_traits(true)
  { m_geom_traits = new Traits_adaptor_2; }

  /*! constructs with a geometry-traits class. */
  Arr_planar_topology_traits_base_2 (const Geometry_traits_2* geom_traits) :
    m_own_geom_traits(false)
  { m_geom_traits = static_cast<const Traits_adaptor_2*>(geom_traits); }

  /*! assigns the contents of another topology-traits class. */
  void assign(const Self& other);

  /*! destructs. */
  virtual ~Arr_planar_topology_traits_base_2()
  {
    // Clear the DCEL.
    m_dcel.delete_all();

    if (m_own_geom_traits && (m_geom_traits != nullptr)) {
      delete m_geom_traits;
      m_geom_traits = nullptr;
    }
  }

  //@}

  ///! \name Common topology-traits methods.
  //@{

  /*! obtains the DCEL (const version). */
  const Dcel& dcel() const { return m_dcel; }

  /*! obtains the DCEL (non-const version). */
  Dcel& dcel() { return (m_dcel); }

  /*! receives a notification on the creation of a new boundary vertex that
   * corresponds to a given point.
   * \param v The new boundary vertex.
   * \param p The point.
   * \param ps_x The boundary condition of the curve end in x.
   * \param ps_y The boundary condition of the curve end in y.
   */
  void notify_on_boundary_vertex_creation(Vertex*,
                                          const Point_2& ,
                                          Arr_parameter_space /* ps_x */,
                                          Arr_parameter_space /* ps_y */)
  {
    // In the planar-topology traits this function should never be invoked:
    return;
  }

  /*! receives a notification on the creation of a new boundary vertex that
   * corresponds to the given curve end.
   * \param v The new boundary vertex.
   * \param cv The x-monotone curve.
   * \param ind The curve end.
   * \param ps_x The boundary condition of the curve end in x.
   * \param ps_y The boundary condition of the curve end in y.
   */
  void notify_on_boundary_vertex_creation(Vertex*,
                                          const X_monotone_curve_2& ,
                                          Arr_curve_end,
                                          Arr_parameter_space /* ps_x */,
                                          Arr_parameter_space /* ps_y */)
  {
    // In the planar-topology traits this function should never be invoked:
    return;
  }

  /*! determines whether the function should decide on swapping the predecssor
   * halfedges that imply two ccb (and whose signs are given here).
   * If true, swap_predecessors will be correctly set. If false,
   * generic way of searching for lexicographically minimal point and checking
   * its incident halfedges will do the job to decide on swapping
   * \param signs1 signs of first implied ccb in x- and y-direction
   * \param signs2 signs of second implied ccb in x- and y-direction
   * \param swap_predecessors Output swap predeccesors or not;
   *        set correctly only if true is returned
   */
  bool
  let_me_decide_the_outer_ccb(std::pair<CGAL::Sign, CGAL::Sign> /* signs1 */,
                              std::pair<CGAL::Sign, CGAL::Sign> /* signs2 */,
                              bool& swap_predecessors) const
  {
    swap_predecessors = false;
    return false;
  }

  /*! given signs of two ccbs that show up when splitting upon insertion of
   * curve into two, determines what happens to the face(s).
   * \param signs1 signs in x and y of the first implied ccb
   * \param signs2 signs in x and y of the secondd implied ccb
   * \return A pair indicating whether the insertion will cause the face
   *         to split (the first flag), and if so - whether the split face
   *         will form a hole in the original face.
   */
  std::pair<bool, bool>
  face_split_after_edge_insertion(std::pair<CGAL::Sign,
                                            CGAL::Sign > /* signs1 */,
                                  std::pair<CGAL::Sign,
                                            CGAL::Sign > /* signs2 */) const
  {
    // In case of a planar topology, connecting two vertices on the same
    // inner CCB closes a new face that becomes a hole in the original face:
    return std::make_pair(true, true);
  }

  /*! determines whether the given point lies in the interior of the given face.
   * \param f The face.
   * \param p The query point.
   * \param v The vertex associated with p (if exists).
   * \param f must not be fictitious, and v must not lie at infinity.
   * \return Whether p is contained in f's interior.
   */
  bool is_in_face(const Face* f, const Point_2& p, const Vertex* v) const;

  //@}

  /// \name Additional accessors, specialized for this topology-traits class.
  //@{

  /*! This function is used by the "walk" point-location strategy. */
  virtual const Face* initial_face () const = 0;
  //@}

  /// \name Additional predicates, specialized for this topology-traits class.
  //@{

  /*! compares the given vertex (which may lie at infinity) and the given point.
   * \param p The point.
   * \param v The vertex.
   * \return The result of the comparison of the x-coordinates of p and v.
   */
  virtual Comparison_result compare_x(const Point_2& p,
                                      const Vertex* v) const = 0;

  /*! compares the given vertex (which may lie at infinity) and the given point.
   * \param p The point.
   * \param v The vertex.
   * \return The result of the xy-lexicographic comparison of p and v.
   */
  virtual Comparison_result compare_xy(const Point_2& p,
                                       const Vertex* v) const = 0;

  /*! compares the relative y-position of the given point and the given edge
   * (which may be fictitious).
   * \param p The point.
   * \param he The edge (one of the pair of halfedges).
   * \pre p should lie in the x-range of the given edge.
   * \return The relative y-position of the point p and the edge.
   */
  virtual Comparison_result compare_y_at_x(const Point_2& p,
                                           const Halfedge* he) const = 0;
  //@}
};

//-----------------------------------------------------------------------------
// Member-function definitions:
//-----------------------------------------------------------------------------

//-----------------------------------------------------------------------------
// Assign the contents of another topology-traits class.
//
template <typename GeomTraits, typename Dcel_>
void
Arr_planar_topology_traits_base_2<GeomTraits, Dcel_>::assign(const Self& other)
{
  // Clear the current DCEL and duplicate the other DCEL.
  m_dcel.delete_all();
  m_dcel.assign(other.m_dcel);

  // Take care of the traits object.
  if (m_own_geom_traits && (m_geom_traits != nullptr)) {
    delete m_geom_traits;
    m_geom_traits = nullptr;
  }

  if (other.m_own_geom_traits) m_geom_traits = new Traits_adaptor_2;
  else m_geom_traits = other.m_geom_traits;

  m_own_geom_traits = other.m_own_geom_traits;
}

//-----------------------------------------------------------------------------
// Determine whether the given vertex lies in the interior of the given face.
//
template <typename GeomTraits, typename Dcel_>
bool Arr_planar_topology_traits_base_2<GeomTraits, Dcel_>::
is_in_face(const Face* f, const Point_2& p, const Vertex* v) const
{
  CGAL_precondition((v == nullptr) || ! v->has_null_point());
  CGAL_precondition((v == nullptr) ||
                    m_geom_traits->equal_2_object()(p, v->point()));

  // In case the face is unbounded and has no outer ccbs, this is the single
  // unbounded face of an arrangement of bounded curves. This face obviously
  // contains any point in its interior.
  if (f->is_unbounded() && (f->number_of_outer_ccbs() == 0)) return true;

  // Keep a counter of the number of x-monotone curves that intersect an upward
  // vertical emanating from p (except for some degenerate cases that are
  // explained below).
  unsigned int       n_ray_intersections = 0;

  // Get a halfedge along the outer CCB of the given face, go over all curves
  // of the boundary component, and count those which are above p.
  // We begin by comparing p to the source vertex of the first halfedge.
  // Note that if p coincides with this vertex, p is obviously not in the
  // interior of the component.
  const Halfedge* first = *(f->outer_ccbs_begin());


  // Some left ends of curves may not yet have the curve assigned,
  // In case they are at TOP/BOTTOM they are not comparable to p
  // We advance first until we find a comparable vertex to start with.
  // We always find such a vertex since on the ccb there is at least one
  // interior vertex or a vertex at LEFT/RIGHT which are comparable.
  while( first->vertex()->parameter_space_in_x()==ARR_INTERIOR
      && first->has_null_curve()
      && first->next()->has_null_curve()){
    first = first->next();
  }


  const Halfedge* curr = first;
  Comparison_result res_source;
  Comparison_result res_target;
  Comparison_result res_y_at_x;

  if (curr->opposite()->vertex() == v) return false;

  res_source = compare_xy(p, curr->opposite()->vertex());

  do {
    // Compare p to the target vertex of the current halfedge.
    // If the vertex v associated with p (if v is given and is not nullptr)
    // on the boundary of the component, p is obviously not in the interior
    // the component.
    if (curr->vertex() == v) return false;

    // We jump over vertices at TOP/BOTTOM that do not yet have a curve
    if ((curr->vertex()->parameter_space_in_x() == ARR_INTERIOR) &&
        curr->has_null_curve() && curr->next()->has_null_curve())
    {
      curr = curr->next();
      continue;
    }

    res_target = compare_xy(p, curr->vertex());

    // In case the current halfedge belongs to an "antenna", namely its
    // incident face is the same as its twin's, we can simply skip it
    // (in order not to count it twice).
    if (! curr->opposite()->is_on_inner_ccb() &&
        curr->outer_ccb()->face() == curr->opposite()->outer_ccb()->face())
    {
      curr = curr->next();
      res_source = res_target;
      continue;
    }

    // Check that if we shoot a "tilted" vertical ray from p upward
    // (by "tilted" we mean the angle it forms with the x-axis is
    //  PI/2 + epsilon, where epsilon is arbitrarily small), then we hit
    // the x-monotone curve associated with curr once.
    if (res_source != res_target) {
      res_y_at_x = compare_y_at_x(p, curr);

      if (res_y_at_x == SMALLER) {
        ++n_ray_intersections;
      }
      else if (res_y_at_x == EQUAL) {
        // In this case p lies on the current edge, so it is obviously not
        // contained in the interior of the component.
        return false;
      }
    }

    // Proceed to the next halfedge along the component boundary.
    // Note that the source vertex of this halfedge is the current target.
    curr = curr->next();
    res_source = res_target;

  } while (curr != first);

  // The query point lies inside the connected components if and only if the
  // ray we shoot from it intersects the boundary an odd number of time.
  return ((n_ray_intersections % 2) != 0);
}

} // namespace CGAL

#endif

