libcgal-dev 4.7-4 / usr / include / CGAL / Arrangement_zone_2.h

// Copyright (c) 2006,2007,2009,2010,2011 Tel-Aviv University (Israel).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
// 
//
// Author(s)     : Ron Wein          <wein@post.tau.ac.il>
//                 Efi Fogel         <efif@post.tau.ac.il>
//                 (based on old version by Eyal Flato)

#ifndef CGAL_ARRANGEMENT_ZONE_2_H
#define CGAL_ARRANGEMENT_ZONE_2_H

/*! \file
 * Defintion of the Arrangement_zone_2 class.
 */

#include <boost/mpl/assert.hpp>
#include <CGAL/Arr_tags.h>
#include <CGAL/Arr_accessor.h>
#include <CGAL/Arrangement_2/Arr_traits_adaptor_2.h>

#include <list>
#include <map>
#include <set>

namespace CGAL {

/*! \class
 * A class for computing the zone of a given $x$-monotone curve in a given
 * arrangement.
 * The arrangement parameter corresponds to the underlying arrangement, and
 * the zone-visitor parameter corresponds to a visitor class which is capable
 * of receiving notifications on the arrangment features the query curve
 * traverses. The visitor has to support the following functions:
 * - init(), for initializing the visitor with a given arrangement.
 * - found_subcurve(), called when a non-intersecting x-monotone curve is
 *                     computed and located in the arrangement.
 * - found_overlap(), called when an x-monotone curve overlaps an existing
 *                    halfedge in the arrangement.
 * Both the second and the third functions return pair<Halfedge_handle, bool>,
 * where the halfedge handle corresponds to the halfedge created or modified
 * by the visitor (if valid), and the Boolean value indicates whether we
 * should halt the zone-computation process.
 */
template <class Arrangement_, class ZoneVisitor_>
class Arrangement_zone_2
{
public:

  typedef Arrangement_                                   Arrangement_2;
  typedef typename Arrangement_2::Geometry_traits_2      Geometry_traits_2;
  typedef typename Arrangement_2::Topology_traits        Topology_traits;

protected:
  
  typedef Arr_traits_adaptor_2<Geometry_traits_2>        Traits_adaptor_2;

  typedef typename Traits_adaptor_2::Left_side_category   Left_side_category;
  typedef typename Traits_adaptor_2::Bottom_side_category Bottom_side_category;
  typedef typename Traits_adaptor_2::Top_side_category    Top_side_category;
  typedef typename Traits_adaptor_2::Right_side_category  Right_side_category;

  BOOST_MPL_ASSERT(
      (typename 
       Arr_sane_identified_tagging< Left_side_category, Bottom_side_category, 
       Top_side_category, Right_side_category >::result)
  );

public:
  
  typedef ZoneVisitor_                                   Visitor;

  typedef typename Arrangement_2::Vertex_handle          Vertex_handle;
  typedef typename Arrangement_2::Halfedge_handle        Halfedge_handle;
  typedef typename Arrangement_2::Face_handle            Face_handle;

  typedef std::pair<Halfedge_handle, bool>               Visitor_result;

  typedef typename Geometry_traits_2::Point_2            Point_2;
  typedef typename Geometry_traits_2::X_monotone_curve_2 X_monotone_curve_2;
  typedef typename Geometry_traits_2::Multiplicity       Multiplicity;

protected:

  typedef typename Arr_are_all_sides_oblivious_tag< 
                     Left_side_category, Bottom_side_category, 
                     Top_side_category, Right_side_category >::result
    Are_all_sides_oblivious_category;
  
  typedef typename Arrangement_2::Vertex_const_handle    Vertex_const_handle;
  typedef typename Arrangement_2::Halfedge_const_handle  Halfedge_const_handle;
  typedef typename Arrangement_2::Face_const_handle      Face_const_handle;

  // Types used for caching intersection points:
  typedef std::pair<Point_2,Multiplicity>        Intersect_point_2;
  typedef std::list<CGAL::Object>                 Intersect_list;
  typedef std::map<const X_monotone_curve_2*,
                   Intersect_list>                Intersect_map;
  typedef typename Intersect_map::iterator        Intersect_map_iterator;

  typedef std::set<const X_monotone_curve_2*>     Curves_set;
  typedef typename Curves_set::iterator           Curves_set_iterator;

  // Data members:
  Arrangement_2&          arr;          // The associated arrangement.
  const Traits_adaptor_2 * m_geom_traits; // Its associated geometry traits.
  Arr_accessor<Arrangement_2> arr_access; // An accessor for the arrangement.
           
  Visitor                *visitor;      // The zone visitor.

  Intersect_map           inter_map;    // Stores all computed intersections.

  const Vertex_handle     invalid_v;    // An invalid vertex handle.
  const Halfedge_handle   invalid_he;   // An invalid halfedge handle.

  X_monotone_curve_2  cv;               // The current portion of the
                                        // inserted curve.
  CGAL::Object        obj;              // The location of the left endpoint.
  bool                has_left_pt;      // Is the left end of the curve
                                        // bounded.
  bool                left_on_boundary; // Is the left point on the boundary.
  Point_2             left_pt;          // Its current left endpoint.
  bool                has_right_pt;     // Is the right end of the curve
                                        // bounded.
  bool                right_on_boundary;// Is the right point on the boundary.
  Point_2             right_pt;         // Its right endpoint (if bounded).

  Vertex_handle       left_v;           // The arrangement vertex associated
                                        // with the current left_pt (if any).
  Halfedge_handle     left_he;          // If left_v is valid, left_he is the
                                        // predecessor for cv around this
                                        // vertex. Otherwise, if it is valid,
                                        // it is the halfedge that contains
                                        // the left endpoint it its interior.

  Vertex_handle       right_v;          // The arrangement vertex associated
                                        // with the current right_pt (if any).
  Halfedge_handle     right_he;         // If right_v is valid, left_he is the
                                        // predecessor for cv around this
                                        // vertex. Otherwise, if it is valid,
                                        // it is the halfedge that contains
                                        // the right endpoint it its interior.

  Point_2             intersect_p;      // The next intersection point.
  unsigned int        ip_mult;          // Its multiplicity
                                        // (0 in case of an overlap).
  bool                found_intersect;  // Have we found an intersection
                                        // (or an overlap).
  X_monotone_curve_2  overlap_cv;       // The currently discovered overlap.
  bool                found_overlap;    // Have we found an overlap.
  bool                found_iso_vert;   // Check if an isolated vertex induces
                                        // the next intersection.
  Vertex_handle       intersect_v;      // The vertex that intersects cv.
  Halfedge_handle     intersect_he;     // The halfedge that intersects cv
                                        // (or overlaps it).

  X_monotone_curve_2  sub_cv1;          // Auxiliary variable (for curve split).
  X_monotone_curve_2  sub_cv2;          // Auxiliary variable (for curve split).

public:

  /*!
   * Constructor.
   * \param _arr The arrangement for which we compute the zone.
   * \param _visitor A pointer to a zone-visitor object.
   */
  Arrangement_zone_2 (Arrangement_2& _arr, Visitor *_visitor) :
    arr (_arr),
    arr_access (_arr),
    visitor (_visitor),
    invalid_v (),
    invalid_he ()
  {
    m_geom_traits = static_cast<const Traits_adaptor_2*> (arr.geometry_traits());

    CGAL_assertion (visitor != NULL);

    // Initialize the visitor.
    visitor->init (&arr);
  }

  /*!
   * Initialize the zone-computation process with a given curve.
   * \param _cv The query curve.
   * \param pl A point-location object associated with the arrangement.
   */
  template <class PointLocation>
  void init (const X_monotone_curve_2& _cv, const PointLocation& pl)
  {
    // Set the curve and check whether its left end has boundary conditions.
    cv = _cv;

    const Arr_parameter_space  bx1 =
      m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MIN_END);
    const Arr_parameter_space  by1 =
      m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MIN_END);

    if (bx1 == ARR_INTERIOR && by1 == ARR_INTERIOR) {
      // The curve has a finite left endpoint with no boundary conditions:
      // locate it in the arrangement.
      has_left_pt = true;
      left_on_boundary = (bx1 != ARR_INTERIOR || by1 != ARR_INTERIOR);
      left_pt = m_geom_traits->construct_min_vertex_2_object() (cv);

      obj = pl.locate (left_pt);
    }
    else {
      // The left end of the curve has boundary conditions: use the topology
      // traits use the arrangement accessor to locate it.
      // Note that if the curve-end is unbounded, left_pt does not exist.
      // Note that if the curve-end is unbounded, left_pt does not exist.
      has_left_pt = m_geom_traits->is_closed_2_object()(cv, ARR_MIN_END);
      left_on_boundary = true;
      if (has_left_pt)
        left_pt = m_geom_traits->construct_min_vertex_2_object() (cv);
      obj = arr_access.locate_curve_end (cv, ARR_MIN_END, bx1, by1);
    }

    // Check the boundary conditions of th right curve end.
    if (m_geom_traits->is_closed_2_object()(cv, ARR_MAX_END)) {
      const Arr_parameter_space  bx2 =
        m_geom_traits->parameter_space_in_x_2_object()(cv, ARR_MAX_END);
      const Arr_parameter_space  by2 =
        m_geom_traits->parameter_space_in_y_2_object()(cv, ARR_MAX_END);

      // The right endpoint is valid.
      has_right_pt = true;
      right_pt = m_geom_traits->construct_max_vertex_2_object() (cv);
      right_on_boundary = (bx2 != ARR_INTERIOR) || (by2 != ARR_INTERIOR);
    }
    else {
      // The right end of the curve lies at infinity.
      has_right_pt = false;
      right_on_boundary = true;
    }

    return;
  }

  /*!
   * Initialize the zone-computation process with a given curve and an object
   * that wraps the location of the curve's left end.
   * \param _cv The query curve.
   * \param _obj An object that represents the location of the left end
   *             of the curve.
   */
  void init_with_hint (const X_monotone_curve_2& _cv, const Object& _obj);

  /*!
   * Compute the zone of the given curve and issue the apporpriate
   * notifications for the visitor.
   */
  void compute_zone ();

private:

  /*!
   * Find a face containing the query curve cv around the given vertex.
   * In case an overlap occurs, sets intersect_he to be the overlapping edge.
   * \param v The query vertex.
   * \param he Output: The predecessor of cv around the vertex.
   * \return (true) if cv overlaps with the curve associated with he;
   *         (false) if there is no overlap.
   */
  bool _find_prev_around_vertex (Vertex_handle v, Halfedge_handle& he);

  /*!
   * Direct the halfedge for the location of the given subcurve around a split
   * point that occurs in the interior of a given edge, when the subcurve lies
   * to the right of the split point.
   * In case of overlaps, it sets also found_overlap and intersect_he.
   * \param cv_ins The curve to be inserted, whose left endpoint coincides
   *               with the edge to be split.
   * \param cv_left_pt The left endpoint of cv_ins.
   * \param query_he The edge that intersects cv_ins.
   * \pre The left endpoint of cv_ins lies in the interior of the curve
   *      associated with query_he.
   * \return The halfedge whose incident face contains cv_ins
   *         (either query_he or its twin).
   */
  Halfedge_handle
  _direct_intersecting_edge_to_right(const X_monotone_curve_2& cv_ins,
                                     const Point_2& cv_left_pt,
                                     Halfedge_handle query_he);

  /*!
   * Direct the halfedge for the location of the given subcurve around a split
   * point that occurs in the interior of a given edge, when the subcurve lies
   * to the left of the split point.
   * \param cv_ins The curve to be inserted, whose right endpoint coincides
   *               with the edge to be split.
   * \param query_he The edge that intersects cv_ins.
   * \pre The right endpoint of cv_ins lies in the interior of the curve
   *      associated with query_he.
   * \return The halfedge whose incident face contains cv_ins
   *         (either query_he or its twin).
   */
  Halfedge_handle
  _direct_intersecting_edge_to_left(const X_monotone_curve_2& cv_ins,
                                    Halfedge_handle query_he);

  /*!
   * Get the next intersection of cv with the given halfedge.
   * \param he A handle to the halfedge.
   * \param skip_first_point Should we skip the first intersection point.
   * \param intersect_on_right_boundary Output: If an intersetion point is
   *                                            computed, marks whether this
   *                                            point coincides with the right
   *                                            curve-end, which lies on the
   *                                            surface boundary.
   * \return An object representing the next intersection: Intersect_point_2
   *         in case of a simple intersection point, X_monotone_curve_2 in
   *         case of an overlap, and an empty object if there is no
   *         intersection.
   */
  CGAL::Object _compute_next_intersection (Halfedge_handle he,
                                           bool skip_first_point,
                                           bool& intersect_on_right_boundary);

  /*!
   * Remove the next intersection of cv with the given halfedge from the map.
   * \param he A handle to the halfedge.
   * \pre The list of intersections with the curve of he has already been
   *      computed, and it is not empty.
   */
  void _remove_next_intersection (Halfedge_handle he);

  /*!
   * Check if the given point lies completely to the left of the given egde.
   * \param p The point.
   * \param he The halfedge.
   * \pre he is not a fictitious edge.
   * \return Whether p lies entirely to the left of the edge.
   */
  bool _is_to_left(const Point_2& p, Halfedge_handle he) const
  {
    return (_is_to_left_impl(p, he, Are_all_sides_oblivious_category()));
  }

  bool _is_to_left_impl(const Point_2& p, Halfedge_handle he,
                        Arr_all_sides_oblivious_tag) const
  {
    return ((he->direction() == ARR_LEFT_TO_RIGHT &&
             m_geom_traits->compare_xy_2_object() 
             (p, he->source()->point()) == SMALLER) ||
            (he->direction() == ARR_RIGHT_TO_LEFT &&
             m_geom_traits->compare_xy_2_object() 
             (p, he->target()->point()) == SMALLER));
  }

  bool _is_to_left_impl(const Point_2& p, Halfedge_handle he,
                        Arr_not_all_sides_oblivious_tag) const;
  
  /*!
   * Check if the given point lies completely to the right of the given egde.
   * \param p The point.
   * \param he The halfedge.
   * \pre he is not a fictitious edge.
   * \return Whether p lies entirely to the right of the edge.
   */
  bool _is_to_right(const Point_2& p, Halfedge_handle he) const
  {
    return (_is_to_right_impl(p, he, Are_all_sides_oblivious_category()));
  }

  bool _is_to_right_impl(const Point_2& p, Halfedge_handle he,
                         Arr_all_sides_oblivious_tag) const
  {
    return ((he->direction() == ARR_LEFT_TO_RIGHT &&
             m_geom_traits->compare_xy_2_object() 
             (p, he->target()->point()) == LARGER) ||
            (he->direction() == ARR_RIGHT_TO_LEFT &&
             m_geom_traits->compare_xy_2_object() 
             (p, he->source()->point()) == LARGER));
  }

  bool _is_to_right_impl(const Point_2& p, Halfedge_handle he,
                         Arr_not_all_sides_oblivious_tag) const;

  /*!
   * Compute the (lexicographically) leftmost intersection of the query
   * curve with the boundary of a given face in the arrangement.
   * The function computes sets intersect_p, intersect_he (or alternatively
   * overlap_cv and intersect_he) and set the flags found_intersect and
   * found_overlap accordingly.
   * \param face A handle to the face.
   * \param on_boundary Specifies whether the left endpoint of the curve lies
   *                    on the face boundary.
   */
  void _leftmost_intersection_with_face_boundary (Face_handle face,
                                                  bool on_boundary);

  /*!
   * Compute the zone of an x-monotone curve in a given arrangement face.
   * The left endpoint of the curve either lies in the face interior or on
   * the boundary of the face.
   * This function updates cv and its left endpoint and also sets left_v
   * and left_he for the remaining portion of the curve.
   * In case of overlaps, it sets also overlap_cv and intersect_he.
   * \param face The given face.
   * \param on_boundary Specifies whether the left endpoint of the curve lies
   *                    on the face boundary.
   * \pre If on_boundary is (true) then left_he must be valid; if it is (false)
   *      then both left_v anf left_he must be invalid.
   * \return (true) if we are done with the zone-computation process;
   *         (false) if we still have a remaining portion of cv to continue
   *         with.
   */
  bool _zone_in_face (Face_handle face,
		      bool on_boundary);

  /*!
   * Compute the zone of an overlapping subcurve overlap_cv of cv and the
   * curve currently associated with intersect_he.
   * This function updates cv and its left endpoint and also sets left_v
   * and left_he for the remaining portion of the curve.
   * \return (true) if we are done with the zone-computation process;
   *         (false) if we still have a remaining portion of cv to continue
   *         with.
   */
  bool _zone_in_overlap ();
};

} //namespace CGAL

// The function definitions can be found under:
#include <CGAL/Arrangement_2/Arrangement_zone_2_impl.h>

#endif