Interception sweep for do_intersect()

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_meta_traits.h

@@ -7,12 +7,11 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
 // Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
 //             Efi Fogel       <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GPS_AGG_META_TRAITS_H
-#define CGAL_BSO_2_GPS_AGG_META_TRAITS_H
+#ifndef CGAL_GPS_AGG_META_TRAITS_H
+#define CGAL_GPS_AGG_META_TRAITS_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op.h

@@ -9,9 +9,10 @@
 //
 // Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
 //             Ophir Setter     <ophir.setter@cs.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GPS_AGG_OP_H
-#define CGAL_BSO_2_GPS_AGG_OP_H
+#ifndef CGAL_GPS_AGG_OP_H
+#define CGAL_GPS_AGG_OP_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -19,8 +20,8 @@
  *
  * The class Gps_agg_op is responsible for aggregated Boolean set operations
  * depending on a visitor template parameter.  It uses the surface-sweep
- * algorithm from the arrangement packages to overlay all the polygon sets, and
- * then it uses a BFS that determines which of the faces is contained in the
+ * algorithm from the surface-sweep package to overlay all the polygon sets, and
+ * then it uses a BFS that determines which of the faces are contained in the
  * result using the visitor.
  */
 
@@ -37,7 +38,7 @@
 
 namespace CGAL {
 
-template <typename Arrangement_, typename BfsVisitor>
+template <typename Arrangement_, typename BfsVisitor, template <typename, typename> class SweepVisitor>
 class Gps_agg_op {
   using Arrangement_2 = Arrangement_;
   using Bfs_visitor = BfsVisitor;
@@ -74,7 +75,7 @@ class Gps_agg_op {
   using Subcurve = Arr_construction_subcurve<Mgt2, Event, Allocator>;
   using Helper_tmp = typename Tt::template Construction_helper<Event, Subcurve>;
   using Helper = typename Helper_tmp::template rebind<Mgt2, Arr, Event, Subcurve>::other;
-  using Visitor = Gps_agg_op_visitor<Helper, Arr>;
+  using Visitor = SweepVisitor<Helper, Arr>;
   using Surface_sweep_2 = Gps_agg_op_surface_sweep_2<Arr, Visitor>;
 
   using Edges_hash = Unique_hash_map<Halfedge_handle, std::size_t>;
@@ -90,7 +91,7 @@ protected:
   Faces_hash m_faces_hash;      // maps face to its IC (inside count)
 
 public:
-  /*! Constructor. */
+  /*! constructs. */
   Gps_agg_op(Arr& arr, std::vector<Vertex_handle>& vert_vec, const Gt2& tr) :
     m_arr(&arr),
     m_traits(new Mgt2(tr)),
@@ -98,38 +99,38 @@ public:
     m_surface_sweep(m_traits, &m_visitor)
   {}
 
-  void sweep_arrangements(std::size_t lower, std::size_t upper,
-                          std::size_t jump, std::vector<Arr_entry>& arr_vec) {
-    std::list<Meta_X_monotone_curve_2> curves_list;
-
+  std::size_t prepare(std::size_t lower, std::size_t upper, std::size_t jump,
+                      std::vector<Arr_entry>& arr_vec, std::list<Meta_X_monotone_curve_2>& curves_list) {
     std::size_t n_inf_pgn = 0;  // number of infinite polygons (arrangement
                                 // with a contained unbounded face
-    std::size_t n_pgn = 0;      // number of polygons (arrangements)
-
-    for (std::size_t i = lower; i <= upper; i += jump, ++n_pgn) {
+    for (auto i = lower; i <= upper; i += jump) {
       // The BFS scan (after the loop) starts in the reference face,
       // so we count the number of polygons that contain the reference face.
       Arr* arr = (arr_vec[i]).first;
       if (arr->reference_face()->contained()) ++n_inf_pgn;
 
-      Edge_iterator itr = arr->edges_begin();
-      for(; itr != arr->edges_end(); ++itr) {
+      for (auto itr = arr->edges_begin(); itr != arr->edges_end(); ++itr) {
         // take only relevant edges (which separate between contained and
         // non-contained faces.
-        Halfedge_iterator he = itr;
-        if (he->face()->contained() == he->twin()->face()->contained())
-          continue;
-        if ((Arr_halfedge_direction)he->direction() == ARR_RIGHT_TO_LEFT)
-          he = he->twin();
+        Halfedge_handle he = itr;
+        if (he->face()->contained() == he->twin()->face()->contained()) continue;
+        if ((Arr_halfedge_direction)he->direction() == ARR_RIGHT_TO_LEFT) he = he->twin();
 
         Curve_data cv_data(arr, he, 1, 0);
         curves_list.push_back(Meta_X_monotone_curve_2(he->curve(), cv_data));
       }
     }
+    return n_inf_pgn;
+  }
 
-    m_surface_sweep.sweep(curves_list.begin(), curves_list.end(),
-                          lower, upper, jump, arr_vec);
-
+  /*! sweeps the plane without interceptions.
+   */
+  void sweep_arrangements(std::size_t lower, std::size_t upper, std::size_t jump,
+                          std::vector<Arr_entry>& arr_vec) {
+    std::size_t n_pgn = upper - lower + 1;      // number of polygons (arrangements)
+    std::list<Meta_X_monotone_curve_2> curves_list;
+    auto n_inf_pgn = prepare(lower, upper, jump, arr_vec, curves_list);
+    m_surface_sweep.sweep(curves_list.begin(), curves_list.end(), lower, upper, jump, arr_vec);
     m_faces_hash[m_arr->reference_face()] = n_inf_pgn;
     Bfs_visitor visitor(&m_edges_hash, &m_faces_hash, n_pgn);
     visitor.visit_ubf(m_arr->faces_begin(), n_inf_pgn);
@@ -138,7 +139,26 @@ public:
     visitor.after_scan(*m_arr);
   }
 
-  /*! Destruct.
+  /*! sweeps the plane without interceptions, but stop when an intersection occurs.
+   */
+  bool sweep_intercept_arrangements(std::size_t lower, std::size_t upper, std::size_t jump,
+                                    std::vector<Arr_entry>& arr_vec) {
+    std::list<Meta_X_monotone_curve_2> curves_list;
+    auto n_inf_pgn = prepare(lower, upper, jump, arr_vec, curves_list);
+    auto res = m_surface_sweep.sweep_intercept(curves_list.begin(), curves_list.end(), lower, upper, jump, arr_vec);
+    if (res) return true;
+
+    m_faces_hash[m_arr->reference_face()] = n_inf_pgn;
+    std::size_t n_pgn = upper - lower + 1;      // number of polygons (arrangements)
+    Bfs_visitor visitor(&m_edges_hash, &m_faces_hash, n_pgn);
+    visitor.visit_ubf(m_arr->faces_begin(), n_inf_pgn);
+    Bfs_scanner scanner(visitor);
+    scanner.scan(*m_arr);
+    visitor.after_scan(*m_arr);
+    return false;
+  }
+
+  /*! destructs.
    */
   ~Gps_agg_op() { delete m_traits; }
 };

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op_surface_sweep_2.h

@@ -9,9 +9,10 @@
 //
 // Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
 //             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GSP_AGG_OP_SURFACE_SWEEP_2_H
-#define CGAL_BSO_2_GSP_AGG_OP_SURFACE_SWEEP_2_H
+#ifndef CGAL_GSP_AGG_OP_SURFACE_SWEEP_2_H
+#define CGAL_GSP_AGG_OP_SURFACE_SWEEP_2_H
 
 #include <vector>
 
@@ -70,9 +71,8 @@ public:
     Base(traits, visitor)
   {}
 
-  /*! Perform the sweep. */
   template <typename CurveInputIterator>
-  void sweep(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+  void pre_process(CurveInputIterator curves_begin, CurveInputIterator curves_end,
                    std::size_t lower, std::size_t upper, std::size_t jump,
                    std::vector<Arr_entry>& arr_vec) {
     CGAL_assertion(this->m_queue->empty() && this->m_statusLine.size() == 0);
@@ -80,7 +80,6 @@ public:
     using Vertices_map = Unique_hash_map<Vertex_handle, Event*>;
     using Compare_xy_2 = typename Gt2::Compare_xy_2;
 
-    this->m_visitor->before_sweep();
     // Allocate all of the Subcurve objects as one block.
     this->m_num_of_subCurves = std::distance(curves_begin, curves_end);
     if (this->m_num_of_subCurves > 0)
@@ -203,13 +202,29 @@ public:
       e_right->add_curve_to_left(this->m_subCurves + index);
       this->_add_curve_to_right(e_left, this->m_subCurves + index);
     }
+  }
 
-    // Perform the sweep:
+  /*! Perform the sweep. */
+  template <typename CurveInputIterator>
+  void sweep(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+             std::size_t lower, std::size_t upper, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    this->m_visitor->before_sweep();
+    pre_process(curves_begin, curves_end,lower, upper, jump, arr_vec);
     this->_sweep();
     this->_complete_sweep();
     this->m_visitor->after_sweep();
+  }
 
-    return;
+  /*! Perform the sweep. */
+  template <typename CurveInputIterator>
+  bool sweep_intercept(CurveInputIterator curves_begin, CurveInputIterator curves_end,
+                       std::size_t lower, std::size_t upper, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    this->m_visitor->before_sweep();
+    pre_process(curves_begin, curves_end,lower, upper, jump, arr_vec);
+    this->_sweep();
+    this->_complete_sweep();
+    this->m_visitor->after_sweep();
+    return this->m_visitor->found_intersection();
   }
 
 private:
@@ -230,7 +245,6 @@ private:
         else return (Event::LEFT_END);
       }
       ++circ;
-
     } while (circ != first);
 
     // If we reached here, we should not keep this vertex.

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h

@@ -7,12 +7,12 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
 // Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
 //             Ron Wein         <wein@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
-#ifndef CGAL_BSO_2_GSP_AGG_OP_VISITOR_H
-#define CGAL_BSO_2_GSP_AGG_OP_VISITOR_H
+#ifndef CGAL_GSP_AGG_OP_VISITOR_H
+#define CGAL_GSP_AGG_OP_VISITOR_H
 
 #include <CGAL/license/Boolean_set_operations_2.h>
 
@@ -43,7 +43,6 @@ public:
 private:
   using Gt2 = Geometry_traits_2;
   using Arr = Arrangement_2;
-
   using Self = Gps_agg_op_base_visitor<Helper, Arr, Visitor_>;
   using Visitor = typename Default::Get<Visitor_, Self>::type;
   using Base = Arr_construction_ss_visitor<Helper, Visitor>;
@@ -127,7 +126,8 @@ template <typename Helper_, typename Arrangement_, typename Visitor_ = Default>
 class Gps_agg_op_visitor :
   public Gps_agg_op_base_visitor<
     Helper_, Arrangement_,
-    Gps_agg_op_visitor<Helper_, Arrangement_, Visitor_>> {
+    typename Default::Get<Visitor_,
+                          Gps_agg_op_visitor<Helper_, Arrangement_, Visitor_>>::type> {
 public:
   using Helper = Helper_;
   using Arrangement_2 = Arrangement_;
@@ -145,6 +145,7 @@ private:
   using Base = Gps_agg_op_base_visitor<Helper, Arr, Visitor>;
 
 public:
+  using Edges_hash = typename Base::Edges_hash;
   using Halfedge_handle = typename Base::Halfedge_handle;
   using Vertex_handle = typename Base::Vertex_handle;
   using X_monotone_curve_2 = typename Gt2::X_monotone_curve_2;
@@ -156,7 +157,7 @@ protected:
                                                 // ascending order.
 
 public:
-  Gps_agg_op_visitor(Arr* arr, typename Base::Edges_hash* hash,
+  Gps_agg_op_visitor(Arr* arr, Edges_hash* hash,
                      std::vector<Vertex_handle>* vertices_vec) :
     Base(arr, hash),
     m_event_count(0),

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_base_visitor.h

@@ -43,7 +43,6 @@ protected:
   std::size_t m_num_of_polygons; // number of polygons
 
 public:
-
   Gps_bfs_base_visitor(Edges_hash* edges_hash,
                        Faces_hash* faces_hash,
                        std::size_t n_pgn):

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_bfs_intersection_visitor.h

@@ -7,10 +7,9 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
-
 // Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
 //             Ophir Setter     <ophir.setter@cs.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_BFS_INTERSECTION_VISITOR_H
 #define CGAL_GPS_BFS_INTERSECTION_VISITOR_H

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_do_intersect_agg_op_visitor.h

@@ -0,0 +1,88 @@
+// Copyright (c) 2005  Tel-Aviv University (Israel).
+// 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) : Efi Fogel        <efifogel@gmail.com>
+
+#ifndef CGAL_GSP_DO_INTERSECT_AGG_OP_VISITOR_H
+#define CGAL_GSP_DO_INTERSECT_AGG_OP_VISITOR_H
+
+#include <vector>
+
+#include <CGAL/license/Boolean_set_operations_2.h>
+#include <CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h>
+#include <CGAL/Default.h>
+
+namespace CGAL {
+
+template <typename Helper_, typename Arrangement_, typename Visitor_ = Default>
+class Gps_do_intersect_agg_op_visitor :
+  public Gps_agg_op_visitor<
+    Helper_, Arrangement_,
+    typename Default::Get<Visitor_, Gps_do_intersect_agg_op_visitor<Helper_, Arrangement_, Visitor_>>::type> {
+public:
+  using Helper = Helper_;
+  using Arrangement_2 = Arrangement_;
+  using Geometry_traits_2 = typename Helper::Geometry_traits_2;
+  using Event = typename Helper::Event;
+  using Subcurve = typename Helper::Subcurve;
+
+private:
+  using Gt2 = Geometry_traits_2;
+  using Arr = Arrangement_2;
+  using Self = Gps_do_intersect_agg_op_visitor<Helper, Arr, Visitor_>;
+  using Visitor = typename Default::Get<Visitor_, Self>::type;
+  using Base = Gps_agg_op_visitor<Helper, Arr, Visitor>;
+
+protected:
+  bool m_found_x;
+
+public:
+  using Edges_hash = typename Base::Edges_hash;
+  using Vertex_handle = typename Base::Vertex_handle;
+  using Status_line_iterator = typename Base::Status_line_iterator;
+  using X_monotone_curve_2 = typename Base::X_monotone_curve_2;
+  using Point_2 = typename Base::Point_2;
+
+  Gps_do_intersect_agg_op_visitor(Arr* arr, Edges_hash* hash,
+                                  std::vector<Vertex_handle>* vertices_vec) :
+    Base(arr, hash, vertices_vec),
+    m_found_x(false)
+  {}
+
+  /*! Update an event that corresponds to a curve endpoint. */
+  void update_event(Event* e, const Point_2& end_point, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new)
+  { return Base::update_event(e, end_point, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const X_monotone_curve_2& cv, Arr_curve_end cv_end, bool is_new )
+  { return Base::update_event(e, cv, cv_end, is_new); }
+
+  /*! Update an event that corresponds to a curve endpoint */
+  void update_event(Event* e, const Point_2& p, bool is_new)
+  { return Base::update_event(e, p, is_new); }
+
+  /*! Update an event that corresponds to an intersection */
+  void update_event(Event* e, Subcurve* sc) { return Base::update_event(e, sc); }
+
+  /*! Update an event that corresponds to an intersection between curves */
+  void update_event(Event*, Subcurve*, Subcurve*, bool is_new) { m_found_x = true; }
+
+  bool after_handle_event(Event* e, Status_line_iterator iter, bool flag) {
+    auto res = Base::after_handle_event(e, iter, flag);
+    if (m_found_x) this->surface_sweep()->stop_sweep();
+    return res;
+  }
+
+  /*! Getter */
+  bool found_intersection() { return m_found_x; }
+};
+
+} // namespace CGAL
+
+#endif

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_merge.h

@@ -8,6 +8,7 @@
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
 // Author(s) : Baruch Zukerman  <baruchzu@post.tau.ac.il>
+//             Efi Fogel        <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_MERGE_H
 #define CGAL_GPS_MERGE_H
@@ -15,6 +16,8 @@
 #include <CGAL/license/Boolean_set_operations_2.h>
 
 #include <CGAL/Boolean_set_operations_2/Gps_agg_op.h>
+#include <CGAL/Boolean_set_operations_2/Gps_agg_op_visitor.h>
+#include <CGAL/Boolean_set_operations_2/Gps_do_intersect_agg_op_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_join_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_xor_visitor.h>
 #include <CGAL/Boolean_set_operations_2/Gps_bfs_intersection_visitor.h>
@@ -23,16 +26,16 @@
 namespace CGAL {
 
 /*! \file Gps_merge.h
- * \brief This file contains classes that are responsible for merging
- *        two sets of polygons in the divide-and-conquer algorithm.
- *        The file contains 3 mergers: Join_merge, Intersection_merge and
- *        Xor_merge. Join_merge is used when we want to merge the two sets,
- *        Intersection_merge is used for intersection, and Xor_merge is used
- *        for symmetric difference.
+ *
+ * This file contains classes that are responsible for merging two sets of
+ * polygons in the divide-and-conquer algorithm.  The file contains 3 mergers:
+ * Join_merge, Intersection_merge and Xor_merge. Join_merge is used when we want
+ * to merge the two sets, Intersection_merge is used for intersection, and
+ * Xor_merge is used for symmetric difference.
  */
 
-//! Base_merge
-/*! Base_merge is the base class for all merger classes.
+/*! Base_merge
+ * Base_merge is the base class for all merger classes.
  * All merges used BFS algorithm with a different visitor when discovering
  * a new face.
  */
@@ -44,17 +47,15 @@ class Base_merge {
   using Arr_entry = std::pair<Arrangement_2*, std::vector<Vertex_handle>*>;
 
 public:
-  void operator()(std::size_t i, std::size_t j, std::size_t jump,
-                  std::vector<Arr_entry>& arr_vec) {
+  void operator()(std::size_t i, std::size_t j, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
     if (i == j) return;
 
-    const typename Arrangement_2::Geometry_traits_2* tr =
-      arr_vec[i].first->geometry_traits();
+    const auto* tr = arr_vec[i].first->geometry_traits();
     Arrangement_2* res = new Arrangement_2(tr);
     std::vector<Vertex_handle>* verts = new std::vector<Vertex_handle>;
 
-    Gps_agg_op<Arrangement_2, Visitor>
-      agg_op(*res, *verts, *(res->traits_adaptor()));
+    using Agg_op = Gps_agg_op<Arrangement_2, Visitor, Gps_agg_op_visitor>;
+    Agg_op agg_op(*res, *verts, *(res->traits_adaptor()));
     agg_op.sweep_arrangements(i, j, jump, arr_vec);
 
     for (std::size_t count = i; count <= j; count += jump) {
@@ -67,29 +68,69 @@ public:
   }
 };
 
-//! Join_merge
-/*! Join_merge is used to join two sets of polygons together in the D&C
+/*! Base_intercepted_merge
+ * Base_intercepted_merge is the base class for all merger classes that can be
+ * interceted (e.g., when an intersection is detected).  All merges used BFS
+ * algorithm with a different visitor when discovering a new face.
+ */
+template <typename Arrangement_, typename Visitor_>
+class Base_intercepted_merge {
+  using Arrangement_2 = Arrangement_;
+  using Visitor = Visitor_;
+  using Vertex_handle = typename Arrangement_2::Vertex_handle;
+  using Arr_entry = std::pair<Arrangement_2*, std::vector<Vertex_handle>*>;
+
+public:
+  bool operator()(std::size_t i, std::size_t j, std::size_t jump, std::vector<Arr_entry>& arr_vec) {
+    if (i == j) return false;
+
+    const auto* tr = arr_vec[i].first->geometry_traits();
+    Arrangement_2* arr = new Arrangement_2(tr);
+    std::vector<Vertex_handle>* verts = new std::vector<Vertex_handle>;
+
+    using Agg_op = Gps_agg_op<Arrangement_2, Visitor, Gps_do_intersect_agg_op_visitor>;
+    Agg_op agg_op(*arr, *verts, *(arr->traits_adaptor()));
+    auto res = agg_op.sweep_intercept_arrangements(i, j, jump, arr_vec);
+
+    for (auto count = i; count <= j; count += jump) {
+      delete (arr_vec[count].first);
+      delete (arr_vec[count].second);
+    }
+
+    arr_vec[i].first = arr;
+    arr_vec[i].second = verts;
+    return res;
+  }
+};
+
+/*! Join_merge
+ * Join_merge is used to join two sets of polygons together in the D&C
  * algorithm. It is a base merge with a visitor that joins faces.
  */
 template <typename Arrangement_>
-class Join_merge : public Base_merge<Arrangement_, Gps_bfs_join_visitor<Arrangement_>>
-{};
+class Join_merge : public Base_merge<Arrangement_, Gps_bfs_join_visitor<Arrangement_>>{};
 
-//! Intersection_merge
-/*! Intersection_merge is used to merge two sets of polygons creating their
+/*! Intersection_merge
+ * Intersection_merge is used to merge two sets of polygons creating their
  * intersection.
  */
 template <typename Arrangement_>
-class Intersection_merge : public Base_merge<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>>
-{};
+class Intersection_merge : public Base_merge<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>>{};
 
-//! Xor_merge
-/*! Xor_merge is used to merge two sets of polygons creating their
+/*! Do_intersect_merge
+ * Do_intersect_merge is used to merge two sets of polygons creating their
+ * intersection. When an intersection in the interior of the boundary curves
+ * is detected, the sweep is intercepted.
+ */
+template <typename Arrangement_>
+class Do_intersect_merge : public Base_intercepted_merge<Arrangement_, Gps_bfs_intersection_visitor<Arrangement_>>{};
+
+/*! Xor_merge
+ * Xor_merge is used to merge two sets of polygons creating their
  * symmetric difference.
  */
 template <typename Arrangement_>
-class Xor_merge : public Base_merge<Arrangement_, Gps_bfs_xor_visitor<Arrangement_>>
-{};
+class Xor_merge : public Base_merge<Arrangement_, Gps_bfs_xor_visitor<Arrangement_>>{};
 
 } //namespace CGAL
 

Boolean_set_operations_2/include/CGAL/Boolean_set_operations_2/Gps_on_surface_base_2.h

@@ -10,7 +10,7 @@
 // Author(s) : Baruch Zukerman <baruchzu@post.tau.ac.il>
 //             Ophir Setter    <ophir.setter@cs.tau.ac.il>
 //             Guy Zucker <guyzucke@post.tau.ac.il>
-
+//             Efi Fogel        <efifogel@gmail.com>
 
 #ifndef CGAL_GPS_ON_SURFACE_BASE_2_H
 #define CGAL_GPS_ON_SURFACE_BASE_2_H
@@ -388,7 +388,6 @@ public:
 
   const Traits_2& traits() const { return *m_traits; }
 
-  bool is_empty() const {
   // We have to check that all the faces of an empty arrangement are not
   // contained in the polygon set (there can be several faces in an empty
   // arrangement, dependent on the topology traits.
@@ -398,8 +397,10 @@ public:
   // result for contained() --- from Boolean operations point of view there
   // can not be an empty arrangement which has several faces with different
   // attributes.
-    return (m_arr->is_empty() && !m_arr->faces_begin()->contained());
-  }
+  bool is_empty() const { this->_is_empty(m_arr); }
+
+  bool _is_empty(Aos_2* arr) const
+  { return (arr->is_empty() && ! arr->faces_begin()->contained()); }
 
   bool is_plane() const {
     // Same comment as in "is_empty" above, just with adjustments.
@@ -493,8 +494,33 @@ public:
   template <typename InputIterator>
   bool do_intersect(InputIterator begin, InputIterator end, std::size_t k = 5) {
     Self other(*this);
-    other.intersection(begin, end, k);
-    return (other.is_empty());
+    return other._do_intersect(begin, end, k);
+  }
+
+  // intersects a range of polygons
+  template <typename InputIterator>
+  inline bool _do_intersect(InputIterator begin, InputIterator end, std::size_t k) {
+    std::vector<Arr_entry> arr_vec(std::distance(begin, end) + 1);
+    arr_vec[0].first = this->m_arr;
+    std::size_t i = 1;
+
+    for (auto it = begin; it != end; ++it, ++i) {
+      ValidationPolicy::is_valid((*it), *m_traits);
+      arr_vec[i].first = new Aos_2(m_traits);
+      _insert(*it, *(arr_vec[i].first));
+    }
+
+    Do_intersect_merge<Aos_2> do_intersect_merge;
+    auto res = do_intersect_divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, do_intersect_merge);
+
+    // The resulting arrangement is at index 0
+    this->m_arr = arr_vec[0].first;
+    delete arr_vec[0].second;
+    if (res) return res;
+
+    _remove_redundant_edges(arr_vec[0].first);
+    _reset_faces(arr_vec[0].first);
+    return (_is_empty(arr_vec[0].first));
   }
 
   template <typename InputIterator1, typename InputIterator2>
@@ -502,8 +528,40 @@ public:
                     InputIterator2 begin2, InputIterator2 end2,
                     std::size_t k = 5) {
     Self other(*this);
-    other.intersection(begin1, end1, begin2, end2, k);
-    return (other.is_empty());
+    return other._do_intersect(begin1, end1, begin2, end2, k);
+  }
+
+  template <typename InputIterator1, typename InputIterator2>
+  bool _do_intersect(InputIterator1 begin1, InputIterator1 end1,
+                     InputIterator2 begin2, InputIterator2 end2,
+                     std::size_t k = 5) {
+    std::vector<Arr_entry> arr_vec(std::distance(begin1, end1) + std::distance(begin2, end2) + 1);
+    arr_vec[0].first = this->m_arr;
+    std::size_t i = 1;
+
+    for (InputIterator1 itr1 = begin1; itr1 != end1; ++itr1, ++i) {
+      ValidationPolicy::is_valid(*itr1, *m_traits);
+      arr_vec[i].first = new Aos_2(m_traits);
+      _insert(*itr1, *(arr_vec[i].first));
+    }
+
+    for (InputIterator2 itr2 = begin2; itr2 != end2; ++itr2, ++i) {
+      ValidationPolicy::is_valid(*itr2,*m_traits);
+      arr_vec[i].first = new Aos_2(m_traits);
+      _insert(*itr2, *(arr_vec[i].first));
+    }
+
+    Do_intersect_merge<Aos_2> do_intersect_merge;
+    auto res = do_intersect_divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, do_intersect_merge);
+
+    // The resulting arrangement is at index 0
+    this->m_arr = arr_vec[0].first;
+    delete arr_vec[0].second;
+    if (res) return res;
+
+    _remove_redundant_edges(arr_vec[0].first);
+    _reset_faces(arr_vec[0].first);
+    return (_is_empty(arr_vec[0].first));
   }
 
   // joins a range of polygons
@@ -533,7 +591,6 @@ public:
     }
 
     Join_merge<Aos_2> join_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, join_merge);
 
     //the result arrangement is at index 0
@@ -556,7 +613,6 @@ public:
     }
 
     Join_merge<Aos_2> join_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, join_merge);
 
     // the result arrangement is at index 0
@@ -585,7 +641,6 @@ public:
     }
 
     Join_merge<Aos_2> join_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, join_merge);
 
     // the result arrangement is at index 0
@@ -620,7 +675,6 @@ public:
     }
 
     Intersection_merge<Aos_2> intersection_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, intersection_merge);
 
     // the result arrangement is at index 0
@@ -643,7 +697,6 @@ public:
     }
 
     Intersection_merge<Aos_2> intersection_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, intersection_merge);
 
     // the result arrangement is at index 0
@@ -672,7 +725,6 @@ public:
     }
 
     Intersection_merge<Aos_2> intersection_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, intersection_merge);
 
     // the result arrangement is at index 0
@@ -708,7 +760,6 @@ public:
     }
 
     Xor_merge<Aos_2> xor_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, xor_merge);
 
     // the result arrangement is at index 0
@@ -731,7 +782,6 @@ public:
     }
 
     Xor_merge<Aos_2> xor_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, xor_merge);
 
     // the result arrangement is at index 0
@@ -761,7 +811,6 @@ public:
     }
 
     Xor_merge<Aos_2> xor_merge;
-    _build_sorted_vertices_vectors(arr_vec);
     _divide_and_conquer(0, arr_vec.size() - 1, arr_vec, k, xor_merge);
 
     // the result arrangement is at index 0
@@ -1155,10 +1204,10 @@ protected:
     }
   }
 
-  void _build_sorted_vertices_vectors(std::vector<Arr_entry>& arr_vec) {
+  //! Allocate, collect , and sort the vertex handles of the arrangements in the given interval
+  void _build_sorted_vertices_vectors(std::size_t lower, std::size_t upper, std::vector<Arr_entry>& arr_vec) {
     Less_vertex_handle comp(m_traits->compare_xy_2_object());
-    const std::size_t n = arr_vec.size();
-    for (std::size_t i = 0; i < n; i++) {
+    for (std::size_t i = lower; i < upper + 1; i++) {
       // Allocate a vector of handles to all vertices in the current arrangement.
       Aos_2* p_arr = arr_vec[i].first;
       arr_vec[i].second = new std::vector<Vertex_handle>;
@@ -1174,11 +1223,16 @@ protected:
     }
   }
 
+  //! Divide & conquer
   template <typename Merge>
   void _divide_and_conquer(std::size_t lower, std::size_t upper,
                            std::vector<Arr_entry>& arr_vec,
                            std::size_t k, Merge merge_func) {
+    static int indent = 0;
+    std::cout << std::setw(indent) << "" << "D&C [" << lower << "," << upper << "," << k << "]\n";
     if ((upper - lower) < k) {
+      std::cout << std::setw(indent) << "" << "Merging [" << lower << "," << upper << "," << 1 << "]\n";
+      _build_sorted_vertices_vectors(lower, upper, arr_vec);
       merge_func(lower, upper, 1, arr_vec);
       return;
     }
@@ -1187,12 +1241,71 @@ protected:
     auto curr_lower = lower;
 
     for (std::size_t i = 0; i < k - 1; ++i, curr_lower += sub_size) {
+      indent += 2;
       _divide_and_conquer(curr_lower, curr_lower + sub_size-1, arr_vec, k, merge_func);
+      indent -= 2;
     }
+    indent += 2;
     _divide_and_conquer(curr_lower, upper, arr_vec, k, merge_func);
+    indent -= 2;
+    std::cout << std::setw(indent) << "" << "Merging [" << lower << "," <<  curr_lower << "," << sub_size << "]\n";
     merge_func(lower, curr_lower, sub_size, arr_vec);
   }
 
+  /*! Divide & conquer tailored for the do_intersect() function.
+   * It returns a Boolean value indicating whether an intersection in the
+   * interiors of the curves have been detected. Also, it terminates
+   * as a sson as such an intersection has been detected.
+   */
+  template <typename Merge>
+  bool do_intersect_divide_and_conquer(std::size_t lower, std::size_t upper,
+                                       std::vector<Arr_entry>& arr_vec,
+                                       std::size_t k, Merge merge_func) {
+    static int indent = 0;
+    std::cout << std::setw(indent) << "" << "D&C [" << lower << "," << upper << "," << k << "]\n";
+    if ((upper - lower) < k) {
+      std::cout << std::setw(indent) << "" << "Merging [" << lower << "," << upper << "," << 1 << "]\n";
+      _build_sorted_vertices_vectors(lower, upper, arr_vec);
+      return merge_func(lower, upper, 1, arr_vec);
+    }
+
+    auto sub_size = ((upper - lower + 1) / k);
+    auto curr_lower = lower;
+
+    bool res = false;
+    for (std::size_t i = 0; i < k - 1; ++i, curr_lower += sub_size) {
+      indent += 2;
+      res = do_intersect_divide_and_conquer(curr_lower, curr_lower + sub_size-1, arr_vec, k, merge_func);
+      indent -= 2;
+      if (res) break;
+    }
+    if (res) {
+      // Clean up the entries that have been created
+      std::cout << std::setw(indent) << "" << "Cleaning [" << lower + sub_size << "," << curr_lower << "," << sub_size << "]\n";
+      for (auto count = lower + sub_size; count <= curr_lower; count += sub_size) {
+        delete (arr_vec[count].first);
+        delete (arr_vec[count].second);
+      }
+      return true;
+    }
+
+    indent += 2;
+    res = do_intersect_divide_and_conquer(curr_lower, upper, arr_vec, k, merge_func);
+    indent -= 2;
+    if (res) {
+      // Clean up the entries that have been created
+      std::cout << std::setw(indent) << "" << "Cleaning [" << lower + sub_size << "," << curr_lower << "," << sub_size << "]\n";
+      for (std::size_t count = lower + sub_size; count <= curr_lower; count += sub_size) {
+        delete (arr_vec[count].first);
+        delete (arr_vec[count].second);
+      }
+      return true;
+    }
+
+    std::cout << std::setw(indent) << "" << "Merging [" << lower << "," <<  curr_lower << "," << sub_size << "]\n";
+    return merge_func(lower, curr_lower, sub_size, arr_vec);
+  }
+
   // marks all faces as non-visited
   void _reset_faces() const { _reset_faces(m_arr); }