diff --git a/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h b/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
index e70e929c9d1..cdea56dfe76 100644
--- a/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
+++ b/Arrangement_on_surface_2/include/CGAL/draw_arrangement_2.h
@@ -45,8 +45,7 @@ namespace CGAL {
 namespace draw_aos {
 
 template <typename Arr, typename GSOptions>
-class Draw_arr_tool
-{
+class Draw_arr_tool {
 public:
   using Halfedge_const_handle = typename Arr::Halfedge_const_handle;
   using Vertex_const_handle = typename Arr::Vertex_const_handle;
@@ -58,39 +57,40 @@ public:
   using Point = typename Arr::Point_2;
   using X_monotone_curve = typename Arr::X_monotone_curve_2;
 
-  /*! Construct
+  /*! constructs
    */
-  Draw_arr_tool(Arr& a_aos, CGAL::Graphics_scene& a_gs, const GSOptions& a_gso)
-      : m_aos(a_aos)
-      , m_gs(a_gs)
-      , m_gso(a_gso) {}
+  Draw_arr_tool(Arr& a_aos, CGAL::Graphics_scene& a_gs, const GSOptions& a_gso) :
+    m_aos(a_aos),
+    m_gs(a_gs),
+    m_gso(a_gso)
+  {}
 
-  /// Add a face.
+  //! adds a face.
   void add_face(Face_const_handle face) {
     // std::cout << "add_face()\n";
-    for(Inner_ccb_const_iterator it = face->inner_ccbs_begin(); it != face->inner_ccbs_end(); ++it) add_ccb(*it);
+    for (Inner_ccb_const_iterator it = face->inner_ccbs_begin(); it != face->inner_ccbs_end(); ++it) add_ccb(*it);
 
-    if(!face->is_unbounded()) {
-      for(Outer_ccb_const_iterator it = face->outer_ccbs_begin(); it != face->outer_ccbs_end(); ++it) {
+    if (! face->is_unbounded()) {
+      for (Outer_ccb_const_iterator it = face->outer_ccbs_begin(); it != face->outer_ccbs_end(); ++it) {
         add_ccb(*it);
         draw_region(*it);
       }
     }
   }
 
-  /// Add a Connected Component of the Boundary.
+  //! adds a Connected Component of the Boundary.
   void add_ccb(Ccb_halfedge_const_circulator circ) {
     // std::cout << "add_ccb()\n";
     auto curr = circ;
     do {
       auto new_face = curr->twin()->face();
-      if(m_visited.find(new_face) != m_visited.end()) continue;
+      if (m_visited.find(new_face) != m_visited.end()) continue;
       m_visited[new_face] = true;
       add_face(new_face);
     } while(++curr != circ);
   }
 
-  /// Draw a region.
+  //! draws a region.
   void draw_region(Ccb_halfedge_const_circulator circ) {
     // std::cout << "draw_region()\n";
     /* Check whether the traits has a member function called
@@ -108,7 +108,7 @@ public:
      *
      * For now we use C++14 features.
      */
-    if(m_gso.colored_face(m_aos, circ->face()))
+    if (m_gso.colored_face(m_aos, circ->face()))
       m_gs.face_begin(m_gso.face_color(m_aos, circ->face()));
     else
       m_gs.face_begin();
@@ -128,21 +128,21 @@ public:
     m_gs.face_end();
   }
 
-  /// Compile time dispatching
+  //! Compile time dispatching
 
-  ///
+  //!
   template <typename T, typename A, std::enable_if_t<!has_approximate_point_v<T, A>, int> = 0>
   void draw_region_impl2(const T& /* traits */, const A& /* approximate */, Halfedge_const_handle curr) {
     draw_exact_region(curr);
   }
 
-  ///
+  //!
   template <typename T, typename A, std::enable_if_t<has_approximate_point_v<T, A>, int> = 0>
   auto draw_region_impl2(const T& /* traits */, const A& approx, Halfedge_const_handle curr) {
     draw_approximate_region(curr, approx);
   }
 
-  /*! Draw a region, where the traits does not has approximate_2_object.
+  /*! draws a region, where the traits does not has approximate_2_object.
    */
   template <typename T, std::enable_if_t<!has_approximate_2_object_v<T> && !is_or_derived_from_agas_v<T>, int> = 0>
   void draw_region_impl1(const T& /* traits */, Halfedge_const_handle curr) {
@@ -156,7 +156,7 @@ public:
     draw_region_impl2(traits, traits.approximate_2_object(), curr);
   }
 
-  /*! Draw a geodesic region
+  /*! draws a geodesic region
    */
   template <typename T, std::enable_if_t<is_or_derived_from_agas_v<T>, int> = 0>
   void draw_region_impl1(const T& traits, Halfedge_const_handle curr) {
@@ -164,7 +164,7 @@ public:
     draw_curve_impl1(traits, curr->curve(), false, CGAL::IO::Color());
   }
 
-  /*! Draw a region using approximate coordinates.
+  /*! draws a region using approximate coordinates.
    * Call this member function only if the geometry traits is equipped with
    * the coordinate-approximation functionality of a curve.
    * This function must be inlined (e.g., a template) to enable the
@@ -177,13 +177,13 @@ public:
     double error(0.01); // TODO? (this->pixel_ratio());
     bool l2r = curr->direction() == ARR_LEFT_TO_RIGHT;
     approx(curr->curve(), error, std::back_inserter(polyline), l2r);
-    if(polyline.empty()) return;
+    if (polyline.empty()) return;
     auto it = polyline.begin();
     auto prev = it++;
-    for(; it != polyline.end(); prev = it++) m_gs.add_point_in_face(*prev);
+    for (; it != polyline.end(); prev = it++) m_gs.add_point_in_face(*prev);
   }
 
-  /*! Draw an exact curve.
+  /*! draws an exact curve.
    */
   template <typename XMonotoneCurve>
   void draw_exact_curve(const XMonotoneCurve& curve, bool colored, const CGAL::IO::Color& c) {
@@ -191,72 +191,72 @@ public:
     auto ctr_min = traits->construct_min_vertex_2_object();
     auto ctr_max = traits->construct_max_vertex_2_object();
     m_gs.add_segment(ctr_min(curve), ctr_max(curve));
-    if(colored)
+    if (colored)
       m_gs.add_segment(ctr_min(curve), ctr_max(curve), c);
     else
       m_gs.add_segment(ctr_min(curve), ctr_max(curve));
   }
 
-  /*! Draw a region in an exact manner.
+  /*! draws a region in an exact manner.
    *  This fallback simply draws the curve in an exact manner (and even this is not guaranteed).
    */
   void draw_exact_region(Halfedge_const_handle curr) { draw_exact_curve(curr->curve(), false, CGAL::IO::Color()); }
 
-  /// Add all faces.
+  //! Add all faces.
   template <typename Traits>
   void add_faces(const Traits&) {
-    for(auto it = m_aos.unbounded_faces_begin(); it != m_aos.unbounded_faces_end(); ++it) add_face(it);
+    for (auto it = m_aos.unbounded_faces_begin(); it != m_aos.unbounded_faces_end(); ++it) add_face(it);
   }
 
-  /// Compile time dispatching
+  //! Compile time dispatching
 
-  /*! Draw a point using approximate coordinates.
+  /*! draws a point using approximate coordinates.
    */
   template <typename Approximate>
   void draw_approximate_point(const Point& p, const Approximate& approx, bool colored, const CGAL::IO::Color& color) {
-    if(colored)
+    if (colored)
       m_gs.add_point(approx(p), color);
     else
       m_gs.add_point(approx(p));
   }
 
-  ///
+  //!
   void draw_exact_point(const Point& p, bool colored, const CGAL::IO::Color& color) {
-    if(colored)
+    if (colored)
       m_gs.add_point(p, color);
     else
       m_gs.add_point(p);
   }
 
-  ///
+  //!
   template <typename T, typename A, std::enable_if_t<!has_approximate_point_v<T, A>, int> = 0>
   void draw_point_impl2(
       const T& /* traits */, const A& /* approximate */, const Point& p, bool colored, const CGAL::IO::Color& c) {
     draw_exact_point(p, colored, c);
   }
 
-  ///
+  //!
   template <typename T, typename A, std::enable_if_t<has_approximate_point_v<T, A>, int> = 0>
   auto
   draw_point_impl2(const T& /* traits */, const A& approx, const Point& p, bool colored, const CGAL::IO::Color& c) {
     draw_approximate_point(p, approx, colored, c);
   }
 
-  /*! Draw a point, where the traits does not has approximate_2_object.
+  /*! draws a point, where the traits does not has approximate_2_object.
    */
   template <typename T, std::enable_if_t<!has_approximate_2_object_v<T> && !is_or_derived_from_agas_v<T>, int> = 0>
   void draw_point_impl1(const T& /* traits */, const Point& p, bool colored, const CGAL::IO::Color& c) {
     draw_exact_point(p, colored, c);
   }
 
-  /*! Draw a point, where the traits does have approximate_2_object.
+  /*! draws a point, where the traits does have approximate_2_object.
    */
   template <typename T, std::enable_if_t<has_approximate_2_object_v<T> && !is_or_derived_from_agas_v<T>, int> = 0>
   auto draw_point_impl1(const T& traits, const Point& p, bool colored, const CGAL::IO::Color& c) {
     draw_point_impl2(traits, traits.approximate_2_object(), p, colored, c);
   }
 
-  /*! Draw a geodesic point.
+  /*! draws a geodesic point.
    */
   template <typename T, std::enable_if_t<is_or_derived_from_agas_v<T>, int> = 0>
   void draw_point_impl1(const T& traits, const Point& p, bool colored, const CGAL::IO::Color& color) {
@@ -271,13 +271,13 @@ public:
     auto z = ap.dz();
     auto l = std::sqrt(x * x + y * y + z * z);
     Approx_point_3 p3(x / l, y / l, z / l);
-    if(colored)
+    if (colored)
       m_gs.add_point(p3, color);
     else
       m_gs.add_point(p3);
   }
 
-  /// Draw a point.
+  //! draws a point.
   void draw_point(const Point& p, bool colored, const CGAL::IO::Color& c) {
     const auto* traits = m_aos.geometry_traits();
     draw_point_impl1(*traits, p, colored, c);
@@ -286,11 +286,10 @@ public:
   ///
   template <typename Kernel, int AtanX, int AtanY>
   Halfedge_const_handle find_smallest(Ccb_halfedge_const_circulator circ,
-                                      Arr_geodesic_arc_on_sphere_traits_2<Kernel, AtanX, AtanY> const&) {
-    return circ;
-  }
+                                      Arr_geodesic_arc_on_sphere_traits_2<Kernel, AtanX, AtanY> const&)
+  { return circ; }
 
-  /*! Find the halfedge incident to the lexicographically smallest vertex
+  /*! finds the halfedge incident to the lexicographically smallest vertex
    * along the CCB, such that there is no other halfedge underneath.
    */
   template <typename Traits>
@@ -302,8 +301,7 @@ public:
 
     // Find the first halfedge directed from left to right
     auto curr = circ;
-    do
-      if(curr->direction() == CGAL::ARR_LEFT_TO_RIGHT) break;
+    do if (curr->direction() == CGAL::ARR_LEFT_TO_RIGHT) break;
     while(++curr != circ);
     Halfedge_const_handle ext = curr;
 
@@ -311,43 +309,43 @@ public:
     //  such that there is no other halfedge underneath.
     do {
       // Discard edges not directed from left to right:
-      if(curr->direction() != CGAL::ARR_LEFT_TO_RIGHT) continue;
+      if (curr->direction() != CGAL::ARR_LEFT_TO_RIGHT) continue;
 
       auto res = cmp_xy(curr->source()->point(), ext->source()->point());
 
       // Discard the edges inciden to a point strictly larger than the point
       // incident to the stored extreme halfedge:
-      if(res == LARGER) continue;
+      if (res == LARGER) continue;
 
       // Store the edge inciden to a point strictly smaller:
-      if(res == SMALLER) {
+      if (res == SMALLER) {
         ext = curr;
         continue;
       }
 
       // The incident points are equal; compare the halfedges themselves:
-      if(cmp_y(curr->curve(), ext->curve(), curr->source()->point()) == SMALLER) ext = curr;
+      if (cmp_y(curr->curve(), ext->curve(), curr->source()->point()) == SMALLER) ext = curr;
     } while(++curr != circ);
 
     return ext;
   }
 
-  /// Add all elements to be drawn.
+  //! adds all elements to be drawn.
   void add_elements() {
     // std::cout << "add_elements()\n";
     // std::cout << "ratio: " << this->pixel_ratio() << std::endl;
     m_visited.clear();
 
-    if(m_aos.is_empty()) return;
+    if (m_aos.is_empty()) return;
 
-    if(m_gso.are_faces_enabled()) add_faces(*(this->m_aos.geometry_traits()));
+    if (m_gso.are_faces_enabled()) add_faces(*(this->m_aos.geometry_traits()));
 
     // Add edges that do not separate faces.
-    if(m_gso.are_edges_enabled()) {
-      for(auto it = m_aos.edges_begin(); it != m_aos.edges_end(); ++it) {
-        if(it->face() != it->twin()->face()) {
-          if(m_gso.draw_edge(m_aos, it)) {
-            if(m_gso.colored_edge(m_aos, it))
+    if (m_gso.are_edges_enabled()) {
+      for (auto it = m_aos.edges_begin(); it != m_aos.edges_end(); ++it) {
+        if (it->face() != it->twin()->face()) {
+          if (m_gso.draw_edge(m_aos, it)) {
+            if (m_gso.colored_edge(m_aos, it))
               draw_curve(it->curve(), true, m_gso.edge_color(m_aos, it));
             else
               draw_curve(it->curve(), false, CGAL::IO::Color());
@@ -357,9 +355,9 @@ public:
     }
 
     // Add all points
-    if(m_gso.are_vertices_enabled()) {
-      for(auto it = m_aos.vertices_begin(); it != m_aos.vertices_end(); ++it) {
-        if(m_gso.colored_vertex(m_aos, it))
+    if (m_gso.are_vertices_enabled()) {
+      for (auto it = m_aos.vertices_begin(); it != m_aos.vertices_end(); ++it) {
+        if (m_gso.colored_vertex(m_aos, it))
           draw_point(it->point(), true, m_gso.vertex_color(m_aos, it));
         else
           draw_point(it->point(), false, CGAL::IO::Color());
@@ -369,7 +367,7 @@ public:
     m_visited.clear();
   }
 
-  /*! Draw a curve using approximate coordinates.
+  /*! draws a curve using approximate coordinates.
    * Call this member function only of the geometry traits is equipped with
    * the coordinate-aproximation functionality of a curve.
    * This function must be inlined (e.g., a template) to enable the
@@ -384,11 +382,11 @@ public:
     std::vector<typename Gt::Approximate_point_2> polyline;
     double error(0.01); // TODO? (this->pixel_ratio());
     approx(curve, error, std::back_inserter(polyline));
-    if(polyline.empty()) return;
+    if (polyline.empty()) return;
     auto it = polyline.begin();
     auto prev = it++;
-    for(; it != polyline.end(); prev = it++) {
-      if(colored)
+    for (; it != polyline.end(); prev = it++) {
+      if (colored)
         m_gs.add_segment(*prev, *it, c);
       else
         m_gs.add_segment(*prev, *it);
@@ -412,14 +410,14 @@ public:
     draw_approximate_curve(xcv, approx, colored, c);
   }
 
-  /*! Draw a curve, where the traits does not has approximate_2_object.
+  /*! draws a curve, where the traits does not has approximate_2_object.
    */
   template <typename T, std::enable_if_t<!has_approximate_2_object_v<T> && !is_or_derived_from_agas_v<T>, int> = 0>
   void draw_curve_impl1(const T& /* traits */, const X_monotone_curve& xcv, bool colored, const CGAL::IO::Color& c) {
     draw_exact_curve(xcv, colored, c);
   }
 
-  /*! Draw a curve, where the traits does have approximate_2_object.
+  /*! draws a curve, where the traits does have approximate_2_object.
    */
   template <typename T, std::enable_if_t<has_approximate_2_object_v<T> && !is_or_derived_from_agas_v<T>, int> = 0>
   auto draw_curve_impl1(const T& traits, const X_monotone_curve& xcv, bool colored, const CGAL::IO::Color& c) {
@@ -427,7 +425,7 @@ public:
     draw_curve_impl2(traits, traits.approximate_2_object(), xcv, colored, c);
   }
 
-  /*! Draw a geodesic curve
+  /*! draws a geodesic curve
    */
   template <typename T, std::enable_if_t<is_or_derived_from_agas_v<T>, int> = 0>
   void draw_curve_impl1(const T& traits, const X_monotone_curve& xcv, bool colored, const CGAL::IO::Color& c) {
@@ -448,13 +446,13 @@ public:
     auto z = it->dz();
     auto l = std::sqrt(x * x + y * y + z * z);
     Approx_point_3 prev(x / l, y / l, z / l);
-    for(++it; it != apoints.end(); ++it) {
+    for (++it; it != apoints.end(); ++it) {
       auto x = it->dx();
       auto y = it->dy();
       auto z = it->dz();
       auto l = std::sqrt(x * x + y * y + z * z);
       Approx_point_3 next(x / l, y / l, z / l);
-      if(colored)
+      if (colored)
         m_gs.add_segment(prev, next, c);
       else
         m_gs.add_segment(prev, next);
@@ -462,7 +460,7 @@ public:
     }
   }
 
-  /// Draw a curve.
+  //! draws a curve.
   template <typename XMonotoneCurve>
   void draw_curve(const XMonotoneCurve& curve, bool colored, const CGAL::IO::Color& c) {
     /* Check whether the traits has a member function called
@@ -511,8 +509,7 @@ static auto map_from_pair_ranges(Range1 range1, Range2 range2) {
                                             boost::make_transform_iterator(end, tuple_to_pair));
 }
 
-/*!
- * \brief tracking changes between an arrangement and its copy that will be later inserted to.
+/*! \brief tracking changes between an arrangement and its copy that will be later inserted to.
  *
  * \note tracks insertions only. If any other actions made(e.g. deletions, merging, etc), the state of the tracker
  * instance may become invalid.
@@ -520,8 +517,7 @@ static auto map_from_pair_ranges(Range1 range1, Range2 range2) {
  * \tparam Arrangement
  */
 template <typename Arrangement>
-class Arr_insertion_tracker : Arr_observer<Arrangement>
-{
+class Arr_insertion_tracker : Arr_observer<Arrangement> {
   using Base = Arr_observer<Arrangement>;
   using Halfedge_handle = typename Arrangement::Halfedge_handle;
   using Halfedge_const_handle = typename Arrangement::Halfedge_const_handle;
@@ -539,17 +535,16 @@ protected:
     m_halfedge_map[e->twin()] = Halfedge_const_handle(); // twin is created as well
   }
 
-  virtual void before_split_edge(Halfedge_handle e,
-                                 Vertex_handle v,
+  virtual void before_split_edge(Halfedge_handle e, Vertex_handle v,
                                  const X_monotone_curve_2& c1,
                                  const X_monotone_curve_2& c2) override {
-    if(m_vertex_map.find(v) == m_vertex_map.end()) m_vertex_map[v] = Vertex_const_handle(); // v is newly created
+    if (m_vertex_map.find(v) == m_vertex_map.end()) m_vertex_map[v] = Vertex_const_handle(); // v is newly created
   }
 
   virtual void after_split_edge(Halfedge_handle e1, Halfedge_handle e2) override {
-    if(auto it = m_halfedge_map.find(e1); it == m_halfedge_map.end())
+    if (auto it = m_halfedge_map.find(e1); it == m_halfedge_map.end())
       m_halfedge_map[e2] = e1;
-    else if(it->second == Halfedge_const_handle())
+    else if (it->second == Halfedge_const_handle())
       m_halfedge_map[e2] = Halfedge_const_handle(); // e1 has no corresponding edge in the original arrangement
     else
       m_halfedge_map[e2] = it->second; // e1 is created by splitting an existing edge
@@ -557,51 +552,47 @@ protected:
 
   virtual void after_split_face(Face_handle f1, Face_handle f2, bool) override {
     // Face cannot be created but by splitting an existing face.
-    if(auto it = m_face_map.find(f1); it == m_face_map.end())
+    if (auto it = m_face_map.find(f1); it == m_face_map.end())
       m_face_map[f2] = f1;
     else
       m_face_map[f2] = it->second; // f1 is created by splitting an existing face
   }
 
 public:
-  Arr_insertion_tracker(Arrangement& arr)
-      : Base(arr) {}
+  Arr_insertion_tracker(Arrangement& arr) : Base(arr) {}
 
-  /*!
-   * \brief Query the original face of a given face.
+  /*! \brief Query the original face of a given face.
    *
    * \param fh a valid face handle in the modified arrangement.
    * \return Face_const_handle
    */
   Face_const_handle original_face(Face_const_handle fh) const {
     auto it = m_face_map.find(fh);
-    if(it == m_face_map.end()) return fh;
+    if (it == m_face_map.end()) return fh;
     return it->second; // new face from splitting an existing face
   }
 
-  /*!
-   * \brief Query the original halfedge of a given halfedge.
+  /*! \brief Query the original halfedge of a given halfedge.
    *
    * \param heh a valid halfedge handle in the modified arrangement.
    * \return Halfedge_const_handle
    */
   Halfedge_const_handle original_halfedge(Halfedge_const_handle he) const {
     auto it = m_halfedge_map.find(he);
-    if(it == m_halfedge_map.end()) return he;
-    if(it->second == Halfedge_const_handle()) return Halfedge_const_handle(); // newly created halfedge
+    if (it == m_halfedge_map.end()) return he;
+    if (it->second == Halfedge_const_handle()) return Halfedge_const_handle(); // newly created halfedge
     return it->second;
   }
 
-  /*!
-   * \brief Query the original vertex of a given vertex.
+  /*! \brief Query the original vertex of a given vertex.
    *
    * \param vh a valid vertex handle in the modified arrangement.
    * \return Vertex_const_handle
    */
   Vertex_const_handle original_vertex(Vertex_const_handle vh) const {
     auto it = m_vertex_map.find(vh);
-    if(it == m_vertex_map.end()) return vh;
-    if(it->second == Vertex_const_handle()) return Vertex_const_handle(); // newly created vertex
+    if (it == m_vertex_map.end()) return vh;
+    if (it->second == Vertex_const_handle()) return Vertex_const_handle(); // newly created vertex
     return it->second;                                                    // it will never reach here.
   }
 
@@ -634,13 +625,12 @@ void draw_impl_planar(
 }
 
 template <typename Arrangement, typename GSOptions>
-void draw_impl_agas(
-    const Arrangement& arr, const GSOptions& gso, const char* title, Bbox_2 initial_bbox, QApplication& app) {
+void draw_impl_agas(const Arrangement& arr, const GSOptions& gso,
+                    const char* title, Bbox_2 initial_bbox, QApplication& app) {
   using Halfedge_const_handle = typename Arrangement::Halfedge_const_handle;
   using Face_const_handle = typename Arrangement::Face_const_handle;
   using Vertex_const_handle = typename Arrangement::Vertex_const_handle;
   using Geom_traits = typename Arrangement::Geometry_traits_2;
-  using X_monotone_curve_2 = typename Geom_traits::X_monotone_curve_2;
   using Direction_3 = typename Geom_traits::Direction_3;
   using Point_2 = typename Geom_traits::Point_2;
   using Agas_template_args = tmpl_args<Geom_traits>;
@@ -650,63 +640,63 @@ void draw_impl_agas(
                                                                                    arr.vertex_handles());
   auto halfedge_map = map_from_pair_ranges<Halfedge_const_handle, Halfedge_const_handle>(derived_arr.halfedge_handles(),
                                                                                          arr.halfedge_handles());
-  auto face_map =
-      map_from_pair_ranges<Face_const_handle, Face_const_handle>(derived_arr.face_handles(), arr.face_handles());
+  auto face_map = map_from_pair_ranges<Face_const_handle, Face_const_handle>(derived_arr.face_handles(),
+                                                                             arr.face_handles());
   // setup tracker and insert the identification curve.
   Arr_insertion_tracker<Arrangement> tracker(derived_arr);
-  X_monotone_curve_2 id_curve = arr.geometry_traits()->construct_x_monotone_curve_2_object()(
-      Point_2(Direction_3(0, 0, -1), Point_2::MIN_BOUNDARY_LOC),
-      Point_2(Direction_3(0, 0, 1), Point_2::MAX_BOUNDARY_LOC),
-      Direction_3(Agas_template_args::atan_y, -Agas_template_args::atan_x, 0));
+  Point_2 src(Direction_3(0, 0, -1), Point_2::MIN_BOUNDARY_LOC);
+  Point_2 trg(Direction_3(0, 0, 1), Point_2::MAX_BOUNDARY_LOC);
+  auto ctr_xcv = arr.geometry_traits()->construct_x_monotone_curve_2_object();
+  auto id_curve = ctr_xcv(src, trg, Direction_3(Agas_template_args::atan_y, -Agas_template_args::atan_x, 0));
   insert(derived_arr, id_curve);
 
   // derived_gso proxies the call to the original gso
   GSOptions derived_gso(gso);
   derived_gso.draw_vertex = [&](const Arrangement&, const Vertex_const_handle& vh) {
     Vertex_const_handle original_vh = tracker.original_vertex(vh);
-    if(original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end()) return false;
+    if (original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end()) return false;
     return gso.draw_vertex(arr, vertex_map.at(original_vh));
   };
   derived_gso.colored_vertex = [&](const Arrangement&, const Vertex_const_handle& vh) {
     Vertex_const_handle original_vh = tracker.original_vertex(vh);
-    if(original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end()) return false;
+    if (original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end()) return false;
     return gso.colored_vertex(arr, vertex_map.at(original_vh));
   };
   derived_gso.vertex_color = [&](const Arrangement&, const Vertex_const_handle& vh) -> CGAL::IO::Color {
     Vertex_const_handle original_vh = tracker.original_vertex(vh);
-    if(original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end())
+    if (original_vh == Vertex_const_handle() || vertex_map.find(original_vh) == vertex_map.end())
       return CGAL::IO::Color();
     return gso.vertex_color(arr, vertex_map.at(original_vh));
   };
   derived_gso.draw_edge = [&](const Arrangement&, const Halfedge_const_handle& he) {
     Halfedge_const_handle original_he = tracker.original_halfedge(he);
-    if(original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end()) return false;
+    if (original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end()) return false;
     return gso.draw_edge(arr, halfedge_map.at(original_he));
   };
   derived_gso.colored_edge = [&](const Arrangement&, const Halfedge_const_handle& he) {
     Halfedge_const_handle original_he = tracker.original_halfedge(he);
-    if(original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end()) return false;
+    if (original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end()) return false;
     return gso.colored_edge(arr, halfedge_map.at(original_he));
   };
   derived_gso.edge_color = [&](const Arrangement&, const Halfedge_const_handle& he) -> CGAL::IO::Color {
     Halfedge_const_handle original_he = tracker.original_halfedge(he);
-    if(original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end())
+    if (original_he == Halfedge_const_handle() || halfedge_map.find(original_he) == halfedge_map.end())
       return CGAL::IO::Color();
     return gso.edge_color(arr, halfedge_map.at(original_he));
   };
   derived_gso.draw_face = [&](const Arrangement&, const Face_const_handle& fh) {
     Face_const_handle original_fh = tracker.original_face(fh);
-    if(face_map.find(original_fh) == face_map.end()) return false;
+    if (face_map.find(original_fh) == face_map.end()) return false;
     return gso.draw_face(arr, face_map.at(original_fh));
   };
   derived_gso.colored_face = [&](const Arrangement&, const Face_const_handle& fh) {
     Face_const_handle original_fh = tracker.original_face(fh);
-    if(face_map.find(original_fh) == face_map.end()) return false;
+    if (face_map.find(original_fh) == face_map.end()) return false;
     return gso.draw_face(arr, face_map.at(original_fh));
   };
   derived_gso.face_color = [&](const Arrangement&, const Face_const_handle& fh) -> CGAL::IO::Color {
     Face_const_handle original_fh = tracker.original_face(fh);
-    if(face_map.find(original_fh) == face_map.end()) return CGAL::IO::Color();
+    if (face_map.find(original_fh) == face_map.end()) return CGAL::IO::Color();
     return gso.face_color(arr, face_map.at(original_fh));
   };
 
@@ -731,8 +721,7 @@ void draw(const Arrangement& arr, const GSOptions& gso, Args&&... args) {
 
 } // namespace draw_aos
 
-/*!
- * \brief Draw an arrangement on surface.
+/*! \brief draws an arrangement on surface.
  *
  * \tparam Arrangement
  * \tparam GSOptions
@@ -762,8 +751,7 @@ void draw(const Arrangement& arr,
   draw_aos::draw(arr, gso, title, initial_bbox, app);
 }
 
-/*!
- * \brief Draw an arrangement on surface with default graphics scene options. Faces are colored randomly.
+/*! \brief draws an arrangement on surface with default graphics scene options. Faces are colored randomly.
  *
  * \tparam Arrangement
  * \param arr the arrangement to be drawn
@@ -820,7 +808,7 @@ template <typename GeometryTraits_2, typename TopologyTraits>
 void add_to_graphics_scene(const CGAL_ARR_TYPE& aos, CGAL::Graphics_scene& graphics_scene) {
   CGAL::Graphics_scene_options<CGAL_ARR_TYPE, typename CGAL_ARR_TYPE::Vertex_const_handle,
                                typename CGAL_ARR_TYPE::Halfedge_const_handle, typename CGAL_ARR_TYPE::Face_const_handle>
-      gso;
+    gso;
   // colored face?
   gso.colored_face = [](const CGAL_ARR_TYPE&, typename CGAL_ARR_TYPE::Face_const_handle) -> bool { return true; };
 
@@ -833,7 +821,7 @@ void add_to_graphics_scene(const CGAL_ARR_TYPE& aos, CGAL::Graphics_scene& graph
   add_to_graphics_scene(aos, graphics_scene, gso);
 }
 
-/// Draw an arrangement on surface.
+//! draws an arrangement on surface.
 template <typename GeometryTraits_2, typename TopologyTraits, class GSOptions>
 void draw_old(const CGAL_ARR_TYPE& aos,
               const GSOptions& gso,
@@ -843,7 +831,7 @@ void draw_old(const CGAL_ARR_TYPE& aos,
   draw_graphics_scene(graphics_scene, title);
 }
 
-/// Draw an arrangement on surface.
+//! draws an arrangement on surface.
 template <typename GeometryTraits_2, typename TopologyTraits>
 void draw_old(const CGAL_ARR_TYPE& aos, const char* title = "2D Arrangement on Surface Basic Viewer") {
   CGAL::Graphics_scene graphics_scene;