Updated

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Arrangement_on_surface_2.txt

@@ -5111,8 +5111,8 @@ instantiate the curve-data traits:
 
 At this point we do not expose the topology traits concept. The
 package contains one topology traits, namely,
-`Arr_spherical_topology_traits_2`. It can be served as a topology
-traits for an arrangement embeded on a sphere. More precisely, for an
+`Arr_spherical_topology_traits_2`. It can serve as a topology traits
+for an arrangement embeded on a sphere. More precisely, for an
 arrangement embeded on a sphere defined over a parameter space the
 left and right boundary sides of which are identified and the top and
 bottom boundary sides are contracted.

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_spherical_topology_traits_2.h

@@ -0,0 +1,104 @@
+namespace CGAL {
+
+/*! \ingroup PkgArrangementOnSurface2Ref
+ *
+ * \anchor arr_ref_spherical_topology_traits
+ *
+ * This class handles the topology for arrangements of great spherical
+ * arcs on the sphere embedded on 2D parametric surdace.
+ *
+ * The `Arr_spherical_topology_traits_2` template has two parameters:
+ * <UL>
+ * <LI>The `GeometryTraits_2` template-parameter should be instantiated with
+ * a model of the `ArrangementBasicTraits_2` concept. The traits
+ * class defines the types of \f$x\f$-monotone curves and two-dimensional
+ * points, namely `ArrangementBasicTraits_2::X_monotone_curve_2` and
+ * `ArrangementBasicTraits_2::Point_2`,
+ *   respectively, and supports basic geometric predicates on them.
+ * <LI>The `Dcel` template-parameter should be instantiated with
+ * a class that is a model of the `ArrangementDcel` concept. The
+ * value of this parameter is by default
+ * `Arr_default_dcel<Traits>`.
+ * </UL>
+ *
+ * \sa `Arr_default_dcel<Traits>`
+ * \sa `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel,x,y>`
+ */
+template <typename GeometryTraits_2,
+          typename Dcel = Arr_default_dcel<GeometryTraits_2> >
+class Arr_spherical_topology_traits_2 {
+public:
+  /// \name Types
+  /// @{
+
+  typedef typename GeometryTraits_2::Point_2            Point_2;
+  typedef typename GeometryTraits_2::X_monotone_curve_2 X_monotone_curve_2;
+
+  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;
+
+  /// @}
+
+  /// \name Creation
+  /// @{
+
+  /*! Default constructor. */
+  Arr_spherical_topology_traits_2();
+
+  /*! Constructor from a geometry-traits object.
+   * \param traits the traits.
+   */
+  Arr_spherical_topology_traits_2(const GeometryTraits_2* traits);
+
+  /// @}
+
+  /// \name Accessors
+  /// @{
+
+  /*! Obtain the DCEL (const version). */
+  const Dcel& dcel() const;
+
+  /*! Obtain the DCEL (non-const version). */
+  Dcel& dcel();
+
+  /*! Obtain the spherical face (const version). */
+  const Face* spherical_face() const;
+
+  /*! Obtain the spherical face (non-const version). */
+  Face* spherical_face();
+
+  /*! Obtain the south pole (const version). */
+  const Vertex* south_pole() const;
+
+  /*! Obtain the south pole (non-const version). */
+  Vertex* south_pole();
+
+  /*! Obtain the north pole (const version). */
+  const Vertex* north_pole() const;
+
+  /*! Obtain the north pole (non-const version). */
+  Vertex* north_pole();
+
+  /*! Obtain a vertex on the line of discontinuity that corresponds to
+   *  the given point (or return NULL if no such vertex exists).
+   */
+  const Vertex* discontinuity_vertex(const Point_2& pt) const;
+
+  /*! Obtain a vertex on the line of discontinuity that corresponds to
+   *  the given point (or return NULL if no such vertex exists).
+   */
+  Vertex* discontinuity_vertex(const Point_2& pt);
+
+  /// @}
+
+  /// \name Modifiers
+  /// @{
+  /// @}
+};
+
+}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt

@@ -225,6 +225,7 @@ implemented as peripheral classes or as free (global) functions.
 - `CGAL::Arr_vertex_index_map<Arrangement>`
 - `CGAL::Arr_face_index_map<Arrangement>`
 - `CGAL::Arr_point_location_result<Arrangement>`
+- `CGAL::Arr_spherical_topology_traits_2<GeometryTraits_2,Dcel>`
 
 \cgalCRPSection{Macros}
 - \link CGAL_ARR_POINT_LOCATION_VERSION `CGAL_ARR_POINT_LOCATION_VERSION` \endlink

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/dual_with_data.cpp

@@ -2,12 +2,16 @@
 // Checking whether there are three collinear points in a given input set
 // using the arrangement of the dual lines.
 
+#include <algorithm>
+
 #include <CGAL/Cartesian.h>
 #include <CGAL/Exact_rational.h>
 #include <CGAL/Arr_linear_traits_2.h>
 #include <CGAL/Arr_curve_data_traits_2.h>
 #include <CGAL/Arrangement_2.h>
 
+#include "read_objects.h"
+
 typedef CGAL::Cartesian<CGAL::Exact_rational>            Kernel;
 typedef CGAL::Arr_linear_traits_2<Kernel>                Linear_traits_2;
 typedef Linear_traits_2::Point_2                         Point_2;
@@ -21,56 +25,30 @@ int main(int argc, char *argv[])
 {
   // Get the name of the input file from the command line, or use the default
   // points.dat file if no command-line parameters are given.
-  const char * filename = (argc > 1) ? argv[1] : "coll_points.dat";
+  const char* filename = (argc > 1) ? argv[1] : "coll_points.dat";
 
-  // Open the input file.
-  std::ifstream     in_file(filename);
+  std::vector<Point_2> points;
 
-  if (! in_file.is_open()) {
-    std::cerr << "Failed to open " << filename << " ..." << std::endl;
-    return (1);
-  }
-
-  // Read the points from the file, and construct their dual lines.
-  std::vector<Point_2>           points;
-  std::list<X_monotone_curve_2>  dual_lines;
-
-  unsigned int n;
-  in_file >> n;
-  points.resize(n);
-  unsigned int k;
-  for (k = 0; k < n; ++k) {
-    int px, py;
-    in_file >> px >> py;
-    points[k] = Point_2(px, py);
-
-    // The line dual to the point (p_x, p_y) is y = p_x*x - p_y,
-    // or: p_x*x - y - p_y = 0:
-    Line_2 dual_line = Line_2(CGAL::Exact_rational(px),
-                              CGAL::Exact_rational(-1),
-                              CGAL::Exact_rational(-py));
-
-    // Generate the x-monotone curve based on the line and the point index.
-    dual_lines.push_back(X_monotone_curve_2(dual_line, k));
-  }
-  in_file.close();
+  read_objects<Point_2>(filename, std::back_inserter(points));
+  std::vector<X_monotone_curve_2> dual_lines(points.size());
+  size_t k{0};
+  std::transform(points.begin(), points.end(), dual_lines.begin(),
+                 [&](const Point_2& p) {
+                   Line_2 dual_line(p.x(), CGAL::Exact_rational(-1), -(p.y()));
+                   return X_monotone_curve_2(dual_line, k++);
+                 });
 
   // Construct the dual arrangement by aggregately inserting the lines.
   Arrangement_2 arr;
-
   insert(arr, dual_lines.begin(), dual_lines.end());
 
   // Look for vertices whose degree is greater than 4.
-  Arrangement_2::Vertex_const_iterator vit;
-  Arrangement_2::Halfedge_around_vertex_const_circulator circ;
-  size_t d;
-
-  for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
+  for (auto vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
     if (vit->degree() > 4) {
       // There should be vit->degree()/2 lines intersecting at the current
       // vertex. We print their primal points and their indices.
-      circ = vit->incident_halfedges();
-      for (d = 0; d < vit->degree() / 2; d++) {
+      auto circ = vit->incident_halfedges();
+      for (auto d = 0; d < vit->degree() / 2; ++d) {
         k = circ->curve().data();     // The index of the primal point.
         std::cout << "Point no. " << k+1 << ": (" << points[k] << "), ";
         ++circ;