Add a geometric traits class TODO: Make it complete

Made Direction_2 public as it in the API
Removed a typename

Cone_spanners_2/doc/Cone_spanners_2/Concepts/ConeBasedSpannerTraits.h

@@ -0,0 +1,59 @@
+/*!
+\ingroup PkgConeBasedSpannersConcepts
+\cgalConcept
+
+All convex hull and extreme point algorithms provided in \cgal are 
+parameterized with a traits class `Traits`, which defines the 
+primitives (objects and predicates) that the cone based spanner algorithms use. 
+
+\cgalHasModel any model of a \cgal %kernel.
+
+*/
+
+class ConeBasedSpannerTraits {
+public:
+
+/// \name Types 
+/// @{
+
+/*!
+The point type. 
+*/ 
+typedef unspecified_type Point_2; 
+
+
+/*!
+Predicate object type that must provide 
+`bool operator()(Point_2 p, Point_2 q, 
+Point_2 r,Point_2 s)`, which returns `true` iff 
+the signed distance from \f$ r\f$ to the line \f$ l_{pq}\f$ through \f$ p\f$ and \f$ q\f$ 
+is smaller than the distance from \f$ s\f$ to \f$ l_{pq}\f$. It is used to 
+compute the point right of a line with maximum unsigned distance to 
+the line. The predicate must provide a total order compatible 
+with convexity, <I>i.e.</I>, for any line segment \f$ s\f$ one of the 
+endpoints 
+of \f$ s\f$ is the smallest point among the points on \f$ s\f$, with respect to 
+the order given by `Less_signed_distance_to_line_2`. 
+*/ 
+typedef unspecified_type Less_signed_distance_to_line_2; 
+
+
+/// @} 
+
+
+
+/// \name Operations 
+/// The following member functions to create instances of the above predicate 
+/// object types must exist. 
+/// @{
+
+
+/*!
+
+*/ 
+Less_signed_distance_to_line_2 less_signed_distance_to_line_2_object(); 
+
+
+/// @}
+
+}; /* end ConeBasedSpannerTraits */

Cone_spanners_2/doc/Cone_spanners_2/PackageDescription.txt

@@ -41,6 +41,7 @@ a global function to generate the data and script files used by Gnuplot to plot
 \cgalClassifedRefPages
 
 ## Concepts ##
+- `ConeBasedSpannerTraits`
 - `ComputeConeBoundaries_2`
 - `ConstructConeBasedSpanner_2`
 

Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h

@@ -136,9 +136,9 @@ private:
     //typedef  typename Kernel_type::FT            FT;
     //typedef  typename Kernel_type::Direction_2   Direction_2;
 	//typedef  typename Kernel_type::Aff_transformation_2   Transformation;
-    typedef  typename Exact_predicates_exact_constructions_kernel_with_sqrt::FT       FT;
+    typedef  Exact_predicates_exact_constructions_kernel_with_sqrt::FT       FT;
-    typedef  typename Exact_predicates_exact_constructions_kernel_with_sqrt::Direction_2   Direction_2;
+    typedef  Exact_predicates_exact_constructions_kernel_with_sqrt::Direction_2   Direction_2;
-	typedef  typename Exact_predicates_exact_constructions_kernel_with_sqrt::Aff_transformation_2   Transformation;
+	typedef  Exact_predicates_exact_constructions_kernel_with_sqrt::Aff_transformation_2   Transformation;
 
 public:
 	/* No member variables in this class, so a Constructor is not needed. */

Cone_spanners_2/include/CGAL/Cone_spanners_2/Less_by_direction_2.h

@@ -60,7 +60,7 @@ public:
     typedef typename Graph_::vertex_descriptor second_argument_type;
     typedef bool     result_type;
 
-    // typedef for Diretion_2 and Line_2
+    // typedef for Direction_2 and Line_2
     typedef typename Kernel_::Direction_2 Direction_2;
     typedef typename Kernel_::Line_2 Line_2;
     typedef typename Kernel_::Point_2 Point_2;

Cone_spanners_2/include/CGAL/Construct_theta_graph_2.h

@@ -49,21 +49,21 @@ namespace CGAL {
    
    \cgalModels `ConstructConeBasedSpanner_2`
  */
-template <typename Kernel_, typename Graph_>
+template <typename Traits, typename Graph_>
 class Construct_theta_graph_2 {
 
 public:
-	/*! Indicate the \cgal kernel type. */
+	/*! is the geometric traits which must be a model of the concept `ConeBasedSpannerTraits`  */
-    typedef Kernel_                          Kernel_type;
+    typedef Traits                          Geom_traits;
 	/*! Indicate the specific type of `boost::adjacency_list`. */
     typedef Graph_                           Graph_type;
 
+    typedef typename Geom_traits::Direction_2             Direction_2;
 private:
-    typedef typename Kernel_::Direction_2             Direction_2;
+    typedef typename Geom_traits::Point_2                 Point_2;
-    typedef typename Kernel_::Point_2                 Point_2;
+    typedef typename Geom_traits::Line_2                  Line_2;
-    typedef typename Kernel_::Line_2                  Line_2;
+    typedef typename Geom_traits::Aff_transformation_2    Transformation;
-    typedef typename Kernel_::Aff_transformation_2    Transformation;
+    typedef Less_by_direction_2<Geom_traits, Graph_>      Less_by_direction;
-    typedef Less_by_direction_2<Kernel_, Graph_>      Less_by_direction;
 
     /* Store the number of cones.  */
     unsigned int  cone_number;
@@ -95,7 +95,7 @@ public:
 		rays.reserve(k);
         /* Initialize a functor, specialization will happen here depending on the kernel type to 
 		 compute the cone boundaries either exactly or inexactly */
-        Compute_cone_boundaries_2<Kernel_> compute_cones;
+        Compute_cone_boundaries_2<Geom_traits> compute_cones;
         // compute the rays using the functor
         compute_cones(k, initial_direction, rays.begin());
     }

Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h

@@ -47,20 +47,20 @@ namespace CGAL {
 
   \cgalModels `ConstructConeBasedSpanner_2`
  */
-template <typename Kernel_, typename Graph_>
+template <typename Traits, typename Graph_>
 class Construct_yao_graph_2 {
 
 public:
-	/*! Indicate the \cgal kernel type. */
+	/*! is the geometric traits which must be a model of the concept `ConeBasedSpannerTraits` */
-    typedef Kernel_                          Kernel_type;
+    typedef Traits                          Geom_traits;
 	/*! Indicate the specific type of `boost::adjacency_list`. */
     typedef Graph_                           Graph_type;
 
+    typedef typename Geom_traits::Direction_2             Direction_2;
 private:
-    typedef typename Kernel_::Direction_2             Direction_2;
+    typedef typename Geom_traits::Point_2                 Point_2;
-    typedef typename Kernel_::Point_2                 Point_2;
+    typedef typename Geom_traits::Line_2                  Line_2;
-    typedef typename Kernel_::Line_2                  Line_2;
+    typedef Less_by_direction_2<Geom_traits, Graph_>      Less_by_direction;
-    typedef Less_by_direction_2<Kernel_, Graph_>      Less_by_direction;
     // a type for the set to store vertices sorted by a direction
     typedef std::set<typename Graph_::vertex_descriptor, Less_by_direction> Point_set;
 
@@ -94,7 +94,7 @@ public:
 		rays.reserve(k);
         /* Initialize a functor, specialization will happen here depending on the kernel type to
          compute the cone boundaries either exactly or inexactly */
-        Compute_cone_boundaries_2<Kernel_> compute_cones;
+        Compute_cone_boundaries_2<Geom_traits> compute_cones;
         // compute the rays using the functor
         compute_cones(k, initial_direction, rays.begin());
     }