Introduced new concept AosApproximateTraits_2

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_circle_segment_traits_2.h

@@ -32,7 +32,7 @@ namespace CGAL {
  * same direction as a precondition. Moreover, `Arr_circle_segment_traits_2`
  * supports the merging of curves of opposite directions.
  *
- * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  *
  */
 template <typename Kernel>

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_conic_traits_2.h

@@ -80,7 +80,7 @@ namespace CGAL {
  * to have the same direction as a precondition. Moreover, `Arr_conic_traits_2`
  * supports the merging of curves of opposite directions.
  *
- * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  *
  * \cgalHeading{Types}
  */
@@ -438,56 +438,13 @@ public:
     Bbox_2 operator()(const X_monotone_curve_2& xcv) const { return bbox(xcv); }
   };
 
-  /*! \name Auxiliary Functor definitions, used gor, e.g., the landmarks
-   * point-location strategy and the drawing function.
+  /*! \name Auxiliary Functor definitions.
    */
-  //@{
+  /// @{
   typedef double                                        Approximate_number_type;
   typedef CGAL::Cartesian<Approximate_number_type>      Approximate_kernel;
   typedef Approximate_kernel::Point_2                   Approximate_point_2;
-
-  /*! \class Approximate_2
-   * A functor that approximates a point and an \f$x\f$-monotone curve.
-   */
-  class Approximate_2 {
-  public:
-    /*! Obtain an approximation of a point coordinate.
-     * \param p The exact point.
-     * \param i The coordinate index (either 0 or 1).
-     * \pre `i` is either 0 or 1.
-     * \return An approximation of p's \f$x\f$-coordinate (if `i` == 0), or an
-     *         approximation of p's \f$y\f$-coordinate (if `i` == 1).
-     */
-    Approximate_number_type operator()(const Point_2& p, int i) const;
-
-    /*! Obtain an approximation of a point.
-     * \param p The exact point.
-     */
-    Approximate_point_2 operator()(const Point_2& p) const;
-
-    /*! approximates a given \f$x\f$-monotone curve. It computes a sequence of
-     * approximate points that represent an approximate polyline, and inserts
-     * them into an output container given through an output iterator.  The
-     * first and last points in the sequence are always approximations of the
-     * endpoints of the given arc.
-     *
-     * \param oi An output iterator for the output container.
-     * \param error The error bound of the polyline approximation. This is the
-     *        Hausdorff distance between the arc and the polyline that
-     *        approximates the arc.
-     * \param xcv The exact \f$x\f$-monotone arc.
-     * \param l2r A Boolean flag that indicates whether the arc direction is
-     *        left to right.
-     * \return The past-the-end iterator of the output container.
-     *
-     * \pre Dereferencing `oi` must yield an object of type
-     *      `Arr_conic_traits_2::Approximate_point_2`.
-     */
-    template <typename OutputIterator>
-    OutputIterator operator()(OutputIterator oi, double error,
-                              const X_monotone_curve_2& xcv,
-                              bool l2r = true) const;
-  };
+  /// @}
 
   /*! \class Trim_2
    * A functor that trims a conic arc.
@@ -521,9 +478,6 @@ public:
   /*! Obtain a `Trim_2` functor. */
   Trim_2 trim_2_object() const;
 
-  /*! Obtain an `Approximate_2` functor. */
-  Approximate_2 approximate_2_object() const;
-
   /// @}
 }; /* end Arr_conic_traits_2 */
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_geodesic_arc_on_sphere_traits_2.h

@@ -39,7 +39,7 @@ namespace CGAL {
  * normalized vector \f$(x,y)\f$ in the \f$xy\f$-plane that bisects the
  * identification curve.
 
- * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosSphericalBoundaryTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosSphericalBoundaryTraits_2}
  */
 template <typename Kernel, typename X, typename Y>
 class Arr_geodesic_arc_on_sphere_traits_2 {

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_polyline_traits_2.h

@@ -36,9 +36,9 @@ namespace CGAL {
  *   - `AosConstructCurveTraits_2`.
  *
  * If, in addition, the GeometryTraits_2 models the concept
- * `AosApproximatePointTraits_2` then `Arr_polycurve_traits_2` models
- * this concept as well. The same holds for the concept
- * `AosOpenBoundaryTraits_2`. If no type is provided, then
+ * `AosApproximateTraits_2` (or `AosApproximatePointTraits_2`) then
+ * `Arr_polycurve_traits_2` models this concept as well. The same holds for the
+ * concept `AosOpenBoundaryTraits_2`. If no type is provided, then
  * `Arr_segment_traits_2` (instantiated with
  * `Exact_predicates_exact_constructions_kernel` as the kernel) is used.
  * Otherwise,
@@ -77,7 +77,7 @@ namespace CGAL {
  * the macro `CGAL_ALWAYS_LEFT_TO_RIGHT` to 1 before any \cgal header is
  * included.
  *
- * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2,AosConstructXMonotoneCurveTraits_2,AosConstructCurveTraits_2,AosApproximatePointTraits_2
+ * \cgalModels{AosTraits_2,AosDirectionalXMonotoneTraits_2,AosConstructXMonotoneCurveTraits_2,AosConstructCurveTraits_2,AosApproximateTraits_2
  * (if the type that substitutes the template parameter `SegmentTraits_2`
  * models the concept as well)}
  *

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/CGAL/Arr_segment_traits_2.h

@@ -52,7 +52,7 @@ namespace CGAL {
  * same direction as a precondition. Moreover, `Arr_segment_traits_2` supports
  * the merging of curves of opposite directions.
  *
- * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosDirectionalXMonotoneTraits_2}
+ * \cgalModels{AosTraits_2,AosLandmarkTraits_2,AosApproximateTraits_2,AosDirectionalXMonotoneTraits_2}
  */
 template <typename Kernel>
 class Arr_segment_traits_2 : public Kernel {

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosApproximatePointTraits_2.h

@@ -7,6 +7,7 @@
  * \cgalRefines{AosBasicTraits_2}
  *
  * \cgalHasModelsBegin
+ * \cgalHasModels{CGAL::Arr_circle_segment_traits_2<Kernel>}
  * \cgalHasModels{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>}
  * \cgalHasModels{CGAL::Arr_geodesic_arc_on_sphere_traits_2}
  * \cgalHasModels{CGAL::Arr_linear_traits_2<Kernel>}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosApproximateTraits_2.h

@@ -0,0 +1,50 @@
+/*! \ingroup PkgArrangementOnSurface2ConceptsTraits
+ * \cgalConcept
+ *
+ * The concept `AosApproximateTraits_2` refines the concept
+ * `AosApproximatePointTraits_2`. A model of this concept is able to
+ * approximate a point and a curve (in addition to the ability to apprximate the
+ * coordinates of a point).
+ *
+ * \cgalRefines{AosApproximatePointTraits_2}
+ *
+ * \cgalHasModelsBegin
+ * \cgalHasModels{CGAL::Arr_circle_segment_traits_2<Kernel>}
+ * \cgalHasModels{CGAL::Arr_conic_traits_2<RatKernel,AlgKernel,NtTraits>}
+ * \cgalHasModels{CGAL::Arr_geodesic_arc_on_sphere_traits_2}
+ * \cgalHasModels{CGAL::Arr_polyline_traits_2<SegmentTraits_2>}
+ * \cgalHasModels{CGAL::Arr_segment_traits_2<Kernel>}
+ * \cgalHasModelsEnd
+ *
+ * \sa `AosApproximatePointTraits_2`
+ * \sa `draw()`
+ */
+class AosApproximateTraits_2 {
+public:
+  /// \name Types
+  /// @{
+
+  //! the approximate kernel.
+  typedef unspecified_type Approximate_kernel;
+
+  //! the approximate point.
+  typedef unspecified_type Approximate_point_2;
+
+  /// @}
+
+  /// \name Functor Types
+  /// @{
+
+  /// models the concept `AosTraits::Approximate_2`.
+  typedef unspecified_type Approximate_2;
+
+  /// @}
+
+  /// \name Accessing Functor Objects
+  /// @{
+
+  ///
+  Approximate_2 approximate_2_object() const;
+
+  /// @}
+}

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/Concepts/AosTraits--Approximate_2.h

@@ -7,6 +7,7 @@ namespace AosTraits {
  *
  * \cgalHasModelsBegin
  * \cgalHasModels{AosApproximatePointTraits_2::Approximate_2}
+ * \cgalHasModels{AosApproximateTraits_2::Approximate_2}
  * \cgalHasModelsEnd
  */
 class Approximate_2 {
@@ -17,9 +18,36 @@ public:
 
   /*! obtains an approximation of `p`'s \f$x\f$-coordinate (if `i == 0`), or of
    * `p`'s \f$y\f$-coordinate (if `i == 1`).
+   * \pre `i` is either 0 or 1.
    */
   CGAL::Approximate_number_type operator()(AosTraits::Point_2 p, int i);
 
+  /*! obtains an approximation of `p`.
+   */
+  CGAL::Approximate_point_2 operator()(AosTraits::Point_2 p);
+
+  /*! approximates a given \f$x\f$-monotone curve. It computes a sequence of
+   * approximate points that represent an approximate polyline, and inserts
+   * them into an output container given through an output iterator.  The
+   * first and last points in the sequence are always approximations of the
+   * endpoints of the given curve.
+   *
+   * \param xcv The exact \f$x\f$-monotone curve.
+   * \param error The error bound of the polyline approximation. This is the
+   *        Hausdorff distance between the curve and the polyline that
+   *        approximates the curve.
+   * \param oi An output iterator for the output container.
+   * \param l2r A Boolean flag that indicates whether the curve direction is
+   *        left to right.
+   * \return The past-the-end iterator of the output container.
+   *
+   * \pre Dereferencing `oi` must yield an object of type
+   *      `Arr_conic_traits_2::Approximate_point_2`.
+   */
+  template <typename OutputIterator>
+  OutputIterator operator()(const X_monotone_curve_2& xcv, double error,
+                            OutputIterator oi, bool l2r = true) const;
+
   /// @}
 }; /* end AosTraits::Approximate_2 */
 

Arrangement_on_surface_2/doc/Arrangement_on_surface_2/PackageDescription.txt

@@ -112,6 +112,7 @@ implemented as peripheral classes or as free (global) functions.
 
 \cgalCRPSection{Concepts}
 
+- `AosApproximateTraits_2`
 - `AosApproximatePointTraits_2`
 - `AosBasicTopologyTraits`
 - `AosBasicTraits_2`
@@ -166,32 +167,32 @@ implemented as peripheral classes or as free (global) functions.
 
 \cgalCRPSection{Function Object Concepts}
 
+- `AosTraits::Approximate_2`
+- `AosTraits::AreMergeable_2`
 - `AosTraits::CompareX_2`
 - `AosTraits::CompareXy_2`
-- `AosTraits::ConstructMinVertex_2`
-- `AosTraits::ConstructMaxVertex_2`
-- `AosTraits::IsVertical_2`
-- `AosTraits::IsOnXIdentification_2`
-- `AosTraits::IsOnYIdentification_2`
 - `AosTraits::CompareYAtX_2`
 - `AosTraits::CompareYAtXLeft_2`
 - `AosTraits::CompareYAtXRight_2`
-- `AosTraits::Equal_2`
-- `AosTraits::ParameterSpaceInX_2`
-- `AosTraits::ParameterSpaceInY_2`
+- `AosTraits::ConstructMinVertex_2`
+- `AosTraits::ConstructMaxVertex_2`
 - `AosTraits::CompareXOnBoundary_2`
 - `AosTraits::CompareYOnBoundary_2`
 - `AosTraits::CompareXNearBoundary_2`
 - `AosTraits::CompareYNearBoundary_2`
 - `AosTraits::CompareXOnBoundaryOfCurveEnd_2`
-- `AosTraits::Intersect_2`
-- `AosTraits::Split_2`
-- `AosTraits::AreMergeable_2`
-- `AosTraits::Merge_2`
-- `AosTraits::MakeXMonotone_2`
-- `AosTraits::Approximate_2`
-- `AosTraits::ConstructXMonotoneCurve_2`
 - `AosTraits::ConstructCurve_2`
+- `AosTraits::ConstructXMonotoneCurve_2`
+- `AosTraits::Equal_2`
+- `AosTraits::Intersect_2`
+- `AosTraits::IsVertical_2`
+- `AosTraits::IsOnXIdentification_2`
+- `AosTraits::IsOnYIdentification_2`
+- `AosTraits::MakeXMonotone_2`
+- `AosTraits::Merge_2`
+- `AosTraits::ParameterSpaceInX_2`
+- `AosTraits::ParameterSpaceInY_2`
+- `AosTraits::Split_2`
 
 \cgalCRPSection{Classes}