CGAL 6.1.2 - 2D Arrangements: CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel > Class Template Reference

CGAL 6.1.2 - 2D Arrangements

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CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel > Class Template Reference
Reference Manual

`#include <CGAL/Arr_spherical_topology_traits_2.h>`

## Definition

template<typename GeometryTraits_2, typename Dcel = Arr_default_dcel<GeometryTraits_2>>
class CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >

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:

- The `GeometryTraits_2` template-parameter should be substituted by a model of the `AosBasicTraits_2` concept. The traits class defines the types of \(x\)-monotone curves and two-dimensional points, namely `AosBasicTraits_2::X_monotone_curve_2` and `AosBasicTraits_2::Point_2`, respectively, and supports basic geometric predicates on them.
- The `Dcel` template-parameter should be substituted by a class that is a model of the `AosDcel` concept. The value of this parameter is by default `Arr_default_dcel<Traits>`.

Is model of
  `AosBasicTopologyTraits`

See also
  `Arr_default_dcel<Traits>`
  `CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel,x,y>`

Examples
  Arrangement_on_surface_2/count_and_trace.cpp.

## Types
typedef GeometryTraits_2::Point_2 | Point_2
typedef GeometryTraits_2::X_monotone_curve_2 | X_monotone_curve_2
typedef Dcel::Size | Size
typedef Dcel::Vertex | Vertex
typedef Dcel::Halfedge | Halfedge
typedef Dcel::Face | Face
typedef Dcel::Outer_ccb | Outer_ccb
typedef Dcel::Inner_ccb | Inner_ccb
typedef Dcel::Isolated_vertex | Isolated_vertex

## Creation
| Arr_spherical_topology_traits_2 ()
| constructs default
| Arr_spherical_topology_traits_2 (const GeometryTraits_2 *traits)
| constructs from a geometry-traits object.

## Accessors
const Dcel & | dcel () const
| obtains the DCEL (const version).
Dcel & | dcel ()
| obtains the DCEL (non-const version).
const Face * | spherical_face () const
| obtains the spherical face (const version).
Face * | spherical_face ()
| obtains the spherical face (non-const version).
const Vertex * | south_pole () const
| obtains the south pole (const version).
Vertex * | south_pole ()
| obtains the south pole (non-const version).
const Vertex * | north_pole () const
| obtains the north pole (const version).
Vertex * | north_pole ()
| obtains the north pole (non-const version).
const Vertex * | discontinuity_vertex (const Point_2 &pt) const
| obtains 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)
| obtains a vertex on the line of discontinuity that corresponds to the given point (or return NULL if no such vertex exists).

## Constructor & Destructor Documentation

## ◆ Arr_spherical_topology_traits_2()

template<typename GeometryTraits_2 , typename Dcel = Arr_default_dcel<GeometryTraits_2>>

CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Arr_spherical_topology_traits_2 | ( | const GeometryTraits_2 * | traits | ) |

constructs from a geometry-traits object.

Parameters

  traits | the traits.