#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, and Arrangement_on_surface_2/polycurve_geodesic.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.

Definition

Types

Creation

Accessors

Constructor & Destructor Documentation

◆ Arr_spherical_topology_traits_2()