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

#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).

Member Typedef Documentation

Face

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

typedef Dcel::Face CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Face

Halfedge

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

typedef Dcel::Halfedge CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Halfedge

Inner_ccb

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

typedef Dcel::Inner_ccb CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Inner_ccb

Isolated_vertex

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

typedef Dcel::Isolated_vertex CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Isolated_vertex

Outer_ccb

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

typedef Dcel::Outer_ccb CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Outer_ccb

Point_2

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

typedef GeometryTraits_2::Point_2 CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Point_2

Size

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

typedef Dcel::Size CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Size

Vertex

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

typedef Dcel::Vertex CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::Vertex

X_monotone_curve_2

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

typedef GeometryTraits_2::X_monotone_curve_2 CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::X_monotone_curve_2

Constructor & Destructor Documentation

Arr_spherical_topology_traits_2() [1/2]

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

(

)

constructs default

Arr_spherical_topology_traits_2() [2/2]

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.

Member Function Documentation

dcel() [1/2]

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

Dcel & CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::dcel

(

)

obtains the DCEL (non-const version).

dcel() [2/2]

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

const Dcel & CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::dcel

(

)

const

obtains the DCEL (const version).

discontinuity_vertex() [1/2]

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

Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::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).

discontinuity_vertex() [2/2]

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

const Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::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).

north_pole() [1/2]

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

Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::north_pole

(

)

obtains the north pole (non-const version).

north_pole() [2/2]

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

const Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::north_pole

(

)

const

obtains the north pole (const version).

south_pole() [1/2]

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

Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::south_pole

(

)

obtains the south pole (non-const version).

south_pole() [2/2]

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

const Vertex * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::south_pole

(

)

const

obtains the south pole (const version).

spherical_face() [1/2]

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

Face * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::spherical_face

(

)

obtains the spherical face (non-const version).

spherical_face() [2/2]

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

const Face * CGAL::Arr_spherical_topology_traits_2< GeometryTraits_2, Dcel >::spherical_face

(

)

const

obtains the spherical face (const version).