CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge Class Reference

#include <CGAL/Nef_polyhedron_3.h>

Definition

template<class Nef_polyhedronTraits_3, class Nef_polyhedronItems_3 = CGAL::Default_items<Nef_polyhedronTraits_3> class Nef_polyhedronMarks = bool>
class CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::Halfedge

A Halfedge has a double meaning.

In the global incidence structure of a Nef_polyhedron_3 it is an oriented edge going from one vertex to another. A halfedge also coincides with an svertex of the sphere map of its source vertex. Because of this, we offer the types Halfedge and SVertex which are the same. Furthermore, the redundant functions center_vertex() and source() are provided. The reason is, that we get the same vertex either if we want to have the source vertex of a halfedge, or if we want to have the vertex in the center of the sphere map a svertex lies on. Figures figureNef3HalfedgeIncidences and figureNef3FacetIncidences illustrate the incidence of a svertex on a sphere map and of a halfedge in the global structure.

As part of the global incidence structure, the member fuctions source and target return the source and target vertex of an edge. The member function twin() returns the opposite halfedge.

Looking at the incidence structure on a sphere map, the member function out_sedge returns the first outgoing shalfedge, and incident_sface returns the incident sface.

Creation

There is no need for a user to create a Halfedge explicitly. The class Nef_polyhedron_3<Traits> manages the needed halfedges internally.

See Also

CGAL::Nef_polyhedron_3::Vertex

CGAL::Nef_polyhedron_3::SHalfedge

CGAL::Nef_polyhedron_3::SFace

CGAL::Nef_polyhedron_S2::Sphere_point

Types
The following types are the same as in Nef_polyhedron_3<Traits>.
typedef unspecified_type	Mark
	type of mark.
typedef unspecified_type	Sphere_point
	sphere point type stored in Halfedge.
typedef unspecified_type	Vertex_const_handle
	const handle to vertex.
typedef unspecified_type	Halfedge_const_handle
	const handle to halfedge.
typedef unspecified_type	SHalfedge_const_handle
	const handle to SHalfedge.
typedef unspecified_type	SFace_const_handle
	const handle to SFace.

Operations
const Mark &	mark () const
	the mark of e .
const Sphere_point &	point () const
	the sphere point of e .
bool	is_isolated () const
	returns |true| if e has no adjacent sedges.
Vertex_const_handle	center_vertex () const
	the center vertex of the sphere map e belongs to.
Vertex_const_handle	source () const
	the source vertex of e .
Vertex_const_handle	target () const
	the target vertex e.
Halfedge_const_handle	twin () const
	the twin of e .
SHalfedge_const_handle	out_sedge () const
	the first out sedge of e .
SFace_const_handle	incident_sface () const
	the incident sface of e .