CGAL::Nef_polyhedron_3< Nef_polyhedronTraits_3, Nef_polyhedronItems_3 >::SHalfedge 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 >::SHalfedge

A shalfedge is a great arc on a sphere map.

Figure figureNef3HalfedgeIncidences depicts the relationship between a shalfedge and its incident shalfedges, svertices, and sfaces on a sphere map. A shalfedge is an oriented sedge between two svertices. It is always paired with a shalfedge pointing in the opposite direction. The twin() member function returns this shalfedge of opposite orientation.

The snext() member function points to the successor shalfedge around this sface while the sprev() member function points to the preceding shalfedge. An successive assignments of the form se = se->snext() cycles counterclockwise around the sface (or hole).

Similarly, the successive assignments of the form se = se->snext()->twin() cycle clockwise around the svertex and traverse all halfedges incident to this svertex. The assignment se = se->cyclic_adj_succ() can be used as a shortcut.

The role of shalfedges in a facet is illustrated in Figure figureNef3FacetIncidences. The facet() member function returns the facet in which the shalfedge is part of one of the facet cycles. The successive assignment of the form se = se->next() cycles counterclockwise around the facet (or a hole of the facet).

A const circulators is provided for each of the three circular orders. The circulators are bidirectional and assignable to SHalfedge_const_handle.

Creation

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

See also

CGAL::Nef_polyhedron_3::Halfedge

CGAL::Nef_polyhedron_3::Halffacet

CGAL::Nef_polyhedron_3::SFace

CGAL::Nef_polyhedron_S2::Sphere_circle

Types
The following types are the same as in Nef_polyhedron_3<Traits>.
typedef unspecified_type	Mark
	type of mark.
typedef unspecified_type	Sphere_circle
	sphere circle type stored in SHalfedge.
typedef unspecified_type	Halffacet_const_handle
	const handle to Halffacet.
typedef unspecified_type	SVertex_const_handle
	const handle to SVertex.
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 se .
const Sphere_circle &	circle () const
	the sphere circle of se .
SHalfedge_const_handle	twin () const
	the twin of se .
SVertex_const_handle	source () const
	the source svertex of se .
SVertex_const_handle	target () const
	equals twin()->source().
SHalfedge_const_handle	prev () const
	the SHalfedge previous to se in a facet cycle.
SHalfedge_const_handle	next () const
	the next SHalfedge of se in a facet cycle.
SHalfedge_const_handle	sprev () const
	the SHalfedge previous to se in a sface cycle.
SHalfedge_const_handle	snext () const
	the next SHalfedge of se in a sface cycle.
SHalfedge_const_handle	cyclic_adj_pred () const
	the edge before se in the cyclic ordered adjacency list of source().
SHalfedge_const_handle	cyclic_adj_succ () const
	the edge after se in the cyclic ordered adjacency list of source().
Halffacet_const_handle	facet () const
	the facet that corresponds to se in the 3D incidence structure.
SFace_const_handle	incident_sface () const
	the incident sface of se .
bool	in_outer_sface_cycle () const
	determines whether se is in an outer sface cycle.
bool	in_inner_sface_cycle () const
	determines whether se is in an inner sface cycle.
bool	in_outer_facet_cycle () const
	determines whether se is in an outer facet cycle.
bool	in_inner_facet_cycle () const
	determines whether se is in an inner facet cycle.