CGAL 4.7 - 2D Boolean Operations on Nef Polygons Embedded on the Sphere
CGAL::Nef_polyhedron_S2< Traits >::SHalfedge Class Reference

#include <CGAL/Nef_polyhedron_S2.h>

## Definition

A shalfedge is a great arc on a sphere map.

The figure below 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.

Incidences of an SHalfedge
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.

A const circulator is provided for each of the two 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_S2<Traits> manages the needed shalfedges internally.

CGAL::Nef_polyhedron_S2::SVertex
CGAL::Nef_polyhedron_S2::SFace
CGAL::Nef_polyhedron_S2::Sphere_circle

## Types

The following types are the same as in Nef_polyhedron_S2<Traits>.

typedef unspecified_type Mark
type of mark.

typedef unspecified_type Sphere_circle
sphere circle type stored in SHalfedge.

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 Markmark () const
the mark of the sedge.

const Sphere_circlecircle () const
the sphere circle of the sedge.

SHalfedge_const_handle twin () const
the twin of the sedge.

SVertex_const_handle source () const
the source svertex of the sedge.

SVertex_const_handle target () const
equals twin()->source().

SHalfedge_const_handle sprev () const
the SHalfedge previous to the sedge in a sface cycle.

SHalfedge_const_handle snext () const
the next SHalfedge of the sedge in a sface cycle.

the edge before the sedge in the cyclic ordered adjacency list of source().
the edge after the sedge in the cyclic ordered adjacency list of source().
the incident sface of the sedge.
determines whether the sedge is in an outer sface cycle.
determines whether the sedge is in an inner sface cycle.