CGAL 5.3  3D Boolean Operations on Nef Polyhedra

#include <CGAL/Nef_polyhedron_3.h>
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.
Types  
The following types are the same as in  
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 .  