HalfedgeDSHalfedge Concept Reference

Definition

The concept HalfedgeDSHalfedge defines the requirements for the local Halfedge type in the HalfedgeDS concept. It is also required in the Halfedge_wrapper<Refs,Traits> member class template of an items class, see the HalfedgeDSItems concept.

A halfedge is an oriented edge between two vertices. It is always paired with a halfedge pointing in the opposite direction. The opposite() member function returns this halfedge of opposite orientation. The next() member function points to the successor halfedge along the face - or if the halfedge is a border halfedge - along the open region. A halfedge optionally stores a reference to the previous halfedge along the face, a reference to an incident vertex, and a reference to an incident face. Type tags indicate whether the related member functions are supported. Figure figureHalfedgeDSOptionalMethods depicts the relationship between a halfedge and its incident halfedges, vertices, and faces.

The three classes Vertex, Halfedge, and Face of the halfedge data structure. Member functions with shaded background are mandatory. The others are optionally supported.

For the protection of the integrity of the data structure classes such as CGAL::Polyhedron_3 are allowed to redefine the modifying member functions to be private. In order to make them accessible for the halfedge data structure they must be derived from a base class Base where the modifying member functions are still public. Even more protection is provided for the set_opposite() member function. The base class Base_base provides access to it. (The protection could be bypassed also by an user, but not by accident.)

Has Models:

CGAL::HalfedgeDS_halfedge_base

CGAL::HalfedgeDS_halfedge_min_base

See also

HalfedgeDS<Traits,Items,Alloc>

HalfedgeDSItems

HalfedgeDSVertex

HalfedgeDSFace

Types
typedef unspecified_type	HalfedgeDS
	instantiated HalfedgeDS ( \( \equiv\) Refs).
typedef unspecified_type	Base
	base class that allows modifications.
typedef unspecified_type	Base_base
	base class to access set_opposite().
typedef unspecified_type	Vertex
	model of HalfedgeDSVertex.
typedef unspecified_type	Face
	model of HalfedgeDSFace.
typedef unspecified_type	Vertex_handle
	handle to vertex.
typedef unspecified_type	Halfedge_handle
	handle to halfedge.
typedef unspecified_type	Face_handle
	handle to face.
typedef unspecified_type	Vertex_const_handle
typedef unspecified_type	Halfedge_const_handle
typedef unspecified_type	Face_const_handle
typedef unspecified_type	Supports_halfedge_prev
	CGAL::Tag_true or CGAL::Tag_false.
typedef unspecified_type	Supports_halfedge_vertex
	CGAL::Tag_true or CGAL::Tag_false.
typedef unspecified_type	Supports_halfedge_face
	CGAL::Tag_true or CGAL::Tag_false.

Creation
	Halfedge ()
	default constructor.

Operations
Halfedge_handle	opposite ()
Halfedge_const_handle	opposite () const
	the opposite halfedge.
void	set_opposite (Halfedge_handle h)
	sets opposite halfedge to h.
Halfedge_handle	next ()
Halfedge_const_handle	next () const
	the next halfedge around the face.
void	set_next (Halfedge_handle h)
	sets next halfedge to h.
bool	is_border () const
	is true if the halfedge is a border halfedge.

Operations available if Supports_halfedge_prev == CGAL::Tag_true
Halfedge_handle	prev ()
Halfedge_const_handle	prev () const
	the previous halfedge around the face.
void	set_prev (Halfedge_handle h)
	sets prev halfedge to h.

Operations available if Supports_halfedge_vertex == CGAL::Tag_true
Vertex_handle	vertex ()
Vertex_const_handle	vertex () const
	the incident vertex of h.
void	set_vertex (Vertex_handle v)
	sets incident vertex to v.

Operations available if Supports_halfedge_face == CGAL::Tag_true
Face_handle	face ()
Face_const_handle	face () const
	the incident face of the halfedge.
void	set_face (Face_handle f)
	sets incident face to f.

Member Function Documentation

face()

Face_const_handle HalfedgeDSHalfedge::face

(

)

const

the incident face of the halfedge.

If the halfedge is a border halfedge the result is default construction of the handle.