CGAL::Polyhedron_3< Traits >::Vertex Class Reference

#include <CGAL/Polyhedron_3.h>

Definition

A vertex optionally stores a point and a reference to an incident halfedge that points to the vertex.

Type tags indicate whether these member functions are supported. Figure figurePolyOptionalMethods depicts the relationship between a halfedge and its incident halfedges, vertices, and facets. The circulator is assignable to the Halfedge_handle. The circulator is bidirectional if the halfedge provided to the polyhedron with the Items template argument provides a member function Halfedge::prev(), otherwise it is of the forward category.

See Also

CGAL::Polyhedron_3::Halfedge

CGAL::Polyhedron_3::Facet

CGAL::Polyhedron_3<Traits>

Types
typedef unspecified_type	Halfedge
	type of incident halfedges. More...
typedef unspecified_type	Facet
	type of incident facets. More...
typedef unspecified_type	Point_3
	point type stored in vertices. More...
typedef unspecified_type	Vertex_handle
	handle to vertex. More...
typedef unspecified_type	Halfedge_handle
	handle to halfedge. More...
typedef unspecified_type	Facet_handle
	handle to facet. More...
typedef unspecified_type	Halfedge_around_vertex_circulator
	circulator of halfedges around a vertex. More...
typedef unspecified_type	Vertex_const_handle
typedef unspecified_type	Halfedge_const_handle
typedef unspecified_type	Facet_const_handle
typedef unspecified_type	Halfedge_around_vertex_const_circulator
typedef unspecified_type	Supports_vertex_halfedge
	\( \equiv\) CGAL::Tag_true or CGAL::Tag_false. More...
typedef unspecified_type	Supports_vertex_point
	\( \equiv\) CGAL::Tag_true or CGAL::Tag_false. More...

Creation
	Vertex ()
	default constructor. More...
	Vertex (const Point &p)
	vertex initialized with a point. More...

Operations available if Supports_vertex_point is CGAL::Tag_true
Point_3 &	point ()
const Point_3 &	point () const
	the point. More...

Operations available if Supports_vertex_halfedge is CGAL::Tag_true
Halfedge_handle	halfedge ()
Halfedge_const_handle	halfedge () const
	an incident halfedge that points to v. More...
Halfedge_around_vertex_circulator	vertex_begin ()
Halfedge_around_vertex_const_circulator	vertex_begin () const
	circulator of halfedges around the vertex (clockwise). More...
void	set_halfedge (Halfedge_handle h)
	sets incident halfedge to h. More...
std::size_t	vertex_degree () const
	the degree of the vertex, i.e., number of edges emanating from this vertex. More...
bool	is_bivalent () const
	returns true if the vertex has exactly two incident edges. More...
bool	is_trivalent () const
	returns true if the vertex has exactly three incident edges. More...

Member Typedef Documentation

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Facet

type of incident facets.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Facet_const_handle

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Facet_handle

handle to facet.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Halfedge

type of incident halfedges.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Halfedge_around_vertex_circulator

circulator of halfedges around a vertex.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Halfedge_around_vertex_const_circulator

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Halfedge_const_handle

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Halfedge_handle

handle to halfedge.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Point_3

point type stored in vertices.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Supports_vertex_halfedge

\( \equiv\) CGAL::Tag_true or CGAL::Tag_false.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Supports_vertex_point

\( \equiv\) CGAL::Tag_true or CGAL::Tag_false.

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Vertex_const_handle

template<typename Traits >

typedef unspecified_type CGAL::Polyhedron_3< Traits >::Vertex::Vertex_handle

handle to vertex.

Constructor & Destructor Documentation

template<typename Traits >

CGAL::Polyhedron_3< Traits >::Vertex::Vertex

(

)

default constructor.

template<typename Traits >

CGAL::Polyhedron_3< Traits >::Vertex::Vertex

(

const Point &

p

)

vertex initialized with a point.

Member Function Documentation

template<typename Traits >

Halfedge_handle CGAL::Polyhedron_3< Traits >::Vertex::halfedge

(

)

template<typename Traits >

Halfedge_const_handle CGAL::Polyhedron_3< Traits >::Vertex::halfedge

(

)

const

an incident halfedge that points to v.

template<typename Traits >

bool CGAL::Polyhedron_3< Traits >::Vertex::is_bivalent

(

)

const

returns true if the vertex has exactly two incident edges.

template<typename Traits >

bool CGAL::Polyhedron_3< Traits >::Vertex::is_trivalent

(

)

const

returns true if the vertex has exactly three incident edges.

template<typename Traits >

Point_3& CGAL::Polyhedron_3< Traits >::Vertex::point

(

)

template<typename Traits >

const Point_3& CGAL::Polyhedron_3< Traits >::Vertex::point

(

)

const

the point.

template<typename Traits >

void CGAL::Polyhedron_3< Traits >::Vertex::set_halfedge

(

Halfedge_handle

h

)

sets incident halfedge to h.

Precondition

h is incident, i.e., h->vertex() == v.

template<typename Traits >

Halfedge_around_vertex_circulator CGAL::Polyhedron_3< Traits >::Vertex::vertex_begin

(

)

template<typename Traits >

Halfedge_around_vertex_const_circulator CGAL::Polyhedron_3< Traits >::Vertex::vertex_begin

(

)

const

circulator of halfedges around the vertex (clockwise).

template<typename Traits >

std::size_t CGAL::Polyhedron_3< Traits >::Vertex::vertex_degree

(

)

const

the degree of the vertex, i.e., number of edges emanating from this vertex.