Polyhedron_3<Traits>::Vertex

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CGAL::Polyhedron_3<Traits>::Vertex

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 23.1 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 prev(), otherwise it is of the forward category.

#include <CGAL/Polyhedron_3.h>

Types

Polyhedron_3<Traits>::Vertex::Halfedge
	type of incident halfedges.
Polyhedron_3<Traits>::Vertex::Facet
	type of incident facets.
Polyhedron_3<Traits>::Vertex::Point_3
	point type stored in vertices.

Polyhedron_3<Traits>::Vertex::Vertex_handle
	handle to vertex.
Polyhedron_3<Traits>::Vertex::Halfedge_handle
	handle to halfedge.
Polyhedron_3<Traits>::Vertex::Facet_handle
	handle to facet.
Polyhedron_3<Traits>::Vertex::Halfedge_around_vertex_circulator
	circulator of halfedges around a vertex.

Polyhedron_3<Traits>::Vertex::Vertex_const_handle
Polyhedron_3<Traits>::Vertex::Halfedge_const_handle
Polyhedron_3<Traits>::Vertex::Facet_const_handle
Polyhedron_3<Traits>::Vertex::Halfedge_around_vertex_const_circulator

Polyhedron_3<Traits>::Vertex::Supports_vertex_halfedge
	≡ CGAL::Tag_true or CGAL::Tag_false.
Polyhedron_3<Traits>::Vertex::Supports_vertex_point
	≡ CGAL::Tag_true or CGAL::Tag_false.

Creation

Polyhedron_3<Traits>::Vertex v;
	default constructor.
Polyhedron_3<Traits>::Vertex v ( Point p);
	vertex initialized with a point.

Operations available if Supports_vertex_point ≡ CGAL::Tag_true

Point_3&	v.point ()
const Point_3&	v.point () const	the point.

Operations available if Supports_vertex_halfedge ≡ CGAL::Tag_true

Halfedge_handle

v.halfedge ()

Halfedge_const_handle

v.halfedge () const

an incident halfedge that points to v.

Halfedge_around_vertex_circulator

v.vertex_begin ()

Halfedge_around_vertex_const_circulator

v.vertex_begin () const

circulator of halfedges around the vertex (clockwise).

void

v.set_halfedge ( Halfedge_handle h)

sets incident halfedge to h.

Precondition:

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

std::size_t

v.vertex_degree () const

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

bool

v.is_bivalent () const

returns true if the vertex has exactly two incident edges.