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  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.
bool	v.is_trivalent () const
		returns true if the vertex has exactly three incident edges.

See Also

CGAL::Polyhedron_3<Traits>::Halfedge
CGAL::Polyhedron_3<Traits>::Facet
CGAL::Polyhedron_3<Traits>