\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.3 - CGAL and the Boost Graph Library

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boost::graph_traits< CGAL::Polyhedron_3< T > > Class Template Reference
Traits Classes

`#include <CGAL/boost/graph/graph_traits_Polyhedron_3.h>`

## Definition

The class `graph_traits` is a partial specialization of `boost::graph_traits` for the class `CGAL::Polyhedron_3`.

It provides the types associated to the graph concepts `BidirectionalGraph` and `EdgeAndVertexListGraph`.

The const specialization, `boost::graph_traits< CGAL::Polyhedron_3<Traits> const>` is also defined, using the constant handles in the polyhedron.

## Types
typedef unspecified_type | vertex_iterator
| An iterator corresponding to `CGAL::Polyhedron_3::Vertex_iterator`, with the difference that its value type is a vertex descriptor and not `CGAL::Polyhedron_3::Vertex`.
typedef unspecified_type | edge_iterator
| An iterator corresponding to `CGAL::Polyhedron_3::Halfedge_iterator` with the difference that its value type is an edge descriptor and not `CGAL::Polyhedron_3::Halfedge`.
typedef unspecified_type | in_edge_iterator
| An edge iterator which only iterates over the incoming edges around a vertex. More...
typedef unspecified_type | out_edge_iterator
| An edge iterator which only iterates over the outgoing halfedges around a vertex. More...
CGAL::Polyhedron_3::Vertex_handle | vertex_descriptor
| The vertex descriptor.
CGAL::Polyhedron_3::Halfedge_handle | edge_descriptor
| The edge descriptor.
boost::disallow_parallel_edge_tag | edge_parallel_category
| Indicates that this graph does not support multiedges.
boost::bidirectional_graph_tag | traversal_category
| Indicates that this graph is bidirectional.
Polyhedron_3::size_type | vertices_size_type
| The size type of the vertex list.
Polyhedron_3::size_type | edges_size_type
| The size type of the edge list.
Polyhedron_3::size_type | degree_size_type
| The size type of the adjacency list.

## Member Typedef Documentation

template<typename T >

typedef unspecified_type boost::graph_traits< CGAL::Polyhedron_3< T > >::in_edge_iterator

An edge iterator which only iterates over the incoming edges around a vertex.

It corresponds to a `CGAL::Polyhedron_3::Halfedge_around_vertex_circulator` with the difference that its value type is an edge descriptor and not `CGAL::Polyhedron_3::Halfedge`.

template<typename T >

typedef unspecified_type boost::graph_traits< CGAL::Polyhedron_3< T > >::out_edge_iterator

An edge iterator which only iterates over the outgoing halfedges around a vertex.

It corresponds to a `CGAL::Polyhedron_3::Halfedge_around_vertex_circulator` with the difference that its value type is an edge descriptor and not `CGAL::Polyhedron_3::Halfedge`.