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CGAL 4.8 - CGAL and the Boost Graph Library

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Specializations of boost::graph_traits
CGAL and the Boost Graph Library Reference

Bgl defines the class template `boost::graph_traits` as a uniform interface to the properties and types of graph types.

We provide specializations of this class template for several CGAL data structures.

# Specialization for the Surface_mesh Class

Defined in `<CGAL/boost/graph/graph_traits_Surface_mesh.h>`

We provide partial specialization for the class `CGAL::Surface_mesh` so that it is a model of the graph concepts `BidirectionalGraph` and `EdgeAndVertexListGraph` and of the concept `MutableFaceGraph`.

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

The traits class `boost::graph_traits< CGAL::Surface_mesh<T> >` provides the following types:

Member | Value | Description
--- | --- | ---
`vertex_descriptor` | `Surface_mesh::Vertex_index` | The vertex descriptor
`edge_descriptor` | `Surface_mesh::Edge_index` | The edge descriptor
`halfedge_descriptor` | `Surface_mesh::Halfedge_index` | The halfedge descriptor
`face_descriptor` | `Surface_mesh::Face_index` | The face descriptor
`adjacency_iterator` | `CGAL::Vertex_around_target_iterator<Surface_mesh<P> >` | Iterates through adjacent vertices
`out_edge_iterator` | `CGAL::Out_edge_iterator<Surface_mesh<P> >` | Iterate through the out-edges of a vertex.
`in_edge_iterator` | `CGAL::Out_edge_iterator<Surface_mesh<P> >` | Iterate through the in-edges of a vertex.
`vertex_iterator` | `Surface_mesh::Vertex_iterator` | Iterate through the vertices of a polyhedron.
`edge_iterator` | `Surface_mesh::Edge_iterator` | Iterate through the edges of a polyhedron.
`halfedge_iterator` | `Surface_mesh::Halfedge_iterator` | Iterate through the halfedges of a polyhedron.
`face_iterator` | `Surface_mesh::Face_iterator` | Iterate through the faces of a polyhedron.
`directed_category` | Inherits from `boost::bidirectional_graph_tag`, `boost::vertex_list_graph_tag` and `boost::edge_list_graph_tag` |
`edge_parallel_category` | `boost::disallow_parallel_edge_tag` | Indicates that this graph does not support multiedges
`traversal_category` | `boost::bidirectional_graph_tag` | Indicates that this graph is bidirectional
`vertices_size_type` | `Surface_mesh::vertices_size_type` | The size type of the vertex list
`edges_size_type` | `Surface_mesh::edges_size_type` | The size type of the edge list
`degree_size_type` | `Surface_mesh::degree_size_type` | The size type of the adjacency list

# Specialization for the Polyhedron Class

Defined in `<CGAL/boost/graph/graph_traits_Polyhedron_3.h>`

We provide partial specialization for the class `CGAL::Polyhedron_3` so that it is a model of the graph concepts `BidirectionalGraph` and `EdgeAndVertexListGraph` and of the concept `MutableFaceGraph`.

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

The traits class `boost::graph_traits< CGAL::Polyhedron_3<T> >` provides the following types:

Member | Value | Description
--- | --- | ---
`vertex_descriptor` | `Polyhedron_3::Vertex_handle` | The vertex descriptor
`edge_descriptor` | `unspecified_type` | The edge descriptor
`halfedge_descriptor` | `Polyhedron_3::Halfedge_handle` | The halfedge descriptor
`face_descriptor` | `Polyhedron_3::Face_handle` | The face descriptor
`adjacency_iterator` | `CGAL::Vertex_around_target_iterator<Polyhedron_3<T> >` | Iterates through adjacent vertices
`out_edge_iterator` | `CGAL::Out_edge_iterator<Polyhedron_3<T> >` | Iterate through the out-edges of a vertex.
`in_edge_iterator` | `CGAL::Out_edge_iterator<Polyhedron_3<T> >` | Iterate through the in-edges of a vertex.
`vertex_iterator` | `unspecified_type` | Iterate through the vertices of a polyhedron.
`edge_iterator` | `unspecified_type` | Iterate through the edges of a polyhedron.
`halfedge_iterator` | `Polyhedron_3::Halfedge_iterator` | Iterate through the halfedges of a polyhedron.
`face_iterator` | `Polyhedron_3::Face_iterator` | Iterate through the faces of a polyhedron.
`directed_category` | Inherits from `boost::bidirectional_graph_tag`, `boost::vertex_list_graph_tag` and `boost::edge_list_graph_tag` |
`edge_parallel_category` | `boost::disallow_parallel_edge_tag` | Indicates that this graph does not support multiedges
`traversal_category` | `boost::bidirectional_graph_tag` | Indicates that this graph is bidirectional
`vertices_size_type` | `Polyhedron_3::size_type` | The size type of the vertex list
`edges_size_type` | `Polyhedron_3::size_type` | The size type of the edge list
`degree_size_type` | `Polyhedron_3::size_type` | The size type of the adjacency list

For convenience, the type `edge_descriptor` is hashable using the functor `CGAL::Handle_hash_function` that is the default hash functor of `CGAL::Unique_hash_map`.

# Specializations for the 2D Triangulation Classes

Defined in `<CGAL/boost/graph/graph_traits_Triangulation_2.h>` and `<CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>`

We provide partial specialization for the classes `CGAL::Triangulation_2` and `CGAL::Delaunay_triangulation_2` so that they are model of the graph concepts `BidirectionalGraph` and `EdgeAndVertexListGraph`.

The mapping between vertices and edges of the triangulation and the graph is rather straightforward, but there are some subtleties. The value type of the Bgl iterators is the vertex or edge descriptor, whereas in CGAL all iterators and circulators are also handles and hence have as value type Vertex or Edge.

The graph traits class for triangulations does not distinguish between finite and infinite vertices and edges. As the edge weight computed with the default property map of Bgl algorithms (obtained with `get(t, boost::edge_weight)`) is the length of the edge, the edge weight is not well defined for infinite edges. For algorithms that make use of the edge weight the user must therefore define a `boost::filtered_graph` or pass a property map to the algorithm that returns "infinity" for infinite edges.

Note also that when you derive from the class `CGAL::Triangulation_2` you must upcast the object in order to use this partial specialization.

For the user convenience, CGAL provides the partial specializations for all 2D triangulation classes.

The traits class `boost::graph_traits< CGAL::Triangulation_2<GT, TDS> >` and `boost::graph_traits< CGAL::Delaunay_triangulation_2<GT, TDS> >` provide the following types:

Member | Value | Description
--- | --- | ---
`vertex_descriptor` | `Triangulation::Vertex_handle` | The vertex descriptor
`edge_descriptor` | `unspecified_type` | It is constructible from and convertible to `Triangulation::Edge`. The edge descriptor is not a simple typedef, but a proper class, because in an undirected graph the edges `(u,v)` and `(v,u)` must be equal. This is not the case for the Edge type of the triangulation.
`adjacency_iterator` | `unspecified_type` | An iterator for the vertices adjacent to a vertex. Its value type is `vertex_descriptor`
`out_edge_iterator` | `unspecified_type` | An iterator for the outgoing edges incident to a vertex. Its value type is `edge_descriptor`.
`in_edge_iterator` | `unspecified_type` | An iterator for the incoming edges incident to a vertex. Its value type is `edge_descriptor`.
`vertex_iterator` | `unspecified_type` | The vertex iterator type. Its value type is `vertex_descriptor`
`edge_iterator` | `unspecified_type` | The edge iterator type, Its value type is `edge_descriptor`
`directed_category` | `boost::undirected_tag` |
`edge_parallel_category` | `boost::disallow_parallel_edge_tag` | Indicates that this graph does not support multiedges
`traversal_category` | `boost::bidirectional_graph_tag` | Indicates that this graph is bidirectional
`vertices_size_type` | `Triangulation::size_type` | The size type of the vertex list
`edges_size_type` | `Triangulation::size_type` | The size type of the edge list
`degree_size_type` | `Triangulation::size_type` | The size type of the adjacency list

# Specialization for the Arrangement Classes

Defined in `<CGAL/boost/graph/graph_traits_Arrangement_2.h>`

We provide partial specialization for the class `Arrangement_2` so that it is model of the graph concepts `BidirectionalGraph` and `EdgeAndVertexListGraph`.

The const specialization, `boost::graph_traits< CGAL::Arrangement_2<Traits,Dcel> const>` is also defined, using the constant handles in the arrangement.

The traits class `boost::graph_traits< CGAL::Arrangement_2<T, DC> >` provides the following types:

Member | Value | Description
--- | --- | ---
`vertex_descriptor` | `Arrangement_2::Vertex_handle` | The vertex descriptor
`edge_descriptor` | `Arrangement_2::Halfedge_handle` | The edge descriptor
`adjacency_iterator` | Not provided |
`out_edge_iterator` | `unspecified_type` | An edge iterator which only iterates over the outgoing halfedges around a vertex. It corresponds to a `Arrangement_2::Halfedge_around_vertex_circulator` with the difference that its value type is an edge descriptor and not `Arrangement_2::Halfedge`
`in_edge_iterator` | `unspecified_type` | An edge iterator which only iterates over the incoming edges around a vertex. It corresponds to a `Arrangement_2::Halfedge_around_vertex_circulator` with the difference that its value type is an edge descriptor and not `Arrangement_2::Halfedge`
`vertex_iterator` | `unspecified_type` | An iterator corresponding to `Arrangement_2::Vertex_iterator`, with the difference that its value type is a vertex descriptor and not `Arrangement_2::Vertex`
`edge_iterator` | `unspecified_type` | An iterator corresponding to `Arrangement_2::Halfedge_iterator` with the difference that its value type is an edge descriptor and not `Arrangement_2::Halfedge`
`directed_category` | `boost::directed_tag` |
`edge_parallel_category` | `boost::disallow_parallel_edge_tag` | Indicates that this graph does support multiedges
`traversal_category` | `boost::bidirectional_graph_tag` | Indicates that this graph is bidirectional
`vertices_size_type` | `Arrangement_2::size_type` | The size type of the vertex list
`edges_size_type` | `Arrangement_2::size_type` | The size type of the edge list
`degree_size_type` | `Arrangement_2::size_type` | The size type of the adjacency list