CGAL 5.5.1  CGAL and the Boost Graph Library

The 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.
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
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and MutableFaceGraph
.
The const specialization, boost::graph_traits< CGAL::Surface_mesh<Traits> const>
is also defined, using the constant handles in the surface mesh.
The traits class boost::graph_traits< CGAL::Surface_mesh<T> >
provides the following types:
Member  Value  Description 

vertex_descriptor  Surface_mesh::Vertex_index  Identify vertices in the graph. 
edge_descriptor  Surface_mesh::Edge_index  Identify edges in the graph. 
halfedge_descriptor  Surface_mesh::Halfedge_index  Identify halfedges in the graph. 
face_descriptor  Surface_mesh::Face_index  Identify faces in the graph. 
adjacency_iterator  CGAL::Vertex_around_target_iterator<Surface_mesh<P> >  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  CGAL::Out_edge_iterator<Surface_mesh<P> >  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  CGAL::In_edge_iterator<Surface_mesh<P> >  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  Surface_mesh::Vertex_iterator  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
edge_iterator  Surface_mesh::Edge_iterator  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
halfedge_iterator  Surface_mesh::Halfedge_iterator  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
face_iterator  Surface_mesh::Face_iterator  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , boost::edge_list_graph_tag , and boost::adjacency_graph_tag  The ways in which the vertices in the graph can be traversed. 
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. 
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
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and 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  Identify vertices in the graph. 
edge_descriptor  unspecified_type  Identify edges in the graph. 
halfedge_descriptor  Polyhedron_3::Halfedge_handle  Identify halfedges in the graph. 
face_descriptor  Polyhedron_3::Face_handle  Identify faces in the graph. 
adjacency_iterator  CGAL::Vertex_around_target_iterator<Polyhedron_3<T> >  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  CGAL::Out_edge_iterator<Polyhedron_3<T> >  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  CGAL::In_edge_iterator<Polyhedron_3<T> >  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  unspecified_type  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
edge_iterator  unspecified_type  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
halfedge_iterator  unspecified_type  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
face_iterator  unspecified_type  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , boost::edge_list_graph_tag , andboost::adjacency_graph_tag  The ways in which the vertices in the graph can be traversed. 
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
, which is the default hash functor of CGAL::Unique_hash_map
.
Defined in <CGAL/boost/graph/graph_traits_Linear_cell_complex_for_combinatorial_map.h>
We provide partial specialization for the class CGAL::Linear_cell_complex_for_combinatorial_map
so that it is a model of the graph concepts BidirectionalGraph
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and MutableFaceGraph
.
The const specialization is also defined, using the constant handles in the linear cell complex.
Let us denote by LCC an instantiation of CGAL::Linear_cell_complex_for_combinatorial_map<...> class. The traits class boost::graph_traits<LCC>
provides the following types:
Member  Value  Description 

vertex_descriptor  LCC::Vertex_attribute_handle  The vertex descriptor 
edge_descriptor  unspecified_type  The edge descriptor 
halfedge_descriptor  LCC::Dart_handle  The halfedge descriptor 
face_descriptor  unspecified_type  The face descriptor 
adjacency_iterator  CGAL::Vertex_around_target_iterator<LCC>  Iterates through adjacent vertices 
out_edge_iterator  CGAL::Out_edge_iterator<LCC>  Iterate through the outedges of a vertex. 
in_edge_iterator  CGAL::Out_edge_iterator<LCC>  Iterate through the inedges of a vertex. 
vertex_iterator  unspecified_type  Iterate through the vertices of LCC. 
edge_iterator  unspecified_type  Iterate through the edges of LCC. 
halfedge_iterator  unspecified_type  Iterate through the halfedges of LCC. 
face_iterator  unspecified_type  Iterate through the faces of LCC. 
directed_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , boost::edge_list_graph_tag , and boost::adjacency_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  LCC::size_type  The size type of the vertex list 
edges_size_type  LCC::size_type  The size type of the edge list 
degree_size_type  LCC::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
.
The item class used by CGAL::Linear_cell_complex_for_combinatorial_map
must have both 0attributes and 2attributes enabled.
No dart is 1free, nor 2free. Holes in a mesh are represented by using the same convention than for CGAL::Polyhedron_3
and CGAL::Surface_mesh
: a dart d
belongs to a border if the 2attribute of beta<2>(d)
is nullptr.
All darts of the linear cell complexes must be associated with a 2attribute, except darts that represent holes.
For darts, this can be done by defining Darts_with_id
as CGAL::Tag_true
in the Dart_wrapper
struct of the item class.
For attributes, it is possible to use CGAL::Cell_attribute_with_id
and CGAL::Cell_attribute_with_point_and_id
classes to define your item class using attributes with id.
You can also use the CGAL::Linear_cell_complex_bgl_min_items
item class, or you can use directly the CGAL::Linear_cell_complex_for_bgl_combinatorial_map_helper
class.
Defined in <CGAL/boost/graph/graph_traits_Triangulation_2.h>
, <CGAL/boost/graph/graph_traits_Delaunay_triangulation_2.h>
, <CGAL/boost/graph/graph_traits_Regular_triangulation_2.h>
, <CGAL/boost/graph/graph_traits_Constrained_Delaunay_triangulation_2.h>
, <CGAL/boost/graph/graph_traits_Constrained_triangulation_2.h>
, <CGAL/boost/graph/graph_traits_Constrained_triangulation_plus_2.h>
, and <CGAL/boost/graph/graph_traits_Triangulation_hierarchy_2.h>
.
We provide partial specialization for the classes CGAL::Triangulation_2
, CGAL::Delaunay_triangulation_2
, CGAL::Regular_triangulation_2
, CGAL::Constrained_triangulation_2
, CGAL::Constrained_Delaunay_triangulation_2
, CGAL::Constrained_triangulation_plus_2
, and CGAL::Triangulation_hierarchy_2
so that they are model of the graph concepts BidirectionalGraph
, VertexAndEdgeListGraph
, and FaceListGraph
.
Only finite simplices exist when viewed through the scope of these graph traits classes. The infinite vertex, halfedges, edges, and faces will thus not appear when looping around a border vertex, or walking through the faces container.
The mapping between vertices, edges, and faces 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.
Member  Value  Description 

vertex_descriptor  unspecified_type  Identify vertices in the graph. 
halfedge_descriptor  unspecified_type  Identify halfedges in the graph. It is constructible from and convertible to Triangulation::Edge . It is not a simple typedef, but a proper class, because there is no representation for halfedges in the 2D triangulation data structure. 
edge_descriptor  unspecified_type  Identify edges in the graph. It is constructible from and convertible to Triangulation::Edge . It 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. 
face_descriptor  unspecified_type  Identify faces in the graph. 
adjacency_iterator  unspecified_type  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  unspecified_type  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  unspecified_type  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  unspecified_type  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
halfedge_iterator  unspecified_type  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
edge_iterator  unspecified_type  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
face_iterator  unspecified_type  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::adjacency_graph_tag , boost::vertex_list_graph_tag , and boost::edge_list_graph_tag  The ways in which the vertices in the graph can be traversed.. 
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. 
Defined in <CGAL/boost/graph/graph_traits_Arrangement_2.h>
We provide partial specialization for the class CGAL::Arrangement_2
so that it is model of the graph concepts BidirectionalGraph
and VertexAndEdgeListGraph
.
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, Dcel> >
provides the following types:
Member  Value  Description 

vertex_descriptor  Arrangement_2::Vertex_handle  Identify vertices in the graph. 
edge_descriptor  Arrangement_2::Halfedge_handle  Identify edges in the graph. 
adjacency_iterator  Vertex_around_target_iterator<Arrangement_2>  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
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  This graph is directed. 
edge_parallel_category  boost::allow_parallel_edge_tag  This graph supports multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , boost::edge_list_graph_tag , and boost::adjacency_graph_tag  The ways in which the vertices in the graph can be traversed. 
vertices_size_type  Arrangement_2::Size  The size type of the vertex list. 
edges_size_type  Arrangement_2::Size  The size type of the edge list. 
degree_size_type  Arrangement_2::Size  The size type of the adjacency list. 
Defined in <CGAL/boost/graph/graph_traits_PolyMesh_ArrayKernelT.h>
We provide partial specialization for the class OpenMesh::PolyMesh_ArrayKernelT
so that it is a model of the graph concepts BidirectionalGraph
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and MutableFaceGraph
.
The traits class boost::graph_traits<OpenMesh::PolyMesh_ArrayKernelT<K> >
provides the following types:
Member  Value  Description 

vertex_descriptor  OpenMesh::PolyMesh_ArrayKernelT<K>::VertexHandle  Identify vertices in the graph. 
edge_descriptor  unspecified_type  Identify edges in the graph. 
halfedge_descriptor  OpenMesh::PolyMesh_ArrayKernelT<K>::HalfedgeHandle  Identify halfedges in the graph. 
face_descriptor  OpenMesh::PolyMesh_ArrayKernelT<K>::FaceHandle  Identify faces in the graph. 
adjacency_iterator  CGAL::Vertex_around_target_iterator<OpenMesh::PolyMesh_ArrayKernelT<K> >  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  CGAL::Out_edge_iterator<OpenMesh::PolyMesh_ArrayKernelT<K> >  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  CGAL::In_edge_iterator<OpenMesh::PolyMesh_ArrayKernelT<K> >  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  OpenMesh::PolyMesh_ArrayKernelT<K>::VertexIter  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
edge_iterator  unspecified_type  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
halfedge_iterator  OpenMesh::PolyMesh_ArrayKernelT<K>::HalfedgeIter  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
face_iterator  OpenMesh::PolyMesh_ArrayKernelT<K>::FaceIter  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag ,boost::edge_list_graph_tag , andboost::adjacency_graph_tag  The ways in which the vertices in the graph can be traversed. 
vertices_size_type  unsigned int  The size type of the vertex list. 
edges_size_type  unsigned int  The size type of the edge list. 
degree_size_type  unsigned int  The size type of the adjacency list. 
Defined in <CGAL/boost/graph/graph_traits_TriMesh_ArrayKernelT.h>
We provide partial specialization for the class OpenMesh::TriMesh_ArrayKernelT
so that it is a model of the graph concepts BidirectionalGraph
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and MutableFaceGraph
.
The traits class boost::graph_traits<OpenMesh::TriMesh_ArrayKernelT<K> >
provides the following types:
Member  Value  Description 

vertex_descriptor  OpenMesh::TriMesh_ArrayKernelT<K>::VertexHandle  Identify vertices in the graph. 
edge_descriptor  unspecified_type  Identify edges in the graph. 
halfedge_descriptor  OpenMesh::TriMesh_ArrayKernelT<K>::HalfedgeHandle  Identify halfedges in the graph. 
face_descriptor  OpenMesh::TriMesh_ArrayKernelT<K>::FaceHandle  Identify faces in the graph. 
adjacency_iterator  CGAL::Vertex_around_target_iterator<OpenMesh::TriMesh_ArrayKernelT<K> >  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  CGAL::Out_edge_iterator<OpenMesh::TriMesh_ArrayKernelT<K> >  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  CGAL::In_edge_iterator<OpenMesh::TriMesh_ArrayKernelT<K> >  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  OpenMesh::PolyMesh_ArrayKernelT<K>::VertexIter  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
edge_iterator  unspecified_type  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
halfedge_iterator  OpenMesh::TriMesh_ArrayKernelT<K>::HalfedgeIter  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
face_iterator  OpenMesh::TriMesh_ArrayKernelT<K>::FaceIter  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , boost::edge_list_graph_tag , and boost::adjacency_graph_tag  The ways in which the vertices in the graph can be traversed. 
vertices_size_type  unsigned int  The size type of the vertex list. 
edges_size_type  unsigned int  The size type of the edge list. 
degree_size_type  unsigned int  The size type of the adjacency list. 
Defined in <CGAL/boost/graph/graph_traits_Seam_mesh.h>
We provide partial specialization for the class CGAL::Seam_mesh
so that it is a model of the graph concepts BidirectionalGraph
, VertexAndEdgeListGraph
, AdjacencyMatrix
, and FaceListGraph
.
The traits class boost::graph_traits< CGAL::Seam_mesh<T> >
provides the following types:
Member  Value  Description 

vertex_descriptor  Seam_mesh::vertex_descriptor  Identify vertices in the graph. 
edge_descriptor  Seam_mesh::edge_descriptor  Identify edges in the graph. 
halfedge_descriptor  Seam_mesh::halfedge_descriptor  Identify halfedges in the graph. 
face_descriptor  Seam_mesh::face_descriptor  Identify faces in the graph. 
adjacency_iterator  CGAL::Vertex_around_target_iterator<CGAL::Seam_mesh<T> >  An iterator to traverse through the vertices adjacent to a vertex. Its value type is vertex_descriptor . 
out_edge_iterator  CGAL::Out_edge_iterator<CGAL::Seam_mesh<T> >  An iterator to traverse through the outgoing edges incident to a vertex. Its value type is edge_descriptor . 
in_edge_iterator  CGAL::In_edge_iterator<CGAL::Seam_mesh<T> >  An iterator to traverse through the incoming edges incident to a vertex. Its value type is edge_descriptor . 
vertex_iterator  Seam_mesh::vertex_iterator  An iterator to traverse through the vertices of the graph. Its value type is vertex_descriptor . 
edge_iterator  Seam_mesh::edge_iterator  An iterator to traverse through the edges of the graph. Its value type is edge_descriptor . 
halfedge_iterator  Seam_mesh::halfedge_iterator  An iterator to traverse through the halfedges of the graph. Its value type is halfedge_descriptor . 
face_iterator  Seam_mesh::face_iterator  An iterator to traverse through the faces of the graph. Its value type is face_descriptor . 
directed_category  boost::undirected_tag  This graph is not directed. 
edge_parallel_category  boost::disallow_parallel_edge_tag  This graph does not support multiedges. 
traversal_category  Inherits from boost::bidirectional_graph_tag , boost::vertex_list_graph_tag , and boost::edge_list_graph_tag  The ways in which the vertices in the graph can be traversed. 
vertices_size_type  Seam_mesh::vertices_size_type  The size type of the vertex list. 
edges_size_type  Seam_mesh::edges_size_type  The size type of the edge list. 
degree_size_type  Seam_mesh::degree_size_type  The size type of the adjacency list. 