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

CGAL 4.8 - CGAL and the Boost Graph Library

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Modules | Functions
CGAL and the Boost Graph Library Reference

##

Andreas Fabri, Fernando Cacciola, Philipp Moeller, and Ron Wein
This package provides a framework for interfacing CGAL data structures with the algorithms of the Boost Graph Library, or BGL for short. It allows to run graph algorithms directly on CGAL data structures which are model of the BGL graph concepts, for example the shortest path algorithm on a Delaunay triangulation in order to compute the Euclidean minimum spanning tree. Furthermore, it introduces several new graph concepts describing halfedge data structures.

Introduced in: CGAL 3.3
BibTeX: cgal:cfw-cbgl-16a
License: LGPL

## Classified Reference Pages

## Concepts

- `HalfedgeGraph`
- `HalfedgeListGraph`
- `MutableHalfedgeGraph`
- `FaceGraph`
- `FaceListGraph`
- `MutableFaceGraph`

## Properties

- `boost::vertex_index_t`
- `boost::halfedge_index_t`
- `boost::edge_index_t`
- `boost::face_index_t`
- `boost::vertex_point_t`

## CGAL Classes Adapted for the Graph API

Different CGAL types have been adapted as graphs for the Bgl. All adapted types are listed here. The pages document which concepts they model, the properties they support, and any possible caveats that a user might encounter.

- `boost::graph_traits< CGAL::Surface_mesh<P> >`
- `boost::graph_traits< CGAL::Polyhedron_3<T> >`
- `boost::graph_traits< CGAL::Triangulation_2<GT, TDS> >`
- `boost::graph_traits< CGAL::Arrangement_2<T,DC> >`

## Helper Classes

- `CGAL::Triangulation_vertex_base_with_id_2`
- `CGAL::Arr_vertex_index_map`
- `CGAL::Arr_face_index_map`
- `CGAL::HalfedgeDS_vertex_max_base_with_id`
- `CGAL::HalfedgeDS_halfedge_max_base_with_id`
- `CGAL::HalfedgeDS_face_max_base_with_id`
- `CGAL::Polyhedron_items_with_id_3`
- `CGAL::set_halfedgeds_items_id()`

## Helper Functions

- `CGAL::is_border()`
- `CGAL::is_border_edge()`
- `CGAL::is_bivalent()`
- `CGAL::is_bivalent_mesh()`
- `CGAL::is_trivalent()`
- `CGAL::is_trivalent_mesh()`
- `CGAL::is_isolated_triangle()`
- `CGAL::is_closed()`
- `CGAL::is_triangle()`
- `CGAL::is_triangle_mesh()`
- `CGAL::is_quad()`
- `CGAL::is_quad_mesh()`
- `CGAL::is_isolated_quad()`
- `CGAL::is_tetrahedron()`
- `CGAL::is_hexahedron()`
- `CGAL::make_triangle()`
- `CGAL::make_tetrahedron()`
- `CGAL::make_quad()`
- `CGAL::make_hexahedron()`
- `CGAL::clear()`

## Iterators

- `CGAL::Halfedge_around_source_iterator`
- `CGAL::Halfedge_around_target_iterator`
- `CGAL::Halfedge_around_face_iterator`
- `CGAL::Vertex_around_target_iterator`
- `CGAL::Vertex_around_face_iterator`
- `CGAL::Face_around_face_iterator`
- `CGAL::Face_around_target_iterator`
- `CGAL::halfedges_around_source()`
- `CGAL::halfedges_around_target()`
- `CGAL::halfedges_around_face()`
- `CGAL::faces_around_face()`
- `CGAL::faces_around_target()`
- `CGAL::vertices_around_face()`
- `CGAL::vertices_around_target()`

## Circulators

- `CGAL::Halfedge_around_source_circulator`
- `CGAL::Halfedge_around_target_circulator`
- `CGAL::Halfedge_around_face_circulator`
- `CGAL::Vertex_around_target_circulator`
- `CGAL::Face_around_target_circulator`
- `CGAL::Face_around_face_circulator`

## Euler Operations

- `CGAL::Euler::add_center_vertex()`
- `CGAL::Euler::add_edge()`
- `CGAL::Euler::add_face()`
- `CGAL::Euler::add_face_to_border()`
- `CGAL::Euler::add_vertex_and_face_to_border()`
- `CGAL::Euler::collapse_edge()`
- `CGAL::Euler::does_satisfy_link_condition()`
- `CGAL::Euler::fill_hole()`
- `CGAL::Euler::flip_edge()`
- `CGAL::Euler::join_face()`
- `CGAL::Euler::join_loop()`
- `CGAL::Euler::join_vertex()`
- `CGAL::Euler::make_hole()`
- `CGAL::Euler::remove_center_vertex()`
- `CGAL::Euler::remove_face()`
- `CGAL::Euler::split_edge()`
- `CGAL::Euler::split_face()`
- `CGAL::Euler::split_loop()`
- `CGAL::Euler::split_vertex()`

## Selection

- `CGAL::expand_face_selection()`
- `CGAL::reduce_face_selection()`
- `CGAL::expand_edge_selection()`
- `CGAL::reduce_edge_selection()`
- `CGAL::expand_vertex_selection()`
- `CGAL::reduce_vertex_selection()`
- `CGAL::select_incident_faces()`

## Miscellaneous

- `CGAL::split_graph_into_polylines()`

## Modules
| Specializations of boost::graph_traits
| Bgl defines the class template `boost::graph_traits` as a uniform interface to the properties and types of graph types.
| Concepts
| We extend the Boost Graph Library(Bgl for short) with a set of new concepts.
| Properties
| The property tags model of the boost concept `PropertyTag`.
| Helper Classes
| Helper Functions
| Iterators and Circulators
| Several iterators and circulators are provided that enable to iterate through the halfedges incident to a given face or vertex.
| Selection Functions
| Euler Operations
| We call high level operations that maintain the validity of a halfedge graph Euler Operations.

## Functions
template<typename Graph , typename Visitor , typename IsTerminal >
void | CGAL::split_graph_into_polylines (const Graph &graph, Visitor &polyline_visitor, IsTerminal is_terminal)
| splits into polylines the graph `g` at vertices of degree greater than 2 and at vertices for which `is_terminal(v,graph)==true`. More...

## Function Documentation

template<typename Graph , typename Visitor , typename IsTerminal >

void CGAL::split_graph_into_polylines | ( | const Graph & | graph,
|  | Visitor & | polyline_visitor,
|  | IsTerminal | is_terminal
| ) |  |

splits into polylines the graph `g` at vertices of degree greater than 2 and at vertices for which `is_terminal(v,graph)==true`.

The polylines are reported using a visitor.

Template Parameters

  Graph | a model of the `boost` concepts `VertexListGraph` and `EdgeListGraph`.
  Visitor | a class that provides: `void start_new_polyline()` called when starting the description of a polyline. `void add_node(typename boost::graph_traits<Graph>::vertex_descriptor v)` called for each vertex `v` of the polyline currently described. `void end_polyline()` called when the description of a polyline is finished.
  IsTerminal | A functor providing `bool operator()(boost::graph_traits<Graph>::vertex_descriptor v, const Graph& g) const` returning true if the vertex `v` of degree 2 is a polyline endpoint and false otherwise.

An overload without `is_terminal` is provided if no vertices but those of degree different from 2 are polyline endpoints.

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

Examples:
  Surface_mesh_skeletonization/simple_mcfskel_example.cpp.