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‎BGL/doc/BGL/BGL.txt‎

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‎BGL/doc/BGL/CGAL/halfedge_graph_traits.h‎

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‎BGL/doc/BGL/CGAL/properties.h‎

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/// Boost Namespace
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namespace boost {
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/// \ingroup PkgBGLProperties
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/// @{
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/// The constant `edge_index` is a property tag which identifies the <i>index</i> property of an edge of a \sc{Bgl}
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/// <a href="http://www.boost.org/libs/graph/doc/Graph.html"><code>Graph</code></a>.
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/// \cgalModels <a href="http://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
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enum edge_index_t { edge_index};
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/// The constant `vertex_index` is a property tag which identifies the <i>index</i> property of a vertex of a \sc{Bgl}
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/// <a href="http://www.boost.org/libs/graph/doc/Graph.html"><code>Graph</code></a>.
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/// \cgalModels <a href="http://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
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enum vertex_index_t { vertex_index };
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/// The constant `halfedge_index` is a property tag which identifies the <i>index</i> property of a halfedge of a `HalfedgeGraph`.
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///
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/// This is a property tag introduced by \cgal.
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/// \cgalModels <a href="http://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
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enum halfedge_index_t { halfedge_index };
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/// The constant `face_index` is a property tag which identifies the <i>index</i> property of a face of a `FaceGraph`.
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///
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/// This is a property tag introduced by \cgal.
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/// \cgalModels <a href="http://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
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enum face_index_t { face_index };
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/// The constant `vertex_point` is a property tag which refers to the geometric embedding property of
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/// a vertex of a `HalfedgeGraph`.
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///
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/// This is a property tag introduced by \cgal.
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/// \cgalModels <a href="http://www.boost.org/libs/graph/doc/PropertyTag.html"><code>PropertyTag</code></a>
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enum vertex_point_t { vertex_point };
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/// @}
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}

‎BGL/doc/BGL/Concepts/FaceGraph.h‎

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/*!
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\ingroup PkgBGLConcepts
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\cgalConcept
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The concept `FaceGraph` refines the concept `HalfedgeGraph`.
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It adds the requirements for a graph to explicitly
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maintain faces described by halfedges, to provide access from a face to
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an incident halfedge, and to provide access from a halfedge to its incident
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face.
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\cgalRefines `HalfedgeGraph`
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\cgalHasModel `CGAL::Polyhedron_3`
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\cgalHeading{Notations}
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<dl>
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<dt>`G`</dt> <dd>A type that is a model of `FaceGraph`.</dd>
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<dt>`g`</dt> <dd>An object of type `G`.</dd>
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<dt>`e`</dt> <dd>An edge descriptor.</dd>
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<dt>`f`</dt> <dd>A face descriptor.</dd>
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<dt>`h`</dt> <dd>A halfedge descriptor.</dd>
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</dl>
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\cgalHeading{Associated Types}
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Type | Description
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-------------------- | ------------
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`boost::graph_traits<G>::%face_descriptor` | A `face_descriptor` corresponds to a unique face in a graph. Must be `DefaultConstructible`, `Assignable`, `EqualityComparable` and `LessThanComparable`.
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\cgalHeading{Valid Expressions}
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Expression | Returns | Description
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-------------------------------------- | ------------------------------------------------------------------------ | ------------------------
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`face(h, g)` | `face_descriptor` | The face incident to halfedge `h`.
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`halfedge(f, g)` | `halfedge_descriptor` | A halfedge incident to face `f`.
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`degree(f,g)` | `degree_size_type` | The number of halfedges, incident to face `f`.
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`boost::graph_traits<G>::%null_face()` | `face_descriptor` | Returns a special face that is not equal to any other face.
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*/
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class FaceGraph {};

‎BGL/doc/BGL/Concepts/FaceListGraph.h‎

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/*!
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\ingroup PkgBGLConcepts
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\cgalConcept
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The concept `FaceListGraph` refines the concept `FaceGraph` and adds
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the requirement for traversal of all faces in a graph.
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\cgalRefines `FaceGraph`
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\cgalHasModel `CGAL::Polyhedron_3`
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\cgalHeading{Notations}
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<dl>
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<dt>`G`</dt> <dd>A type that is a model of `FaceListGraph`.</dd>
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<dt>`g`</dt> <dd>An object of type `G`.</dd>
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</dl>
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\cgalHeading{Associated Types}
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Type | Description
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----------------- | -----------
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`boost::graph_traits<G>::%face_iterator` | %Iterator over all faces.
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`boost::graph_traits<G>::%faces_size_type` | Unsigned integer type for number of faces.
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\cgalHeading{Valid Expressions}
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Expression | returns | Description
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----------------- | --------------- | -----------------------
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`faces(g)` | `std::pair<face_iterator, face_iterator>` | An iterator range over all faces.
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`num_faces(g)` | `faces_size_type` | An upper bound of the number of faces of the graph.
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\attention `num_faces()` may return a number larger than `std::distance(faces(g).first, faces(g).second)`.
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This is the case for implementations only marking faces deleted in the face container.
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<!--
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This is for example the case for `CGAL::Surface_mesh` or `OpenMesh::PolyMesh_ArrayKernelT`.
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-->
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*/
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class FaceListGraph{};

‎BGL/doc/BGL/Concepts/HalfedgeGraph.h‎

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/*!
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\ingroup PkgBGLConcepts
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\cgalConcept
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The concept `HalfedgeGraph` describes the requirements for a graph that is
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structurally equivalent to a polyhedral surface represented by a
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halfedge data structure, and it provides an interface for efficient
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access to the opposite edge of an edge, and to the successor and
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predecessor of an edge in the iterator range of the incoming edges of
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a vertex. Each vertex has a geometric position in space. As in a
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halfedge data structure we define the face adjacent to a halfedge to be
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to the <I>left</I> of the halfedge.
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\cgalHeading{Requirements}
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The concept `HalfedgeGraph` is a refinement of the \sc{Bgl} concept
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<A HREF="http://www.boost.org/libs/graph/doc/Graph.html">`Graph`</A> and adds the notion of a *halfedge*: Each edge is
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associated with two *opposite* halfedges with source and target vertices swapped.
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Furthermore, halfedges have a *successor* and *predecessor*,
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and form cycles we call *faces*. However, this concept
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does not introduce a face type.
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A `HalfedgeGraph` is undirected and does not allow parallel edges.
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For each <I>directed edge</I> `e=(v,w)` its opposite edge `e2=(w,v)`
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must be part of the graph.
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Using the composition of the *successor* and *opposite* functions results
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in another cycle, namely the cycle of halfedges which are incident to
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the same vertex. We refer to \ref PkgBGLIterators for a description of
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iterators and circulators for these halfedge cycles.
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The incoming edges of a vertex `v` have a fixed order, that is all
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calls of `in_edges(v,g)` must return the same iterator range,
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modulo a cyclic permutation. The order must be <I>clockwise</I>.
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As the `HalfedgeGraph` is equivalent to a polyhedral surface there must exist an embedding
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for the vertices and edges such that the ordered edges do not intersect.
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\cgalRefines <A HREF="http://www.boost.org/libs/graph/doc/Graph.html">`Graph`</A>
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\cgalRefines <A HREF="http://www.boost.org/libs/graph/doc/PropertyGraph.html">`PropertyGraph`</A>
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\cgalRefines <A HREF="http://www.boost.org/libs/graph/doc/BidirectionalGraph.html">BidirectionalGraph</A>
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\cgalRefines <A HREF="http://www.boost.org/libs/graph/doc/PropertyGraph.html">PropertyGraph</A>
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A model of `HalfedgeGraph` must have the interior property `vertex_point` attached to its vertices.
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A model of `HalfedgeGraph` must have the <I>interior properties</I>
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`edge_is_border` attached to its edges, and it must have
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`vertex_is_border` and `vertex_point` attached to its vertices.
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\cgalHeading{Associated Types}
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\cgalHasModel `CGAL::Polyhedron_3`
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Because (directed) edges must come in pairs, there is the
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additional notion of an <I>undirected edge</I>
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\cgalFootnote{The directed edges are not called `halfedges` (as in a `HalfedgeDS`) because from the point of view of this graph, being a refinement of a Bgl graph, each directed edge is an edge in itself. In other words, the unqualified term edge refers to one and only one directed edge and not to a pair.}
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for a pair of opposite directed edges. The number of undirected
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edges is exactly half the number of directed edges. Note that the
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notion of directed and undirected edges does not imply the
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existence of two different types. The type `%edge_descriptor` is
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used for both. An undirected edge must be implicitly handled, and
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there is no requirement on which of the directed edges of the
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undirected edge must be used to represent it.
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\cgalHeading{Notations}
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<dl>
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<dt>`G`</dt> <dd>A type that is a model of `HalfedgeGraph`.</dd>
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<dt>`g`</dt> <dd>An object of type `G`.</dd>
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<dt>`u`, `v`</dt> <dd>Vertex descriptors.</dd>
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<dt>`e`</dt> <dd>An edge descriptor.</dd>
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<dt>`h`</dt> <dd>A halfedge descriptor.</dd>
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</dl>
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Associated Type | Explanation
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----------------|-------------
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halfedge_graph_traits<HalfedgeGraph>::Point; | The type of the geometric location of a vertex.
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halfedge_graph_traits<HalfedgeGraph>::undirected_edge_iterator; | An iterator that iterates over one and only one of the directed edges in each pair of opposite directed edges. The value type of the iterator is `boost::graph_traits<HalfedgeGraph>::%edge_descriptor`.
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\cgalHeading{Associated Types}
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Type | Description
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--------------------------------------------------------- | ------------
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`boost::graph_traits<G>::%halfedge_descriptor` | A `halfedge_descriptor` corresponds to a halfedge in a graph. Must be `DefaultConstructible`, `Assignable`, `EqualityComparable` and `LessThanComparable`.
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\cgalHeading{Valid Expressions}
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Following the \sc{Bgl} design, the following graph operations are defined as free
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rather than member functions.
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\cgalHasModel `CGAL::Polyhedron_3<Traits>`
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Expression | Returns | Description
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--------------------------------------- | ---------------------------------------------------------------------------- | -----------
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`edge(h, g)` | `edge_descriptor` | The edge corresponding to `h` and `opposite(h)`.
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`halfedge(e, g)` | `halfedge_descriptor` | One of the halfedges corresponding to `e`.
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`halfedge(v, g)` | `halfedge_descriptor` | A halfedge with target `v`.
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`halfedge(u, v, g)` | `std::pair<halfedge_descriptor,bool>` | The halfedge with source `u` and target `v`. The Boolean is `true`, iff this halfedge exists.
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`opposite(h, g)` | `halfedge_descriptor` | The halfedge with source and target swapped.
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`source(h,g)` | `vertex_descriptor` | The source vertex of `h`.
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`target(h,g)` | `vertex_descriptor` | The target vertex of `h`.
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`next(h, g)` | `halfedge_descriptor` | The next halfedge around its face.
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`prev(h, g)` | `halfedge_descriptor` | The previous halfedge around its face.
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*/
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class HalfedgeGraph {
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};
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/*!
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Returns the undirected edges of `g`.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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std::pair<typename halfedge_graph_traits<HalfedgeGraph>::undirected_edge_iterator,
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typename halfedge_graph_traits<HalfedgeGraph>::undirected_edge_iterator>
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undirected_edges(const Graph& g);
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/*!
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Returns the opposite edge of `e`.
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An edge `e=(v,w)` is said to be the <I>opposite edge</I> of edge
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`e2=(w,v)`.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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typename boost::graph_traits<Graph const>::edge_descriptor
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opposite_edge(typename boost::graph_traits<Graph const>::edge_descriptor e, Graph const& g );
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/*!
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Returns the clockwise neighbor of `e`.
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An edge `e2=(v,w)` is called the <I>clockwise neighbor</I> of
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edge `e=(u,w)`, and `e` the <I>counterclockwise neighbor</I>
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of `e2`, iff there exist two iterators `it` and `it2`
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in the iterator range `in_edges(w,g)` such that `**it == e` and `**it2
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== e2`, and `it2 == it++` or `it` is the last and `it2` the first
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iterator of the iterator range.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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typename boost::graph_traits<Graph const>::edge_descriptor
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next_edge_cw(typename boost::graph_traits<Graph const>::edge_descriptor e, Graph const& g );
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/*!
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Returns the counterclockwise neighbor of `e`.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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typename boost::graph_traits<Graph const>::edge_descriptor
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next_edge_ccw(typename boost::graph_traits<Graph const>::edge_descriptor e, Graph const& g );
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/*!
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Returns the successor of `e`.
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An edge `e2=(v,w)` is called the <I>successor</I> of edge `
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e=(u,v)`, and `e` the <I>predecessor</I> of `e2`, iff `
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e2` is the clockwise neighbor of the opposite edge of `e`.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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typename boost::graph_traits<Graph const>::edge_descriptor
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next_edge(typename boost::graph_traits<Graph const>::edge_descriptor e, Graph const& g );
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/*!
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Returns the predecessor of `e`.
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An edge `e2=(v,w)` is called the <I>successor</I> of edge `
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e=(u,v)`, and `e` the <I>predecessor</I> of `e2`, iff `
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e2` is the clockwise neighbor of the opposite edge of `e`.
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\relates HalfedgeGraph
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*/
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template<class Graph>
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typename boost::graph_traits<Graph const>::edge_descriptor
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prev_edge(typename boost::graph_traits<Graph const>::edge_descriptor e, Graph const& g );
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class HalfedgeGraph {};

‎BGL/doc/BGL/Concepts/HalfedgeListGraph.h‎

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/*!
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\ingroup PkgBGLConcepts
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\cgalConcept
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The concept `HalfedgeListGraph` refines the concept `HalfedgeGraph`
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and adds the requirements for traversal of all halfedges in the graph.
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\cgalRefines `HalfedgeGraph`
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\cgalHasModel `CGAL::Polyhedron_3`
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\cgalHeading{Notations}
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<dl>
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<dt>`G`</dt> <dd>A type that is a model of `HalfedgeListGraph`.</dd>
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<dt>`g`</dt> <dd>An object of type `G`.</dd>
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</dl>
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\cgalHeading{Associated Types}
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Type | Description
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-------------------- | ------------
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`boost::graph_traits<G>::%halfedge_iterator` | A `BidirectionalIterator` over all halfedges in a graph. Must be `DefaultConstructible`, `Assignable`, `EqualityComparable`.
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`boost::graph_traits<G>::%halfedges_size_type` | A size type.
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\cgalHeading{Valid Expressions}
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Expression | Returns | Description
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------------------------------------- | ---------------------------------------------------- | -----------
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`num_halfedges(g)` | `halfedges_size_type` | An upper bound of the number of halfedges of the graph.
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`halfedges(g)` | `std::pair<halfedge_iterator,halfedge_iterator>` | An iterator range over the halfedges of the graph.
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\attention `num_halfedges()` may return a number larger than `std::distance(halfedges(g).first,halfedges(g).second)`.
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This is the case for implementations only marking halfedges deleted in the halfedge container.
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<!--
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This is for example the case for `CGAL::Surface_mesh` or `OpenMesh::PolyMesh_ArrayKernelT`.
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-->
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*/
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class HalfedgeListGraph {};

‎BGL/doc/BGL/Concepts/MutableFaceGraph.h‎

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/*!
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\ingroup PkgBGLConcepts
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\cgalConcept
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The concept `MutableFaceGraph` refines the concepts `FaceGraph` and `MutableHalfedgeGraph` and adds
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the requirement for operations to add faces and to modify face-halfedge relations.
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\cgalRefines `FaceGraph`
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\cgalRefines `MutableHalfedgeGraph`
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\cgalHasModel `CGAL::Polyhedron_3`
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\cgalHeading{Notations}
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<dl>
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<dt>`G`</dt> <dd>A type that is a model of `MutableFaceGraph`.</dd>
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<dt>`g`</dt> <dd>An object of type `G`.</dd>
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<dt>`h`</dt> <dd>A halfedge descriptor.</dd>
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<dt>`f`</dt> <dd>A face descriptor.</dd>
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</dl>
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\cgalHeading{Valid Expressions}
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Expression | returns | Description
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----------------------- | ------------ | -----------
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`add_face(g)` | `face_descriptor` | Adds a new face to the graph with no corresponding halfedge set.
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`remove_face(f, g)` | `void` | Removes `f` from the graph.
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`set_face(h, f, g)` | `void` | Sets the corresponding face of `h` to `f`.
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`set_halfedge(f, h, g)` | `void` | Sets the corresponding halfedge of `f` to `h`.
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*/
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class MutableFaceGraph{};

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