The concept SurfaceMeshComplex_2InTriangulation_3 describes a data structure designed to represent a two dimensional pure complex embedded in a three dimensional triangulation.
A complex is a set $$C of faces such that:
 any subface of a face in $$C is a face of $$C
 two faces of $$C are disjoint or share a common subface
The complex is two dimensional, if its faces have dimension at most
two. It is pure if any face in the complex is a subface
of some face of maximal dimension.
Thus, a two dimensional pure complex is a set of facets
together with their edges and vertices.
A two dimensional pure complex embedded
in a three dimensional triangulation
is a subset of the facets
of this triangulation, together with their edges and vertices.
The concept SurfaceMeshComplex_2InTriangulation_3 is particularly suited to handle surface meshes obtained as the restriction to a surface of a three dimensional Delaunay triangulation. A model of this concept is a type to be plugged as first template parameter in the function template make_surface_mesh.
 
The type of the
embedding 3D triangulation. Must be a model of
SurfaceMeshTriangulation_3.

 
A type to describe the status of a face (facet, edge, or vertex) with respect to
the 2D pure complex. A NOT_IN_COMPLEX face does not belong to the 2D complex.
Facets can only be NOT_IN_COMPLEX or REGULAR
depending on whether they belong to the 2D complex on not.
Edges and vertices can be NOT_IN_COMPLEX, BOUNDARY,
REGULAR or SINGULAR.
An edge in the complex is
BOUNDARY,
REGULAR, or SINGULAR,
if it is incident to respectively 1, 2, or 3 or
more facets in the complex.
The status of a vertex is determined by
the adjacency graph of the facets of the 2D complex
incident to that vertex.
The vertex of the 2D complex is BOUNDARY, if this adjacency graph
is a simple path, it is REGULAR, if the adjacency graph is cyclic,
and SINGULARin any other case.
 
 
An iterator type to visit the facets
of the 2D complex.
 
 
An iterator type to visit the
edges of the 2D complex.
 
 
An iterator type to visit
vertices of the 2D complex.
 
 
An iterator type to visit the
boundary edges of the 2D complex.

 
Builds an empty 2D complex embedded in the triangulation t3
 
 
 
Builds a 2D complex embedded in the triangulation t3,
including in the 2D complex the facets of t3 for
which the predicate select returns true. The type FacetSelector must be a function object with an operator to select facets: bool operator()(Facet f);.


 Returns the reference to the triangulation. 

 Adds facet f to the 2D complex. 

 
Adds facet (c,i) to the 2D complex.  

 
Removes facet f from the 2D complex.  

 
Removes facet (c,i) from the 2D complex. 

 Returns the number of facets that belong to the 2D complex.  

 Returns the status of the facet f with respect to the 2D complex.  

 
Returns the status of the facet (c,i) with respect to the 2D complex.  

 Returns the status of edge e in the 2D complex.  

 
Returns the status of edge (c,i,j) in the 2D complex.  

 
Returns the status of vertex v in the 2D complex.  

 Returns true, if the facet f belongs to the 2D complex.  

 
Returns true, if the facet (c,i) belongs to the 2D complex.  

 Returns true, if the edge e belongs to the 2D complex.  

 
Returns true, if the edge (c,i,j) belongs to the 2D complex.  

 
Returns true, if the vertex v belongs to the 2D complex.  

 
Returns true if the status of vertex v is REGULAR or BOUNDARY.

The data structure provides iterators to visit the facets, edges and vertices of the complex. All those iterators are bidirectional and non mutable.
Surface_mesh_complex_2_in_triangulation_3<Tr>