The concept SurfaceMeshVertexBase_3 describes the vertex base type of the three dimensional triangulation used to embed the surface mesh.
More precisely, the first template parameter SurfaceMeshC2T3 of the surface mesher make_surface_mesh is a model of the concept SurfaceMeshComplex_2InTriangulation_3 which describes a data structure to store a pure two dimensional complex embedded in a three dimensional triangulation. In particular, the type SurfaceMeshC2T3 is required to provide a three dimensional triangulation type SurfaceMeshC2T3::Triangulation_3 The concept SurfaceMeshVertexBase_3 describes the vertex base type required in this triangulation type.
The surface mesher algorithm issues frequent queries about the status of the vertices with respect to the two dimensional complex that represents the current surface approximation. The class SurfaceMeshVertexBase_3 offers a caching mechanism to answer more efficiently these queries. The caching mechanism includes two cached integers, which, when they are valid, store respectively the number of complex facets incident to the vertex and the number of connected components of the adjacency graph of those facets.

 Returns true if the cache is valid. 

 Invalidates the cash. 

 
Returns the cached number of facets of the complex incident to the vertex.  

 This method concerns the adjacency graph of the facets of the complex incident to the vertex and returns a cached value for the number of connected components this graph. 
Surface_mesh_vertex_base_3<Gt,Vb>
Surface_mesh_default_triangulation_3::Vertex
SurfaceMesherComplex_2InTriangulation_3
Surface_mesh_complex_2_in_triangulation_3<Tr>
Surface_mesh_default_triangulation_3.