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

CGAL 4.3 - 3D Surface Mesh Generation

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SurfaceMeshVertexBase_3 Concept Reference
Concepts

## Definition

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 function template `CGAL::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.

Refines:
  `TriangulationVertexBase_3` 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.

Has Models:

  `CGAL::Surface_mesh_vertex_base_3<Gt,Vb>`

  `CGAL::Surface_mesh_default_triangulation_3::Vertex`

See Also
  `SurfaceMeshComplex_2InTriangulation_3`
  `CGAL::Surface_mesh_complex_2_in_triangulation_3<Tr>`
  `CGAL::Surface_mesh_default_triangulation_3`

## Operations
bool | is_c2t3_cache_valid ()
| Returns `true` if the cache is valid.
void | invalidate_c2t3_cache ()
| Invalidates the cache.
int | cached_number_of_incident_facets ()
| Returns the cached number of facets of the complex incident to the vertex.
int | cached_number_of_components ()
| 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.