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

CGAL 4.3 - 3D Mesh Generation

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MeshCellBase_3 Concept Reference
Secondary Concepts

## Definition

The concept `MeshCellBase_3` describes the requirements for the `Cell` type of the triangulation used in the 3D mesh generation process. The type `MeshCellBase_3` refines the concept `RegularTriangulationCellBase_3`. The concept `MeshCellBase_3` includes a way to store and retrieve if a given cell of the triangulation is inside the domain or not and which subdomain it belongs to in case of a multi-domain.

Moreover, this concept adds four markers per cell to mark the facets of the triangulation that are surface facets, and four additional helper markers used in some operations to mark for instance the facets that have been visited.

This concept also provides storage for the centers of Delaunay surface balls. Each surface facet has a Delaunay surface ball, i. e. a circumscribing ball, centered on an input complex surface patch, and empty of triangulation vertices. In the following we call `surface center` of a surface facet, the center of its biggest Delaunay surface ball.

The optimizers also need this concept to provide read-write access to two `Cell_handle` called 'intrusive'.

Refines:
  `RegularTriangulationCellBase_3`

Has Models:

  `CGAL::Compact_mesh_cell_base_3<Gt,MD,Tds>`

  `CGAL::Mesh_cell_base_3<Gt,MD,Cb>`

See Also
  `CGAL::make_mesh_3()`
  `MeshDomain_3`
  `MeshComplex_3InTriangulation_3`

## Types
typedef unspecified_type | Point
| Point type, required to match the point type of the 3D triangulation in which the mesh is embedded.
typedef unspecified_type | Subdomain_index
| Type of indices for cells of the input complex. More...
typedef unspecified_type | Surface_patch_index
| Type of indices for surface patches of the input complex. More...

## Operations
Subdomain_index | subdomain_index ()
| Returns the index of the input subdomain that contains the cell `cell` of the triangulation.
void | set_subdomain_index (Subdomain_index index)
| Sets the subdomain index of the cell.
bool | is_facet_on_surface (int i)
| returns `true` iff `facet(i)` is a surface facet.
Surface_patch_index | surface_patch_index (int i)
| returns `Surface_patch_index` of facet `i`.
void | set_surface_patch_index (int i, Surface_patch_index index)
| sets `Surface_patch_index` of facet `i` to `index`.
bool | is_facet_visited (int i)
| Returns `true` iff `facet(i)` has been visited.
void | set_facet_visited (int i, bool b)
| Marks `facet(i)` as visited if `b` is `true` and non-visited otherwise.
const Point & | facet_surface_center (int i)
| Returns a const reference to the surface center of `facet(i)`.
void | set_facet_surface_center (int i, Point p)
| Sets point `p` as the surface center of `facet(i)`.
void | invalidate_circumcenter ()
| Invalidates the circumcenter value stored in the cell. More...

## Internal
These functions are used internally by mesh optimizers. The class should provide storage, accessors and modificators for two `Vertex_handle` and two `Cell_handle`.
Cell_handle | next_intrusive () const
void | set_next_intrusive (Cell_handle)
Cell_handle | previous_intrusive () const
void | set_previous_intrusive (Cell_handle)

## Member Typedef Documentation

typedef unspecified_type MeshCellBase_3::Subdomain_index

Type of indices for cells of the input complex.

Must match the type `MeshDomain_3::Subdomain_index`.

typedef unspecified_type MeshCellBase_3::Surface_patch_index

Type of indices for surface patches of the input complex.

Must match the type `MeshDomain_3::Surface_patch_index`.

## Member Function Documentation

void MeshCellBase_3::invalidate_circumcenter | ( | ) |  |

Invalidates the circumcenter value stored in the cell.

This value is usually stored in the cell, but the optimizers need to be able to invalidate this cache value.