CGAL 6.1 - 3D Surface Mesh Generation

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SurfaceMeshCellBase_3 Concept Reference
Reference Manual » Concepts

## Definition

The concept `SurfaceMeshCellBase_3` describes the cell 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 `SurfaceMeshCellBase_3` describes the cell base type required in this triangulation type.

Refines
  `DelaunayTriangulationCellBase_3`

The concept `SurfaceMeshCellBase_3` adds four markers to mark the facets of the triangulation that belong to the two dimensional complex, and four markers that are helpers used in some operations to mark for instance the facets that have been visited.
This concept also provides storage for the center of a Delaunay surface ball. Given a surface and a 3D Delaunay triangulation, a Delaunay surface ball is a ball circumscribed to a facet of the triangulation and centered on the surface and empty of triangulation vertices. Such a ball does exist when the facet is part of the restriction to the surface of a three dimensional triangulation. In the following we call surface center of a facet, the center of its biggest Delaunay surface ball.

Has models
  `CGAL::Surface_mesh_cell_base_3<Gt,Vb>`
  `CGAL::Surface_mesh_default_triangulation_3::Cell`

See also
  `SurfaceMeshTriangulation_3`
  `SurfaceMeshComplex_2InTriangulation_3`
  `CGAL::Surface_mesh_complex_2_in_triangulation_3<Tr>`
  `CGAL::Surface_mesh_default_triangulation_3`
  `CGAL::make_surface_mesh()`

## Types
typedef unspecified_type | Point
| The point type, required to match the point type of the three dimensional triangulation in which the surface mesh is embedded.

## Operations
bool | is_facet_on_surface (int i)
| returns `true`, if `facet(i)` is in the 2D complex.
void | set_facet_on_surface (int i, bool b)
| Sets `facet(i)` as part of the 2D complex, if `b` is `true`, and `NOT_IN_COMPLEX`, otherwise.
bool | is_facet_visited (int i)
| Returns `true`, if `facet(i)` has been visited, `false` otherwise.
void | set_facet_visited (int i, bool b)
| Marks `facet(i)` as visited, if `b` is `true`, and non visited otherwise.
const Point & | get_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)`.