\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 5.0 - 3D Surface Mesh Generation
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SurfaceMeshFacetsCriteria_3 Concept Reference
3D Surface Mesh Generation Reference » Concepts

Definition

The Delaunay refinement process involved in the function template CGAL::make_surface_mesh() is guided by a set of refinement criteria. The concept SurfaceMeshFacetsCriteria_3 describes the type which handles those criteria. It corresponds to the requirements for the template parameter FacetsCriteria of the surface mesher function CGAL::make_surface_mesh<SurfaceMeshC2T3,Surface,FacetsCriteria,Tag>().

Typically the meshing criteria are a set of elementary criteria, each of which has to be met by the facets of the final mesh. The meshing algorithm eliminates in turn bad facets, i.e., facets that do not meet all the criteria.

The size and quality of the final mesh depends on the order according to which bad facets are handled. Therefore, the meshing algorithm needs to be able to quantify the facet qualities and to compare the qualities of different faces. The type SurfaceMeshFacetsCriteria_3::Quality measures the quality of a mesh facet. Typically this quality is a multicomponent variable. Each component corresponds to one criterion and measures how much the facet deviates from meeting this criterion. Then, the comparison operator on qualities is just a lexicographical comparison. The meshing algorithm handles facets with lowest quality first. The qualities are computed by a function is_bad(const Facet& f, const Quality& q).

Has Models:
CGAL::Surface_mesh_default_criteria_3<Tr>
See also
CGAL::make_surface_mesh()

Types

typedef unspecified_type Facet
 The type of facets. More...
 
typedef unspecified_type Quality
 Default constructible, copy constructible, assignable, and less-than comparable type.
 

Operations

bool is_bad (const Facet &f, const Quality &q)
 Assigns the quality of the facet f to q, and returns true is f does not meet the criteria.
 

Member Typedef Documentation

◆ Facet

typedef unspecified_type SurfaceMeshFacetsCriteria_3::Facet

The type of facets.

This type has to match the Facet type in the triangulation type used by the mesher function. (This triangulation type is the type SurfaceMeshC2T3::Triangulation provided by the model of SurfaceMeshComplex_2InTriangulation_3 plugged as first template parameter of CGAL::make_surface_mesh()).