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

CGAL 4.8 - 3D Surface Mesh Generation

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SurfaceMeshFacetsCriteria_3 Concept 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

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()`).