CGAL 4.7 - 3D Mesh Generation: Main Concepts

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

CGAL 4.7 - 3D Mesh Generation

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Main Concepts
3D Mesh Generation Reference

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The main concepts of this package.

## Concepts

concept | MeshCellCriteria_3

The Delaunay refinement process involved in the template functions `make_mesh_3()` and `refine_mesh_3()` is guided by a set of elementary refinement criteria that concern either mesh tetrahedra or surface facets. The concept `MeshCellCriteria_3` describes the types that handle the refinement criteria for mesh tetrahedra. More...

concept | MeshComplex_3InTriangulation_3

The concept `MeshComplex_3InTriangulation_3` describes a data structure to represent and maintain a 3D complex embedded in a 3D triangulation. More precisely, the concept `MeshComplex_3InTriangulation_3` is a minimal version designed to represent 3D complexes that have only faces with dimension \( 2\) and \( 3\). Embedded 3D complexes with faces of dimension \( 0\), \( 1\), \( 2\) and \( 3\), are more conveniently represented by the refined concept `MeshComplexWithFeatures_3InTriangulation_3`. More...

concept | MeshComplexWithFeatures_3InTriangulation_3

The concept `MeshComplexWithFeatures_3InTriangulation_3` describes a data structure to represent and maintain a 3D complex embedded in a 3D triangulation. The concept `MeshComplexWithFeatures_3InTriangulation_3` refines the minimal concept `MeshComplex_3InTriangulation_3`, designed to represent 3D complexes having only faces with dimension 2 and 3. Therefore, the concept `MeshComplexWithFeatures_3InTriangulation_3` may represent embedded complexes including features, i.e. faces with dimension \( 0\) and \( 1\). More...

concept | MeshCriteria_3

The Delaunay refinement process involved in the template functions `make_mesh_3()` and `refine_mesh_3()` is guided by a set of elementary refinement criteria that concern either mesh tetrahedra or surface facets. The refinement criteria for tetrahedra are described through the concept `MeshCellCriteria_3` while the refinement criteria for surface facets are described by the concept `MeshFacetCriteria_3`. The concept `MeshCriteria_3` encapsulates these concepts. More...

concept | MeshCriteriaWithFeatures_3

The concept `MeshCriteriaWithFeatures_3` refines the concept `MeshCriteria_3`. The concept `MeshCriteria_3` encapsulates the concepts `MeshCellCriteria_3` and `MeshFacetCriteria_3` describing the refinement criteria for, respectively, mesh cells and surface facets. For domains with features, the concept `MeshCriteriaWithFeatures_3` additionnally encapsulates the concept `MeshEdgeCriteria_3`, that describes the requirements, in terms of sizing, for the discretization of the domain \( 1\)-dimensional features. More...

concept | MeshDomain_3

The concept `MeshDomain_3` describes the knowledge required on the object to be discretized. The concept `MeshDomain_3` is the concept to be used when the input domain does not have \( 0\) or \( 1\)-dimensional features that need to be accurately approximated by the mesh. In such a case, the queries issued by the meshing process concern only the faces of the input domain with dimension \( 3\) and \( 2\), that are respectively called subdomains and surface patches. More...

concept | MeshDomainWithFeatures_3

The concept `MeshDomainWithFeatures_3` refines the concept `MeshDomain_3`. While the concept `MeshDomain_3` only exposes the 2-dimensional and 3-dimensional features of the domain through different queries, the concept `MeshDomainWithFeatures_3` also exposes 0 and 1-dimensional features. The exposed features of the domain are respectively called subdomains, surface patches, curve segments and corners according to their respective dimensions 3,2,1 and 0. More...

concept | MeshEdgeCriteria_3

The function object concept `MeshEdgeCriteria_3` is designed to drive the process which samples the 1-dimensional features of the domain. It provides an upper bound for the distance between two protecting ball centers that are consecutive on a 1-feature. More...

concept | MeshFacetCriteria_3

The Delaunay refinement process involved in the template functions `make_mesh_3()` and `refine_mesh_3()` is guided by a set of elementary refinement criteria that concern either mesh tetrahedra or surface facets. The concept `MeshFacetCriteria_3` describes the types that handle the refinement criteria for surface facets. More...