\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.11 - 3D Mesh Generation
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CGAL::Mesh_triangulation_3< MD, Gt, Concurrency_tag, Vertex_base, Cell_base > Class Template Reference
Mesh Classes

#include <CGAL/Mesh_triangulation_3.h>

Definition

The class Mesh_triangulation_3 is a metafunctor which provides the triangulation type to be used for the 3D triangulation embedding the mesh.

Template Parameters
MDmust be a model of MeshDomain_3.
Gtmust be a model of RegularTriangulationTraits_3 or Default and defaults to Kernel_traits<MD>::Kernel.
Concurrency_tagenables sequential versus parallel meshing and optimization algorithms. Possible values are Sequential_tag (the default) and Parallel_tag.
Vertex_basemust be a model of MeshVertexBase_3 or Default and defaults to Mesh_vertex_base_3<Gt, MD>.
Cell_basemust be a model of MeshCellBase_3 or Default and defaults to Compact_mesh_cell_base_3<Gt, MD>.
Warning
To improve the robustness of the meshing process, the input traits Gt is wrapped with the traits class Robust_weighted_circumcenter_filtered_traits_3. The class Robust_weighted_circumcenter_filtered_traits_3<Gt> upgrades the functors models of Kernel::ConstructWeightedCircumcenter_3, Kernel::ComputeSquaredRadius_3, and Kernel::ComputeSquaredRadiusSmallestOrthogonalSphere_3 that are provided by Gt to use exact computations when the geometric configuration is close to degenerate (e.g. almost coplanar points).
Users should therefore be aware that the traits class of the triangulation will have type Robust_weighted_circumcenter_filtered_traits_3<Gt>.
See Also
make_mesh_3()
Mesh_complex_3_in_triangulation_3<Tr,CornerIndex,CurveSegmentIndex>

Types

typedef unspecified_type type
 The triangulation type to be used for the 3D triangulation embedding the mesh. More...
 

Member Typedef Documentation

template<typename MD, typename Gt, typename Concurrency_tag, typename Vertex_base, typename Cell_base>
typedef unspecified_type CGAL::Mesh_triangulation_3< MD, Gt, Concurrency_tag, Vertex_base, Cell_base >::type

The triangulation type to be used for the 3D triangulation embedding the mesh.

This type is a Regular_triangulation_3 type whose vertex and cell base classes are respectively Vertex_base and Cell_base.