\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.14.3 - 3D Periodic Mesh Generation
List of all members
CGAL::Periodic_3_mesh_triangulation_3< MD, GT, Vertex_base, Cell_base > Class Template Reference
3D Periodic Mesh Generation Reference » Mesh Classes

#include <CGAL/Periodic_3_mesh_triangulation_3.h>

Definition

The class Periodic_3_mesh_triangulation_3 is a class template which provides the triangulation type to be used for the 3D periodic triangulation embedding the mesh.

Template Parameters
MDmust be a model of Periodic_3MeshDomain_3 or Periodic_3MeshDomainWithFeatures_3.
GTmust be a model of MeshTriangulationTraits_3. Default may be used, with default value Kernel_traits<MD>::Kernel.
Vertex_basemust be a model of MeshVertexBase_3 and Periodic_3TriangulationDSVertexBase_3. Default may be used, with default value Mesh_vertex_base_3<GT, MD, Regular_triangulation_vertex_base_3<Gt, Periodic_3_triangulation_ds_vertex_base_3> >.
Cell_basemust be a model of MeshCellBase_3 and Periodic_3TriangulationDSCellBase_3. Default may be used, with default value Mesh_cell_base_3<GT, MD, Regular_triangulation_cell_base_with_weighted_circumcenter_3<Gt, Regular_triangulation_cell_base_3<Gt, Periodic_3_triangulation_ds_cell_base_3> > >.
Warning
The input traits GT are wrapped multiple times to handle periodicity and to improve the robustness of the meshing process: for example, wrapping GT with Robust_weighted_circumcenter_filtered_traits_3<GT> allows 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 type of the traits class of the triangulation will not be GT.
See also
make_periodic_3_mesh_3()
refine_periodic_3_mesh_3()
Mesh_triangulation_3

Types

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

Member Typedef Documentation

◆ type

template<typename MD, typename GT, typename Vertex_base, typename Cell_base>
typedef unspecified_type CGAL::Periodic_3_mesh_triangulation_3< MD, GT, Vertex_base, Cell_base >::type

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

This type is a wrapper around the type CGAL::Periodic_3_regular_triangulation_3, whose vertex and cell base classes are respectively Vertex_base and Cell_base.