CGAL 6.2 - 3D Periodic Mesh Generation

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CGAL::Periodic_3_mesh_triangulation_3< MD, GT, Vertex_base, Cell_base > Class Template Reference
Reference Manual » Mesh Classes

`#include <CGAL/Periodic_3_mesh_triangulation_3.h>`

## Definition

template<typename MD, typename GT, typename Vertex_base, typename Cell_base>
class CGAL::Periodic_3_mesh_triangulation_3< MD, GT, Vertex_base, Cell_base >

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

  MD | must be a model of `Periodic_3MeshDomain_3` or `Periodic_3MeshDomainWithFeatures_3`.
  GT | must be a model of `MeshTriangulationTraits_3`. `Default` may be used, with default value `Kernel_traits<MD>::Kernel`.
  Vertex_base | must 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_base | must 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.

## 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`.