refine_mesh

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CGAL::refine_mesh_3

Definition

The function refine_mesh_3 is a 3D mesh generator. It produces simplicial meshes which discretize 3D domains.

The mesh generation algorithm is a Delaunay refinement process followed by an optimization phase. The criteria driving the Delaunay refinement process may be tuned to achieve the user needs with respect to the size of mesh elements, the accuracy of boundaries approximation, etc.

The optimization phase is a succession of optimization processes, including possibly a Lloyd smoothing, an odt-smoothing, a perturber and an exuder. Each optimization process can be activated or not, according to the user requirements and available time. By default, only the perturber and the exuder are activated. Note that the benefits of the exuder will be lost if the mesh is further refined afterward.

template <class C3T3, class MeshDomain_3, class MeshCriteria>

void

refine_mesh_3 ( C3T3& c3t3,
MeshDomain_3 mesh_domain,
MeshCriteria mesh_criteria,
Lloyd lloyd = parameters::no_lloyd(),
Odt odt = parameters::no_odt(),
Perturb perturb = parameters::perturb(),
Exude exude = parameters::exude())

The function template refine_mesh_3 may be used to refine a previously computed mesh, e.g.:

C3T3 c3t3 = CGAL::make_mesh_3<C3T3>(domain,criteria);
CGAL::refine_mesh_3(c3t3, domain, new_criteria);

Please note that we guarantee the result if and only if the domain does not change from one refinement to the next one.

Parameters

Parameter C3T3 is required to be a model of the concept MeshComplex_3InTriangulation_3. The argument c3t3 is passed by reference as this object is modified by the refinement process. As the refinement process only adds points to the triangulation, all vertices of the triangulation of c3t3 remain in the mesh during the refinement process. Object c3t3 can be used to insert specific points in the domain to ensure that they will be contained in the final triangulation.

The type C3T3 is in particular required to provide a nested type C3T3::Triangulation for the 3D triangulation embedding the mesh. The vertex and cell base classes of the triangulation C3T3::Triangulation are required to be models of the concepts MeshVertexBase_3 and MeshCellBase_3 respectively.

Template parameter MeshDomain_3 is required to be a model of the concept MeshDomain_3 or of the refined concept MeshDomainWithFeatures_3 if 0 and 1-dimensional features of the input complex have to be accurately represented in the mesh. The argument domain is the sole link through which the domain to be discretized is known by the mesh generation algorithm.

The template parameter MeshCriteria has to be a model of the concept MeshCriteria_3, or a model of the refined concept MeshCriteriaWithFeatures_3 if the domain has exposed features. The argument criteria of type MeshCriteria specifies the size and shape requirements for mesh tetrahedra and surface facets. These criteria form the rules which drive the refinement process. All mesh elements satisfy those criteria at the end of the refinement process. In addition, if the domain has features, the argument criteria provides a sizing field to guide the discretization of 1-dimensional exposed features.

The four additional parameters are optimization parameters. They control which optimization processes are performed and allow the user to tune the parameters of the optimization processes. We do not describe the types of optimization parameters as they are internal types. The package defines two global functions for each optimization parameter to generate appropriate value of this parameter.

parameters::lloyd() and parameters::no_lloyd() are designed to trigger or not a call to lloyd_optimize_mesh_3 function and to set the parameters of this optimizer. If one parameter is not set, the default value of lloyd_optimize_mesh_3 is used for this parameter.
parameters::odt() and parameters::no_odt() are designed to trigger or not a call to odt_optimize_mesh_3 function and to set the parameters of this optimizer If one parameter is not set, the default value of odt_optimize_mesh_3 is used for this parameter.
parameters::perturb() and parameters::no_perturb() are designed to trigger or not a call to perturb_mesh_3 function and to set the parameters of this optimizer. If one parameter is not set, the default value of perturb_mesh_3 is used for this parameter, except for the time bound which is set to be equal to the refinement CPU time.
parameters::exude() and parameters::no_exude() are designed to trigger or not a call to exude_mesh_3 function and to override to set the parameters of this optimizer. If one parameter is not set, the default value of exude_mesh_3 is used for this parameter, except for the time bound which is set to be equal to the refinement CPU time.

The optimization parameters can be passed in random order. If one parameter is not passed, its default value is used. The default values are no_lloyd(), no_odt(), perturb() and exude(). Note that whatever may be the optimization processes activated, they are always launched in the order that is a suborder of the following (see user manual for further details): lloyd, odt, perturb, exude.

Beware that optimization of the mesh is obtained by perturbing mesh vertices and modifying the mesh connectivity and that this has an impact on the strict compliance to the refinement criteria. Though a strict compliance to mesh criteria is granted at the end of the Delaunay refinement, this may no longer be true after some optimization processes. Also beware that the default behavior does involve some optimization processes.

CGAL::refine_mesh_3

Definition

Parameters

See Also