CGAL 5.1 - Tetrahedral Remeshing
Tetrahedral Remeshing Reference

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Jane Tournois, Noura Faraj
The package provides a function for remeshing tetrahedral meshes, targetting high quality meshes with respect to dihedral angles.
Introduced in: CGAL 5.1
Depends on: 3D Triangulations
BibTeX: faraj2016mvr-20a
License: GPL
Windows Demo: Polyhedron demo
Common Demo Dlls: dlls

Classified Reference Pages

Concepts

Classes

Function Templates

Modules

 Named Parameters for Tetrahedral Remeshing
 How to use BGL Optional Named Parameters

 
 Concepts
 
 Classes
 

Functions

template<typename Traits , typename TDS , typename SLDS , typename NamedParameters >
void CGAL::tetrahedral_isotropic_remeshing (CGAL::Triangulation_3< Traits, TDS, SLDS > &tr, const double &target_edge_length, const NamedParameters &np)
 remeshes a tetrahedral mesh. More...
 

Function Documentation

◆ tetrahedral_isotropic_remeshing()

template<typename Traits , typename TDS , typename SLDS , typename NamedParameters >
void CGAL::tetrahedral_isotropic_remeshing ( CGAL::Triangulation_3< Traits, TDS, SLDS > &  tr,
const double &  target_edge_length,
const NamedParameters &  np 
)

#include <CGAL/tetrahedral_remeshing.h>

remeshes a tetrahedral mesh.

It is recommended to use CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3 for the first parameter, as it inherits from Triangulation_3 with a TDS suitable for this function.

This function takes as input a 3-dimensional triangulation and performs a sequence of atomic operations in order to generate as output a high quality mesh with a prescribed uniform density. These atomic operations are performed as follows:

  • edge splits, until all edges satisfy a prescribed length criterion,
  • edge collapses, until all edges satisfy a prescribed length criterion,
  • edge flips, to locally improve dihedral angles, until they can no longer be improved by flipping,
  • global smoothing by vertex relocations,
  • re-projection of boundary vertices to the initial surface.

This remeshing function can deal with multi-domains, boundaries, and features. It preserves the geometry of subdomains throughout the remeshing process.

Subdomains are defined by indices that are stored in the cells of the input triangulation, following the MeshCellBase_3 concept (refined by RemeshingCellBase_3). The surfacic interfaces between subdomains are formed by facets whose two incident cells have different subdomain indices. The edges where three or more subdomains meet form feature polylines, and are considered as constrained edges.

Template Parameters
Traitsis the geometric traits, model of RemeshingTriangulationTraits_3
TDSis the triangulation data structure for Triangulation_3, model of TriangulationDataStructure_3, with cell base model of RemeshingCellBase_3 and vertex base model of RemeshingVertexBase_3.
SLDSis an optional parameter for Triangulation_3, that specifies the type of the spatial lock data structure.
NamedParametersa sequence of Named Parameters
Parameters
trthe triangulation to be remeshed, of type Triangulation_3<Traits, TDS, SLDS>. Remeshing_triangulation is a helper class that satisfies all the requirements of its template parameters.
target_edge_lengththe uniform target edge length. This parameter provides a mesh density target for the remeshing algorithm.
npoptional sequence of Named Parameters among the ones listed below
Named Parameters
number_of_iterationsthe number of iterations for the full sequence of atomic operations performed (listed in the above description)
remesh_boundariesIf false, none of the input volume boundaries can be modified. Otherwise, the topology is preserved, but atomic operations can be performed on the surfaces, and along feature polylines, such that boundaries are remeshed.
edge_is_constrained_mapa property map containing the constrained - or - not status of each edge of tr. A constrained edge can be split or collapsed, but not flipped.
facet_is_constrained_mapa property map containing the constrained - or - not status of each facet of tr. A constrained facet can be split or collapsed, but not flipped.
cell_is_selected_mapa property map containing the selected - or - not status for each cell of tr for remeshing. Only selected cells are modified (and possibly their neighbors if surfaces are modified) by remeshing. By default, all cells with a non-zero Subdomain_index are selected.
See also
CGAL::Tetrahedral_remeshing::Remeshing_triangulation_3
Examples:
Tetrahedral_remeshing/tetrahedral_remeshing_example.cpp, Tetrahedral_remeshing/tetrahedral_remeshing_of_one_subdomain.cpp, and Tetrahedral_remeshing/tetrahedral_remeshing_with_features.cpp.