Jane Tournois, Noura Faraj, Jean-Marc Thiery, and Tamy Boubekeur

The package provides a function for remeshing tetrahedral meshes, targeting high quality meshes with respect to dihedral angles. This practical iterative remeshing algorithm is designed to remesh multi-material tetrahedral meshes, by iteratively performing a sequence of elementary operations such as edge splits, edge collapses, edge flips, and vertex relocations following a Laplacian smoothing. The algorithm results in high-quality uniform isotropic meshes, with the desired mesh density, while preserving the input geometric curve and surface features.

converts the triangulation contained in the input to a Triangulation_3.

This function should be used to generate a valid triangulation for tetrahedral remeshing, when the input triangulation is generated with the tetrahedral mesh generation package.

the complex containing the triangulation to be remeshed.

np

optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

a property map containing the constrained-or-not status of each edge of c3t3.triangulation(). For each edge e for which c3t3.is_in_complex(e) returns true, the constrained status of e is set to true.

Default: a default property map where no edge is constrained

a property map containing the constrained-or-not status of each vertex of c3t3.triangulation(). For each vertex v for which c3t3.is_in_complex(v) returns true, the constrained status of v is set to true.

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 SimplicialMeshCellBase_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.

the 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.

sizing

the target edge length. This parameter provides a mesh density target for the remeshing algorithm. It can be a number convertible to double, or an instance of a model of RemeshingSizingField_3.

np

optional sequence of Named Parameters among the ones listed below

Optional Named Parameters

the number of iterations for the full sequence of atomic operations performed (listed in the above description)

Type: unsigned int

Default: 1

If 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.

Type: bool

Default: true

Extra: Boundaries are between the exterior and the interior, between two subdomains, between the areas selected or not for remeshing (cf Remeshing_cell_is_selected_map), or defined by Remeshing_edge_is_constrained_map and Remeshing_facet_is_constrained_map.

a property map containing the constrained-or-not status of each facet of tr.

Default: a default property map where no edge is constrained

Extra: A constrained edge can be split or collapsed, but not flipped.

Extra: The pairs must be ordered to ensure consistency.

Extra: During the meshing process, the set of constrained edges evolves consistently with edge splits and collapses, so the property map must be writable.

a property map containing the constrained-or-not status of each vertex of tr.

Default: a default property map where no vertex is constrained

Extra: A constrained vertex cannot be removed by collapse, nor moved by smoothing.

a 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.

Default: a default property map where all cells of the domain (i.e. with a non-zero Subdomain_index) are selected.

Extra: During the meshing process, the set of selected cells evolves consistently with the atomic operations that are performed, so the property map must be writable.

If true, the end vertices of the edges set as constrained in edge_is_constrained_map move along the constrained polylines they belong to.

Type: bool

Default: false

Extra: The endvertices of constraints listed by edge_is_constrained_map, and edges incident to at least three subdomains are made eligible to one dimensional smoothing, along the constrained polylines they belong to. Corners (i.e. vertices listed by vertex_is_constrained_map or incident to more than 2 constrained edges) are not allowed to move at all.
Note that activating the smoothing step on polyline constraints tends to reduce the quality of the minimal dihedral angle in the mesh.
If remesh_boundaries is set to false, this parameter is ignored.