CGAL::exude_mesh_3

Definition

The function exude_mesh_3 performs a sliver exudation process on a Delaunay mesh.

The sliver exudation process consists in turning the Delaunay triangulation into a weighted Delaunay triangulation and optimizing the weights of vertices in such a way that slivers disappear and the quality of the mesh improves.

#include <CGAL/exude_mesh_3.h>

Precondition

Parameters

Parameter C3T3 is required to be a model of the concept MeshComplex_3InTriangulation_3. The argument c3t3, passed by reference, provides the initial mesh and is modified by the algorithm to represent the final optimized mesh.

The function has two optional parameters which are named parameters (we use the Boost.Parameter library). Therefore, when calling the function, the parameters can be provided in any order provided that the names of the parameters are used (see example at the bottom of this page).

• Parameter time_limit, whose name is parameters::time_limit, is used to set up, in seconds, a CPU time limit after which the optimization process is stopped. This time is measured using the CGAL::Timer class. The default value is 0 and means that there is no time limit.
• Parameter sliver_bound, whose name is parameters::sliver_bound, is designed to give, in degree, a targeted lower bound on dihedral angles of mesh cells. The exudation process considers in turn all the mesh cells that have a smallest dihedral angle less than sliver_bound and tries to make them disappear by weighting their vertices. The optimization process stops when every cell in the mesh achieves this quality. The default value is 0 and means that there is no targeted bound : the exuder then runs as long as it can improve the smallest dihedral angles of the set of cells incident to some vertices.

Return Values

• BOUND_REACHED when the targeted bound for the smallest dihedral angle in the mesh is reached.
• TIME_LIMIT_REACHED when the time limit is reached.
• CANT_IMPROVE_ANYMORE when exudation process stops because it can no longer improve the smallest dihedral angle of the set of cells incident to some vertex in the mesh.

Example

// Exude without sliver_bound, using at most 10s CPU time
exude_mesh_3(c3t3, parameters::time_limit=10);

See Also

CGAL::Mesh_optimization_return_code
CGAL::make_mesh_3
CGAL::refine_mesh_3
CGAL::perturb_mesh_3
CGAL::lloyd_optimize_mesh_3
CGAL::odt_optimize_mesh_3