Mesh and CAD Repair Based on Parametrizations with Radial Basis Functions
Piret, Cecile, Jean-Francois Remacle and Emilie Marchandise
20th International Meshing Roundtable, Springer-Verlag, pp.419-436, October 23-26 2011
20th International Meshing Roundtable
October 23-26, 2011
Universitie catholique de Louvain, Institute of Mechanics, Materials and Civil
Engineering (iMMC), Place du Levant 1, 1348 Louvain-la-Neuve, Belgium
The goal of this paper is to present a new repair process that includes
both model/mesh repair and mesh generation. The repair algorithm is based on an
initial mesh of the CAD that may contain topological and geometrical errors. This
initial mesh is then remeshed by computing a discrete parametrization with radial
basis functions (RBF's).
 showed that a discrete parametrization can be computed by solving PDE's
on an initial correct triangulation using nite elements. Paradoxically, the meshless
character of the RBF's makes it an attractive numerical method for solving the
PDE's for the parametrization in the case where the initial mesh contains errors.
In this work, we implement the Orthogonal Gradients method which was recently
introduced in , as a technique to solve PDE's on arbitrary surfaces with RBF's.
We will implement the low order version of the algorithm, which already gives great
results in this context.
Different examples show that the presented method is able to deal with errors
such as gaps, overlaps, T-joints and simple holes and that the resulting meshes are
of high quality. Moreover, the presented algorithm can be used as a hole-filling algorithm to repair meshes with undesirable holes. The overall procedure is implemented
in the open-source mesh generator Gmsh .
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