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Article
CAD and mesh repair with Radial Basis Functions
Journal of Computational Physics (2012)
  • Emily Marchandise, Université catholique de Louvain
  • Cecile M Piret, Universite Catholique de Louvain
  • J F Remacle, Université catholique de Louvain
Abstract
In this paper we present a process that includes both model/mesh repair and mesh generation. The repair algorithm is based on an initial mesh that may be either an initial mesh of a dirty CAD model or STL triangulation with many errors such as gaps, overlaps and T-junctions. This initial mesh is then remeshed by computing a discrete parametrization with Radial Basis Functions (RBF’s).

We showed in [1] that a discrete parametrization can be computed by solving Partial Differential Equations (PDE’s) on an initial correct mesh using finite 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 or holes. In this work, we implement the Orthogonal Gradients method to be described in [2], as a RBF solution method for solving PDE’s on arbitrary surfaces.

Different examples show that the presented method is able to deal with errors such as gaps, overlaps, T-junctions 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 [3].
Keywords
  • Geometry processing,
  • Hole filling algorithm,
  • Radial Basis Functions,
  • RBF,
  • Surface remeshing,
  • Surface parametrization,
  • STL file format,
  • Surface mapping,
  • Harmonic map,
  • Orthogonal Gradients method
Disciplines
Publication Date
March 1, 2012
DOI
10.1016/j.jcp.2011.11.033
Publisher Statement
© 2012 Journal of Computational Physics. Deposited in compliance with publisher policies. Publisher's version of record: https://doi.org/10.1016/j.jcp.2011.11.033
Citation Information
Emily Marchandise, Cecile M Piret and J F Remacle. "CAD and mesh repair with Radial Basis Functions" Journal of Computational Physics Vol. 231 Iss. 5 (2012) p. 2376 - 2387
Available at: http://works.bepress.com/cecile_piret/4/