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Optimal parametrizations for surface remeshing

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Abstract

We present different linear parametrization techniques for the purpose of surface remeshing: the energy minimizing harmonic map, the convex map, and the least square conformal map. The implementation of those mappings as well as the associated boundary conditions is presented in a unified manner and the issues of triangle flipping and folding that may arise with discrete linear mappings are discussed. We explore the optimality of these parametrizations for surface remeshing by applying several classical 2D meshing algorithms in the parametric space and by comparing the quality of the generated elements. We present various examples that permit to draw guidelines that a user can follow in choosing the best parametrization scheme for a specific topology, geometry, and characteristics of the target output mesh.

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Notes

  1. Non-closed surfaces are surfaces of zero genius with at least one boundary. The genus of a surface is defined as the number of handles in the surface.

  2. For example, a non-closed surface with one hole (see Fig. 9) has N = 2 closed boundaries.

  3. The STL triangulation of the aorta and the tooth can be downloaded from the INRIA database http://www-roc.inria.fr/gamma/gamma.php and the STL triangulation of the pelvis is presented in [28].

  4. The model can be downloaded at the following web site: http://www.sonycsl.co.jp/person/nielsen/visualcomputing/programs/bunny-conformal.obj.

  5. Access the wiki with username gmsh and password gmsh.

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Authors and Affiliations

  1. Institute of Mechanics, Materials and Civil Engineering (iMMC), Université catholique de Louvain, Place du Levant 1, 1348, Louvain-la-Neuve, Belgium

    Emilie Marchandise & Jean-François Remacle

  2. Department of Electrical Engineering and Computer Science, Montefiore Institute B28, Université de Liège, Grande Traverse 10, 4000, Liège, Belgium

    Christophe Geuzaine

Authors
  1. Emilie Marchandise
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  2. Jean-François Remacle
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  3. Christophe Geuzaine
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Correspondence to Emilie Marchandise.

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Marchandise, E., Remacle, JF. & Geuzaine, C. Optimal parametrizations for surface remeshing. Engineering with Computers 30, 383–402 (2014). https://doi.org/10.1007/s00366-012-0309-3

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