License: Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license (CC BY-NC-ND 3.0)
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DOI: 10.4230/DFU.SciViz.2010.30
URN: urn:nbn:de:0030-drops-26956
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Lehner, Burkhard ; Hamann, Bernd ; Umlauf, Georg

Generalized Swap Operation for Tetrahedrizations

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Mesh optimization of 2D and 3D triangulations is used in multiple applications extensively. For example, mesh optimization is crucial in the context of adaptively discretizing geometry, typically representing the geometrical boundary conditions of a numerical simulation, or adaptively discretizing the entire space over which various dependent variables of a numerical simulation must be approximated. Together with operations applied to the vertices the so-called edge or face swap operations are the building block of all optimization approaches. To speed up the optimization or to avoid local minima of the function measuring overall mesh quality these swaps are combined to generalized swap operations with a less local impact on the triangulation.

Despite the fact that these swap operations change only the connectivity of a triangulation, it depends on the geometry of the triangulation whether the generalized swap will generate inconsistently oriented or degenerate simplices. Because these are undesirable for numerical reasons, this paper is concerned with geometric criteria that guarantee the generalized swaps for a 3D triangulation to yield only valid, non-degenerate triangulations.

BibTeX - Entry

  author =	{Burkhard Lehner and Bernd Hamann and Georg Umlauf},
  title =	{{Generalized Swap Operation for Tetrahedrizations}},
  booktitle =	{Scientific Visualization: Advanced Concepts},
  pages =	{30--44},
  series =	{Dagstuhl Follow-Ups},
  ISBN =	{978-3-939897-19-4},
  ISSN =	{1868-8977},
  year =	{2010},
  volume =	{1},
  editor =	{Hans Hagen},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-26956},
  doi =		{10.4230/DFU.SciViz.2010.30},
  annote =	{Keywords: 3D Triangulation, Geometric Conditions, Swap Operations}

Keywords: 3D Triangulation, Geometric Conditions, Swap Operations
Collection: Scientific Visualization: Advanced Concepts
Issue Date: 2010
Date of publication: 02.08.2010

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