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Combinatorial Vector Field Topology in Three Dimensions

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Book cover Topological Methods in Data Analysis and Visualization II

Part of the book series: Mathematics and Visualization ((MATHVISUAL))

Abstract

In this paper, we present two combinatorial methods to process 3-D steady vector fields, which both use graph algorithms to extract features from the underlying vector field. Combinatorial approaches are known to be less sensitive to noise than extracting individual trajectories. Both of the methods are a straightforward extension of an existing 2-D technique to 3-D fields. We observed that the first technique can generate overly coarse results and therefore we present a second method that works using the same concepts but produces more detailed results. We evaluate our method on a CFD-simulation of a gas furnace chamber. Finally, we discuss several possibilities for categorizing the invariant sets with respect to the flow.

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Acknowledgements

We want to thank Tomasz Kaczynski, Matthias Schwarz, the people from the Krakau research group for “Computer Assisted Proofs in Dynamics” and the reviewers for many valuable hints and comments. We also thank the DFG for funding the project by grant SCHE 663/3-8.

Author information

Authors and Affiliations

  1. University of Leipzig, Leipzig, Germany

    Wieland Reich, Dominic Schneider, Christian Heine & Gerik Scheuermann

  2. Max-Planck-Institut for Human Cognitive and Brian Sciences, Leipzig, Leipzig, Germany

    Alexander Wiebel

  3. University of Utah, UT, Salt Lake City, USA

    Guoning Chen

Authors
  1. Wieland Reich
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  2. Dominic Schneider
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  3. Christian Heine
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  4. Alexander Wiebel
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  5. Guoning Chen
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  6. Gerik Scheuermann
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Corresponding author

Correspondence to Wieland Reich .

Editor information

Editors and Affiliations

  1. Inst. Computational Science, CAB G 65.1, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Ronald Peikert

  2. , Dept. of Informatics, University of Bergen, Bergen, Norway

    Helwig Hauser

  3. , School of Computing, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT, United Kingdom

    Hamish Carr

  4. , Computational Science, ETH Zürich, Universitätsstraße 6, Zürich, 8092, Switzerland

    Raphael Fuchs

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© 2012 Springer-Verlag Berlin Heidelberg

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Reich, W., Schneider, D., Heine, C., Wiebel, A., Chen, G., Scheuermann, G. (2012). Combinatorial Vector Field Topology in Three Dimensions. In: Peikert, R., Hauser, H., Carr, H., Fuchs, R. (eds) Topological Methods in Data Analysis and Visualization II. Mathematics and Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23175-9_4

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