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Finite Time Steady 2D Vector Field Topology

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Topological Methods in Data Analysis and Visualization IV (TopoInVis 2015)

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Abstract

Vector Field Topology describes the asymptotic behavior of a flow in a vector field, i.e., the behavior for an integration time converging to infinity. For some applications, a segmentation of the flow in areas of similar behavior for a finite integration time is desired. We introduce an approach for a finite-time segmentation of a steady 2D vector field which avoids the systematic evaluation of the flow map in the whole flow domain. Instead, we consider the separatrices of the topological skeleton and provide them with additional information on how the separation evolves at each point with ongoing integration time. We analyze this behavior and its distribution along a separatrix, and we provide a visual encoding for it. The result is an augmented topological skeleton. We demonstrate the approach on several artificial and simulated vector fields.

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Acknowledgements

We wish to thank Niklas Röber and Michael Böttinger from the DKRZ for providing the South Pacific ocean dataset, as well as Tobias Günther for his general support.

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Authors and Affiliations

  1. University of Magdeburg, Magdeburg, Germany

    Anke Friederici, Christian Rössl & Holger Theisel

Authors
  1. Anke Friederici
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  2. Christian Rössl
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  3. Holger Theisel
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Corresponding author

Correspondence to Anke Friederici .

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Editors and Affiliations

  1. University of Leeds, Leeds, United Kingdom

    Hamish Carr

  2. Department of Computer Science, Technical University of Kaiserslautern, Kaiserslautern, Germany

    Christoph Garth

  3. School of Computer Science and Communication, KTH Royal Institute of Technology, Stockholm, Sweden

    Tino Weinkauf

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Friederici, A., Rössl, C., Theisel, H. (2017). Finite Time Steady 2D Vector Field Topology. In: Carr, H., Garth, C., Weinkauf, T. (eds) Topological Methods in Data Analysis and Visualization IV. TopoInVis 2015. Mathematics and Visualization. Springer, Cham. https://doi.org/10.1007/978-3-319-44684-4_15

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