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Topological Methods in Data Analysis and Visualization II pp 177–190Cite as

Glyphs for Non-Linear Vector Field Singularities

Part of the Mathematics and Visualization book series (MATHVISUAL)

Abstract

Glyphs are a widespread technique to depict local properties of different kinds of fields. In this paper we present a new glyph for singularities in non-linear vector fields. We do not simply show the properties of the derivative at the singularities as most previous methods do, but instead illustrate the behavior that goes beyond the local linear approximation. We improve the concept of linear neighborhoods to determine the size of the vicinity from which we derive the data for the glyph. To obtain data from outside this neighborhood we use integration in the vector field. The gathered information is used to depict convergence and divergence of the flow, and non-linear behavior in general. These properties are communicated by color, radius, the overall shape of the glyphs and streamlets on their surface. This way we achieve a depiction of the non-linear behavior of the flow around the singularities.

Keywords

  • Diffusion Tensor Imaging
  • IEEE Computer Society
  • Binary Search
  • Lagrangian Coherent Structure
  • Iconic Representation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Acknowledgements

First of all the authors would like to thank the reviewers for their many constructive remarks and suggestions which greatly helped to improve the paper. The authors would like to thank Markus Rütten from DLR in Göttingen for providing the datasets. Thanks also go to Wieland Reich and Roxana Bujack for helpful discussions. Special thanks go to the FAnToM development group for providing the environment for the implementation of the presented work. This work was partially supported by DFG grant SCHE 663/3-8. During the course of this work Alexander Wiebel was hired by the Max Planck Institute for Human Cognitive and Brain Sciences in Leipzig. The first two authors contributed equally to this work.

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Authors and Affiliations

  1. Zuse-Institut Berlin, Takustr. 7, 14195, Berlin-Dahlem, Deutschland

    Alexander Wiebel

  2. Institut für Informatik, Universität Leipzig, PF 100920, 04009, Leipzig, Deutschland

    Stefan Koch & Gerik Scheuermann

Authors
  1. Alexander Wiebel
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  2. Stefan Koch
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  3. Gerik Scheuermann
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Corresponding author

Correspondence to Alexander Wiebel .

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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Wiebel, A., Koch, S., Scheuermann, G. (2012). Glyphs for Non-Linear Vector Field Singularities. 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_12

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