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On the Applicability of Topological Methods for Complex Flow Data

  • Holger Theisel
  • Tino Weinkauf
  • Hans-Christian Hege
  • Hans-Peter Seidel
Part of the Mathematics and Visualization book series (MATHVISUAL)

Summary

In this paper we study the applicability of topological methods for creating expressive, feature revealing visualizations of 3D vector fields. 3D vector fields can become very complex by having a high number of critical points and separatrices. Moreover, they may have a very sparse topology due to a small number of critical points or their total absence. We show that classical topological methods based on the extraction of separation surfaces are poorly suited for creating expressive visualizations of topologically complex fields. We show this fact by pointing out that the number of sectors of different flow behavior grows quadratically with the number of critical points - contrary to 2D vector fields. Although this limits the applicability of topological methods to a certain degree, we demonstrate the extensibility of this limit by using further simplifying methods like saddle connectors. For 3D vector fields with a very sparse topology, topological visualizations may fail to reveal the features inherent to the field. We show how to overcome this problem for a certain class of flow fields by removing the ambient part of the flow.

Keywords

Saddle Point Stream Line Topological Method Topological Complexity Stream Surface 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Holger Theisel
    • 1
  • Tino Weinkauf
    • 2
  • Hans-Christian Hege
    • 3
  • Hans-Peter Seidel
    • 4
  1. 1.Bielefeld UniversityGermany
  2. 2.Zuse Institute Berlin (ZIB)Germany
  3. 3.Zuse Institute Berlin (ZIB)Germany
  4. 4.MPI Informatik SaarbrückenGermany

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