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Topological Structures in Two-Parameter-Dependent 2D Vector Fields

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons45606

Theisel,  Holger
Computer Graphics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45449

Seidel,  Hans-Peter
Computer Graphics, MPI for Informatics, Max Planck Society;

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Zitation

Weinkauf, T., Theisel, H., Hege, H.-C., & Seidel, H.-P. (2006). Topological Structures in Two-Parameter-Dependent 2D Vector Fields. In EUROGRAPHICS 2006 (EG'06) (pp. 607-616). Oxford, UK: Blackwell.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-2443-5
Zusammenfassung
In this paper we extract and visualize the topological skeleton of two-parameter-dependent vector fields. This kind of vector data depends on two parameter dimensions, for instance physical time and a scale parameter. We show that two important classes of local bifurcations – fold and Hopf bifurcations – build line structures for which we present an approach to extract them. Furthermore we show that new kinds of structurally stable local bifurcations exist for this data, namely fold-fold and Hopf-fold bifurcations. We present a complete classification of them. We apply our topological extraction method to analyze a number of two-parameter-dependent vector fields with different physical interpretations of the two additional dimensions.