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EUROGRAPHICS 2006 / E. Grller and L. Szirmay-Kalos (Guest Editors)

Summary: EUROGRAPHICS 2006 / E. Gröller and L. Szirmay-Kalos
(Guest Editors)
Volume 25 (2006), Number 3
Topological Structures in
Two-Parameter-Dependent 2D Vector Fields
T. Weinkauf1
, H. Theisel2
, H.-C. Hege1
and H.-P. Seidel2
1 Zuse Institute Berlin (ZIB), Berlin, Germany -- {weinkauf, hege}@zib.de
2 MPI Informatik, Saarbrücken, Germany -- {theisel, hpseidel}@mpi-sb.mpg.de
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.
Categories and Subject Descriptors (according to ACM CCS): I.3.3 [Computer Graphics]: Line and Curve Genera-


Source: Andrzejak, Artur - Konrad-Zuse-Zentrum für Informationstechnik Berlin


Collections: Computer Technologies and Information Sciences