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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
Abstract
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-
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