2006
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Topological Structures in Two-Parameter-Dependent 2D Vector Fields
Computer Graphics Forum (Proc. Eurographics) 25(3), September 2006
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.
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- Video explaining bifurcations (DivX) [2.9 MB]
- Video showing topological structures in the hurricane Isabel data set (DivX) [2.5 MB]
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