Topological Structures in Two-Parameter-Dependent 2D Vector Fields
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Date
2006
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and Blackwell Publishing, Inc
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 Generation I.3.3 [Computer Graphics]: Picture/Image Generation
Description
@article{10.1111:j.1467-8659.2006.00980.x,
journal = {Computer Graphics Forum},
title = {{Topological Structures in Two-Parameter-Dependent 2D Vector Fields}},
author = {Weinkauf, T. and Theisel, H. and Hege, H.-C. and Seidel, H.-P.},
year = {2006},
publisher = {The Eurographics Association and Blackwell Publishing, Inc},
ISSN = {1467-8659},
DOI = {10.1111/j.1467-8659.2006.00980.x}
}