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

Weinkauf, T.; Theisel, H.; Hege, H.-C.; Seidel, H.-P.

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

Date

2006

Authors

Weinkauf, T.
Theisel, H.
Hege, H.-C.
Seidel, H.-P.

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

        @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
}
}