[vita]

[publications]

[gallery]

[teaching]

[notes]

[contact]

[links]

weinkauf/gallery

Topological Structures in Two-Parameter-Dependent 2D Vector Fields Corresponding Publication
Logo 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. T. Weinkauf, H. Theisel, H.-C. Hege, H.-P. Seidel
Topological Structures in Two-Parameter-Dependent 2D Vector Fields
Computer Graphics Forum (Proc. Eurographics) 25(3), September 2006
[slideshow]
ANoiseMT_DFF_After
ANoiseMT_DFF_After
ANoiseMT_DFF_Before
ANoiseMT_DFF_Before
ANoiseMT_DFF_Event
ANoiseMT_DFF_Event
ANoiseMT_OverviewLIC
ANoiseMT_OverviewLIC
BBFold
BBFold
Cylinder2DMTFoldFoldsInS
Cylinder2DMTFoldFoldsInS
Cylinder2DMTLICSlice_T0_S1
Cylinder2DMTLICSlice_T0_S1
Cylinder2DMTLICSlice_T0_S30
Cylinder2DMTLICSlice_T0_S30
Cylinder2DMT_S02
Cylinder2DMT_S02
Cylinder2DMT_S08
Cylinder2DMT_S08
Cylinder2DMT_S10
Cylinder2DMT_S10
Cylinder2DMT_S12
Cylinder2DMT_S12
explainVisu
explainVisu
IsabelMainVortexPath
IsabelMainVortexPath
Isabel_T075
Isabel_T075
Isabel_T240
Isabel_T240
Isabel_T325_Top
Isabel_T325_Top
Isabel_T333
Isabel_T333
Isabel_T425
Isabel_T425
SFoldFoldSaddleBifurcation
SFoldFoldSaddleBifurcation
SimpleFeatures
SimpleFeatures
STFoldFoldBifurcation
STFoldFoldBifurcation
TFoldFoldClosedCollapseBifurcation
TFoldFoldClosedCollapseBifurcation
THopfFoldBifurcation
THopfFoldBifurcation
List of all images categories