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Topological methods for 2D time-dependent vector fields based on stream lines and path lines

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4 Author(s)
Theisel, H. ; MPI Informatik, Saarbrucken, Germany ; Weinkauf, T. ; Hege, H.-C. ; Seidel, H.-P.

This paper describes approaches to topologically segmenting 2D time-dependent vector fields. For this class of vector fields, two important classes of lines exist: stream lines and path lines. Because of this, two segmentations are possible: either concerning the behavior of stream lines or of path lines. While topological features based on stream lines are well established, we introduce path line oriented topology as a new visualization approach in this paper. As a contribution to stream line oriented topology, we introduce new methods to detect global bifurcations like saddle connections and cyclic fold bifurcations as well as a method of tracking all isolated closed stream lines. To get the path line oriented topology, we segment the vector field into areas of attracting, repelling, and saddle-like behavior of the path lines. We compare both kinds of topologies and apply them to a number of test data sets.

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Visualization and Computer Graphics, IEEE Transactions on  (Volume:11 ,  Issue: 4 )