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Summary: IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS (TVCG), VOL. 11, NO. 4, JULY/AUGUST 2005 1
Topological Methods for 2D Time-Dependent
Vector Fields Based on Stream Lines and Path Lines
Holger Theisel, Tino Weinkauf, Hans-Christian Hege, and Hans-Peter Seidel
(Invited Paper)
Abstract-- This paper describes approaches to topologi-
cally 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 segmenta-
tions 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 to 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
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