title: Topological methods for 2D time-dependent vector fields based on stream lines and path lines.
abstract: 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.
authors.affiliation: MPI Informatik, AG4, Stuhlsatzenhausweg 85, 66123 Saarbrucken, Germany. theisel@mpi-sb.mpg.de
authors.forename: Holger
authors.initials: H
authors.lastname: Theisel
authors.forename: Tino
authors.initials: T
authors.lastname: Weinkauf
authors.forename: Hans-Christian
authors.initials: HC
authors.lastname: Hege
authors.forename: Hans-Peter
authors.initials: HP
authors.lastname: Seidel
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008962:Models, Theoretical; D009716:Numerical Analysis, Computer-Assisted; D009862:Online Systems; D012212:Rheology / Q000379:methods*; D014584:User-Computer Interface