@Article{theisel05a,
  author    = {H.~Theisel and T.~Weinkauf and H.-C.~Hege and H.-P.~Seidel},
  title     = {Topological Methods for {2D} Time-Dependent Vector Fields Based on Stream Lines and Path Lines},
  journal   = {IEEE Transactions on Visualization and Computer Graphics},
  year      = {2005},
  volume    = {11},
  number    = {4},
  pages     = {383--394},
  month     = {July - August},
  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 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 apply them to
              a number of test data sets.},
  editor    = {David~S.~Ebert and Charles~D.~Hansen},
  keywords  = {flow visualization, vector field topology, bifurcations, stream lines, path lines},
  url = {http://tinoweinkauf.net/publications/abstheisel05a.html},
}