@Article{weinkauf12a,
  author    = {T.~Weinkauf and H.-C.~Hege and H.~Theisel},
  title     = {Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields},
  journal   = {Computer Graphics Forum (Proc. Eurographics)},
  year      = {2012},
  volume    = {31},
  number    = {2},
  pages     = {825--834},
  month     = {May},
  abstract  = {We present the first general scheme to describe all four types of
              characteristic curves of flow fields -- stream, path, streak, and
              time lines -- as tangent curves of a derived vector field. Thus,
              all these lines can be obtained by a simple integration of an autonomous
              ODE system. Our approach draws on the principal ideas of the recently
              introduced tangent curve description of streak lines. We provide
              the first description of time lines as tangent curves of a derived
              vector field, which could previously only be constructed in a geometric
              manner. Furthermore, our scheme gives rise to new types of curves.
              In particular, we introduce advected stream lines as a parameter-free
              variant of the time line metaphor. With our novel mathematical description
              of characteristic curves, a large number of feature extraction and
              analysis tools becomes available for all types of characteristic
              curves, which were previously only available for stream and path
              lines. We will highlight some of these possible applications including
              the computation of time line curvature fields and the extraction
              of cores of swirling advected stream lines.},
  keywords  = {unsteady flow visualization, time lines, time surfaces, feature extraction},
  url = {http://tinoweinkauf.net/publications/absweinkauf12a.html},
}