Beads Problem: Streak Line Vector Fields
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For the 2D time-dependent *Beads Problem* flow - as described in the paper "Streak Lines as Tangent Curves of a Derived Vector Field" (Weinkauf and Theisel, IEEE Vis 2010) - the cores of swirling stream, path, and streak lines are provided together with the ground truth for the attractor.

More information (file format, resolution, previous visualizations, etc.) can be found on http://tinoweinkauf.net/

Also, the formula for the original flow field is available on http://tinoweinkauf.net/


How to Acknowledge
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You are free to use these data sets as long as you give proper acknowledgement. Please use a LaTeX snippet similar to the following:

    The streak line vector fields as well as the extracted core lines
    are courtesy of Weinkauf and Theisel \cite{weinkauf10c}.
    
with the following BibTeX entries:

    @ARTICLE{weinkauf10c,
      author = {T.~Weinkauf and H.~Theisel},
      title = {Streak Lines as Tangent Curves of a Derived Vector Field},
      journal = {IEEE Transactions on Visualization and Computer Graphics (Proceedings Visualization 2010)},
      year = {2010},
      volume = {16},
      pages = {1225--1234},
      number = {6},
      month = {November - December},
      abstract = {Characteristic curves of vector fields include stream, path, and streak
                  lines. Stream and path lines can be obtained by a simple vector field
                  integration of an autonomous ODE system, i.e., they can be described
                  as tangent curves of a vector field. This facilitates their mathematical
                  analysis including the extraction of core lines around which stream
                  or path lines exhibit swirling motion, or the computation of their
                  curvature for every point in the domain without actually integrating
                  them. Such a description of streak lines is not yet available, which
                  excludes them from most of the feature extraction and analysis tools
                  that have been developed in our community. In this paper, we develop
                  the first description of streak lines as tangent curves of a derived
                  vector field -- the streak line vector field -- and show how it can
                  be computed from the spatial and temporal gradients of the flow map,
                  i.e., a dense path line integration is required. We demonstrate the
                  high accuracy of our approach by comparing it to solutions where
                  the ground truth is analytically known and to solutions where the
                  ground truth has been obtained using the classic streak line computation.
                  Furthermore, we apply a number of feature extraction and analysis
                  tools to the new streak line vector field including the extraction
                  of cores of swirling streak lines and the computation of streak line
                  curvature fields. These first applications foreshadow the large variety
                  of possible future research directions based on our new mathematical
                  description of streak lines.},
      keywords = {unsteady flow visualization, streak lines, streak surfaces, feature extraction},
      url = {http://tinoweinkauf.net/}
    }

    @ARTICLE{gerrisflowsolver,
      author = {S. Popinet},
      title = {Free Computational Fluid Dynamics},
      journal = {ClusterWorld},
      year = {2004},
      volume = {2},
      number = {6},
      url = {http://gfs.sf.net/}
    }
