The paper Advected Tangent Curves: A General Scheme for Characteristic Curves of Flow Fields of the research group of Tino Weinkauf has been accepted at EuroGraphics 2012.

In this paper, 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 is presented. Thus, all these lines can be obtained by a simple integration of an autonomous ODE system. This is in particular interesting for time lines, since they could previously only be constructed in a geometric manner.

Furthermore, the scheme gives rise to new types of curves. In particular, the group introduces advected stream lines as a parameter-free variant of the time line metaphor.

With their 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. They highlight some of these possible applications including the computation of time line curvature fields and the extraction of cores of swirling advected stream lines.

See the group’s videos at YouTube.