Flowspace: The Space Spanned by Pathlines, Timelines, Streaklines.

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Scientific visualization - that is, presenting computed or measured scientific data to human senses - is a vital area of research. Pictures are often the clearest and fastest way to give a scientist an intuitive feeling for an experiment or simulation. Unfortunately, visualization of time-dependent vector fields (such as velocity of a fluid at all points) is currently limited to a few basic techniques that originally came from experimental methods. Every technique is a variation on streaklines and timelines, both built from particle paths. Crude extensions to algorithms developed for steady flows have recently supplemented these. Most notable among these are the computation and display of streamlines, but these are only physically relevant for steady-state fluid flows.This project will place these commonly used techniques within a general geometric and mathematical framework, and advance the notion that no single method is best suited for all flows. Therefore, it will study a more general class of algorithms, and will seek to match a vector field representation to the display of a desired time-dependent feature of the flow (e.g. vortices, eddies, or shocks). To explore this parameter space, the project will develop a suite of interactive vector field visualization tools using both software- and hardware-based techniques. The methods will be tested on prototypical unsteady vector fields, namely linear and quadratic fields in the spatial and temporal variables.