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Summary

If you have an important point to make, don't try to be subtle or clever. Use a pile driver. Hit the point once. Then come back and hit it again. Then hit it a third time - a tremendous whack.
Winston Churchill (1874-1965)

Flow visualization and the visualization of dynamical systems make up an important research area in the field of visualization. Complex dynamics apparent over multi-dimensional domains require sophisticated visualization techniques to be investigated efficiently. Either simulated data - usually huge data-sets resulting from finite element calculations - or analytic models - differential equations representing a dynamical system - significantly extend the size of easily and quickly understandable information. This, generally, is the point where visualization is required.

Quite a reasonable number of useful visualization techniques already are available for the purpose of getting insight in data-sets of that size. Direct visualization by means of direct visual encoding of the given dynamics probably is the most intuitive and, thus, the oldest approach to the visualization task. Hedgehog plots, streamlets and stream lines already have a long tradition in flow visualization. Especially in 2D they directly and intuitively represent the motion to be visualized.

More elaborated techniques like spot noise and line integral convolution, stream lines in 3D and stream surfaces, stream balls, stream ribbons, stream polygons and stream tube, flow volumes, as well as particle systems enrich the possibilities of directly visualizing a dynamical system or flow data.

Instead of directly representing the flow dynamics, sometimes local or abstract data derived from the dynamical system should be visualized. Critical points, for example, usually are especially interesting. Thus, local information extracted from higher-order derivatives, are visualized using, for instance, glyphs or icons. Abstract data, like lower-dimensional skeletons that describe the flow dynamics just qualitatively, i.e., the topological structure of a dynamical system, often are of special interest also. Combining those two approaches appears to be especially useful, since a dense representation is used, the most important information is conveyed.



 


next up previous contents
Next: Stream arrows Up: Helwig's PhD thesis Previous: System capabilities
Helwig Löffelmann, November 1998,
mailto:helwig@cg.tuwien.ac.at.