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Discussion

Stream surfaces are a useful technique to visualize three-dimensional flow data. For an entire continuous set of initial conditions the temporal evolution is depicted. Using stream arrows, some of the disadvantages related to stream surfaces are omitted or diminished: by texturing the surface according to the flow of the 3D dynamical system, flow direction and velocity is visualized even for interior points of the stream surface. Less occlusion is achieved, using selective semi-transparency. Combining stream arrows with anisotropic spot noise and selective cuts yields expressive images of three-dimensional flows.

One difficulty with stream arrows is the number of parameters. To generate useful images in a certain situation it is necessary to tune the stream arrows parameters, for instance, scaling factor a for hierarchical stream arrows. To come up with a completely automatic parameter set-up, seems to be a non-trivial problem. Another problem with stream arrows is the number of triangles being handled, when high-quality images are to be generated. Geometric segmentation of stream arrows usually causes many triangles of the original stream surface mesh to be split in even more polygons. Thus, the use of stream arrows within an interactive set-up (e.g., a virtual/augmented environment set-up [26]) might cause performance problems.

It is useful to sub-structure stream surfaces by the use of texture that is generated with respect to the underlying flow. Important local information, e.g., flow direction and velocity, is additionally integrated in the visualization. Stream arrows are quite useful to generate high-quality representations of three-dimensional dynamical systems or flow data. The cover image of this chapter (see page [*]) shows a visualization, which is quite similar to one of the expressive images presented by Abraham and Shaw [1] (see Fig. 4.2).


next up previous contents
Next: Poincaré maps and visualization Up: Stream arrows Previous: Additional extensions
Helwig Löffelmann, November 1998,
mailto:helwig@cg.tuwien.ac.at.