Spatially quantitative insights are gained from building the geometry of behavior. Location and shape of the topological entities are composed to a geometry within phase space [1,31]. The topological structure is extended by the spatial attributes of its elements. Thereby at least some quantitative information is provided. The geometry of behavior is a rather dense description of the flow without flow details apart from characteristic structures.
Detailed (local) information is gained by directly visualizing the
dynamics using stream lines, stream surfaces, particle systems, or
other integral objects [67]. Selected
trajectories are visualized through these techniques.
This kind of visualization technique always lacks completeness.
As the previously described approaches have their advantages and disadvantages each (see Tab. 6.1 for a summary), a combination of them is appropriate. Most approaches found in literature, on the other hand, concentrate on either the one or the other.
In this chapter we first present two new techniques for the
visualization of a continuous dynamical system in 3D space, which
belong to two different approaches concerning the analysis of the
flow data. Furthermore, we demonstrate that combining both
methods yields better results.