Another class of approaches deals with the direct visualization of the system behavior. Integral curves visualize the evolution of specific seed points which change according to the dynamics of the underlying flow. Many techniques are already available for the 2D case. Spot noise [87] and line integral convolution (LIC) [14], for example, provide an overview of 2D dynamics within a 2D domain. In 3D, however, direct visualization is difficult. Rendered images tend to be overloaded when entire portions of flow in three-space are simultaneously visualized. Some attempts into this direction are illuminated stream lines [94] and volume-rendered 3D flow [25]. Work by Interrante et al. [35] also addresses this problem.
In addition of the visualization of characteristic elements and direct visualization, a third class of techniques deals with the representation of local properties [52]. Glyphs [19,86] can represent quantities derived from the Jacobian matrix (local linearization of the flow) as, e.g., acceleration, rotation, or divergence. Another approach [75] transforms a polygon positioned perpendicular to a trajectory to represent local information.
In this chapter we present a technique which to a certain extent
belongs to all of the three classes mentioned above. It was
inspired by the concept of modeling knit wear as yarn with a
complex micro-structure [28]. A yarn thereby consists
of many fibres with similar spatial location and orientation.
We visualize the vicinity of
interesting trajectories, e.g., the stream lines emanating from
critical points. A large number of short integral curves
(streamlets) is used to directly code the system's behavior near
the base trajectory. By this approach of
selectively placing streamlets we omit distracting image
cluttering while still providing direct cues to the (local) system
behavior. Visualizing the vicinity of characteristic
stream lines enhances the abstract representation of the system's
behavior by local cues of direct visualization.