Stream arrows for stream surfaces

The main extension to the standard stream surface technique is the introduction of stream arrows. A stream surface is thereby segmented into a set of arrow-shaped objects, i.e., the stream arrows, and the remaining surface portion. By assigning a certain level of semi-transparency to the stream arrows the viewer sees through the ``holes'' in the stream surface and gets more information about the structure of the model. In addition to that, the use of stream arrows allows to visualize local information that is available on the stream surface, e.g., direction of evolution, velocity, and local divergence or convergence (see Fig. 4.3).

  

Figure 4.3: Stream arrows for mixed-mode oscillations.

  

Figure 4.4: Varying the shape of the stream arrows texture. [left image] [right image]

The segmentation of the surface into stream arrows and the remaining surface portions is performed by mapping a regularly tiled texture of arrow-shaped patterns onto the stream surface and cutting its patches along stream arrows borders. The texture is constructed by specifying a base tile, i.e., the shape of one stream arrow, and tessellating the texture using this base tile. See Fig. 4.4 for a comparison of two different shapes of the base tile. Three sets of geometric objects, namely the inside of stream arrows, the outside, and the separating border, are extracted. After this segmentation either the stream arrows or the remaining surface portions can be assigned a certain level of semi-transparency. See Fig. 4.5 for an illustration of this method and Fig. 4.6 for an example, where both possibilities were used.

  

Figure 4.5: Mapping the stream arrows texture to a stream surface.

  

Figure 4.6: Using semi-transparency either for the arrows or the remaining stream surface portions.

A segmentation of a stream surface into an entirely opaque portion and highly transparent holes (stream arrows) gives a good impression of the interior structure of a curved stream surface while still retaining a good overview of the spatial arrangement of the stream surface itself. Using homogeneously transparent surfaces would produce several layers of overlapping stream surface segments which are quite difficult to interpret spatially [71].

mailto:helwig@cg.tuwien.ac.at.