Stream arrows, i.e., the use of a special texture featuring semi-transparent arrows within the stream surface, enhances the visualization of three-dimensional flow by several means:
Next, the stream arrows texture is defined. Vertical lines in texture space are correlated to stream lines, horizontal lines correspond to time lines within the stream surface. In the implementation the texture is defined on the basis of a base tile representing one arrow and a tiling mechanism generating implicitly as many stream arrows as necessary. Instead of one single stream arrows texture, an entire stack of textures can be used (hierarchical stream arrows). This eliminates some problems with the standard stream arrows technique in cases of great local divergence/convergence. See Fig. 4.8 for an illustration of this extension.
There are (at least) two possibilities to realize stream arrows within stream surfaces. One is to specify an alpha-texture for the surface element, and let the renderer care about semi-transparency. Another technique is to geometrically segment the stream surface into three separate triangle sets, one for the opaque parts, the border elements (1D), and the semi-transparent parts. An efficient segmentation algorithm is described in Sect. 4.3.
Anisotropic spot noise is generated using the same texture coordinates specification as used for the stream arrows and again exploiting the correlation between u-/v-lines and stream/time lines. A cyclic texture is generated in texture space. Constant flow along u-lines is assumed and an anisotropic spot is used to emphasis stream and time lines, simultaneously. See Fig. 4.10 for an (enlarged) image of the spot and the resulting texture. Mapping such an anisotropic spot noise texture to the stream surface illustrates stream and time lines.
Another approach to diminish the problem of occlusion is to use selective cuts through the visualization model. Parts in front of others, also important parts of the visualization are rendered almost transparently to allow insight within the model. Animation is used to move cut planes and help the viewer to understand the cutting operation performed. See Fig. 4.12 for two images out of an animation where the cut plane was moved through the model. The intersection of cut plane and stream surface was enhanced by white tubes.
In addition to selective cuts there are several other points in
the stream arrows technique, where animation easily and useful can
be hooked in. Arrows can be move over the stream surface into the
direction of flow, the initial conditions may be altered within an
animation. Viewpoint animation also improves the
perceptibility of visualization models generated using the stream
arrows technique.