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Another part of the proposed approach is the use of spot noise as an
additional stream surface texture. Spot noise (see
Fig. 4.10) has been introduced
to the computer graphics community by Jarke van Wijk in
1991 [87]. It is a powerful technique to generate
various random textures that are suitable for different purposes.
By constructing a spot noise texture, which emphasizes stream lines
and time lines on a stream surface, the visualization of flow using
stream surfaces can be improved. See
Fig. 4.11 for a typical image.
To find an appropriate spot is facilitated by
the fact that spot noise
textures directly reflect the geometric characteristics of the spot used
for its construction. As we want
to use
the texture to emphasize stream lines and time lines,
we parameterize the stream surface such that parameter lines
directly correspond to stream lines and time lines. This
parameterization is easily achieved, since the construction of
stream surfaces is based on stream line integration. Using this
type of stream surface parameterization a spot emphasizing horizontal
and vertical directions in texture space, e.g., a cross or a hash,
should be used.
In Fig. 4.10 the
spot we use and the resulting spot noise texture is shown.
Fig. 4.11 shows a textured stream surface of the
mixed-mode oscillations model.
Figure 4.10:
spot (enlarged) and the resulting spot noise
texture.
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We also thought of using line integral
convolution [14] as an alternative to spot
noise, but mainly two reasons induced us to use spot noise instead.
First, the use of spot noise allows to emphasize both stream lines
and time lines simultaneously. Using line integral convolution on the
other hand, just stream lines or time lines could be emphasized.
Another reason for the use of spot noise is, that it is less
costly than line integral convolution.
Combining spot noise texture and stream arrows produces an
expressive stream surface visualization technique. While the use
of the stream arrows texture might raise a problem at ill-behaved
areas of the stream surface, e.g., regions of large divergence or
convergence, spot noise textures suffer from less
problems in this situations.
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Helwig Löffelmann, November 1998, mailto:helwig@cg.tuwien.ac.at.