Master's Thesis - Studierstube Augmented Reality Project - Graz ...

2.1 Technical Visualization
of N. ⃗ N ⃗ can be approximated by choosing it in a plane perpendicular to the tangent
⃗T so that ( L ⃗ · ⃗N) and ( V ⃗ · ⃗R) are maximized. Following [Banks1994; Stalling1997;
Peeters2006] T ⃗ is given so that ( L ⃗ · ⃗N) and ( V ⃗ · ⃗R) can be approximated by
√
⃗L · ⃗N = 1 − ( L ⃗ · ⃗T ) 2
√
⃗V · ⃗R = ( L ⃗ · ⃗N) 1 − ( V ⃗ · ⃗T ) 2 − ( L ⃗ · ⃗T )( V ⃗ · ⃗T ). (2.7)
With these considerations an illumination of even diameter-less lines or particles can be
implemented directly.
Figure 2.14 gives an overview of the above described techniques
on certain examples from different publications.
Accordingly a view onto dense vector field representations will be taken next. Since
these techniques are not as exploited as particle traces in this work, only the main
representatives are presented but none of them have been implemented.
The class of dense flow visualization attempts to provide a complete, dense representation
of the flow field. This may be achieved by influencing an arbitrary texture
with an underlying velocity field, which is commonly known as convolution. For example,
facilitating a filter kernel to smooth and convolute a given vector field with a
white noise texture leads to the first and popular method of Line Integral Convolution
(LIC).
LIC, as defined by [Cabral1993], is basically capable of 2D vector fields, steady flows
and computational expensive. Figure 2.15(a) shows an example for a LIC based visualization
with additional velocity magnitude coloring. Due to these deficiencies several
extensions to LIC have been developed. Pseudo LIC (PLIC) [Vivek1999] figure 2.15(b),
for example uses template textures mapped onto a spares streamline representation of
a field which reduces the calculation work. Subsequent updating of the LIC-texture
for unsteady flow has been resolved reasonably efficient by Accelerated Unsteady Flow
LIC (AUFLIC) by [Liu2002] which is an extension on UFLIC [Shen1998].
However, extending LIC to 3D may seem to be straightforward from an algorithmic
point of view but the crux of this idea is the problem of occlusion in a three dimensional
space. As always for volumetric data several approaches try to deal with these problems.
Firstly an interactive approach with cutting planes can be chosen to either show a
2D-LIC texture on the cutting plane or only the volumetric rendered 3D-LIC texture
behind the cutting plane [Rezk-Salama1999]. Secondly more complex algorithms can be
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