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Selective cuts

The use of 2D cross-sections is a well-established method to reduce the problem of occlusion in 3D. A similar effect can be achieved, when parts of the model are cut away and removed. Simple geometric objects, e.g., planes, are used to cut through a 3D model. We use this method for the stream surface representation of the given dynamical system, but do not remove surface parts entirely. Specifying a certain cut plane the stream surface is separated into three parts, i.e., components of the stream surface behind, on, and in front of the cut plane. The geometrical separation of the stream surface allows to specify different visibility parameters for all three parts. Components in front of the cut plane may be rendered semi-transparently. The intersection curves of the stream surface with the cut plane may be emphasized by representing them as tubes. Several arbitrary cut planes may be applied simultaneously so that, for example, a wedge-shaped part of the stream surface is extracted. Fig. 4.11 gives an example, where parts in front of the plane are rendered semi-transparently. Enhancing some of the stream lines, for example, the edges of the stream surface, facilitates the perception of the spatial arrangement of the semi-transparent portions.
  
Figure 4.12: Two snapshots from an animation sequence - the first from the beginning and the second from the end of the animation sequence.
\framebox[\textwidth]{\parbox{.93\textwidth}{\begin{center}
\includegraphics[wi...
...t1.ps}\\
\includegraphics[width=.8\textwidth]{pics/result2.ps}
\end{center}}}

The location and orientation of objects, that are used for model separation and components removal, are crucial for the benefit of this method. These parameters can be determined either automatically or interactively by the user. An automatic approach would mean to search for an optimal position and orientation of the cut such that the most important parts of the visual representation are kept and less important parts are removed. Obviously an automated approach is easily extended to support the calculation of animation sequences. On the other hand it is quite difficult to meet the user's requirements automatically, when studying the system representation. In the case of this thesis an automated `intelligent' approach for the placement of cut planes was not implemented. Animation sequences were generated by specifying simple movements of the cut plane. The cut plane can, for example, move along one coordinte axis while remaining orthogonal to this axis during the entire animation. See Fig. 4.12 for two snapshots out of an animation sequence.


next up previous contents
Next: Animation aspects Up: Stream arrows Previous: Anisotropic spot noise
Helwig Löffelmann, November 1998,
mailto:helwig@cg.tuwien.ac.at.