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