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Previous and related work
Figure 5.2:
(a) An example of a traditional Poincaré map
visualization [76].
(b) An example of a 3D Poincaré map [15].
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Figure 5.3:
Poincaré map visualization by Abraham and
Shaw [1].
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Visualization techniques have been used for the illustration of
Poincaré maps since they were introduced by Henry Poincaré. Most of
these imaging methods are 2D or 1D plots that are calculated by
numerically integrating the underlying flow.
See Fig. 5.2(a) for an example of such a
technique. Rarely
Poincaré maps in 3D or even higher dimensions are investigated.
See Fig. 5.2(b) for an example.
In addition to these traditional 2D plots a few more general
techniques can be found in the literature. Hand-drawn images in the
book by Abraham and Shaw [1] demonstrate that
a combination of the Poincaré section and the underlying 3D flow
within a single image convey a better understanding of the
underlying flow
characteristics (see Fig. 5.3). The book by Abraham
and Shaw is in effect quite an inspirational source. We think
that a number of artistic techniques used for the hand-drawn
images in the book are well-suited for computer-supported
visualization techniques.
Next: Visualizing Poincaré map p
Up: Poincaré maps and visualization
Previous: About Poincaré maps
Helwig Löffelmann, November 1998, mailto:helwig@cg.tuwien.ac.at.