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].

  

Figure 5.3: Poincaré map visualization by Abraham and Shaw [1].

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.

mailto:helwig@cg.tuwien.ac.at.