Abstract
We present a set of advanced techniques for the visualization of 2D Poincaré maps. Since 2D Poincaré maps are a mathematical abstraction of periodic or quasi-periodic 3D flows, we propose to embed the 2D visualization with standard 3D techniques to improve the understanding of the Poincaré maps. Methods to enhance the representation of the relation x ↔ P(x), e.g., the use of spot noise, are presented as well as techniques to visualize the repeated application of P, e.g., the approximation of P as a warp function. It is shown that animation can be very useful to further improve the visualization. For example, the animation of the construction of Poincaré map P is a very intuitive visualization. During the paper we present a set of examples which demonstrate the usefulness of our techniques.
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© 1998 Springer-Verlag Berlin Heidelberg
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Löffelmann, H., Kučera, T., Gröller, E. (1998). Visualizing Poincaré Maps together with the Underlying Flow. In: Hege, HC., Polthier, K. (eds) Mathematical Visualization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03567-2_23
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DOI: https://doi.org/10.1007/978-3-662-03567-2_23
Publisher Name: Springer, Berlin, Heidelberg
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