## Information

- Publication Type: Technical Report
- Workgroup(s)/Project(s): not specified
- Date: March 1997
- Number: TR-186-2-97-06
- Keywords: Poincare maps, dynamical systems, visualization

## Abstract

We present a set of advanced techniques for the visualization of 2D Poincare maps. Since 2D Poincare maps are a mathematical abstraction of periodic or quasiperiodic 3D flows, we propose to embed the 2D visualization with standard 3D techniques to improve the understanding of the Poincare maps. Methods to enhance the representation of the relation $x\leftrightarrow{}P(x)$, 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 Poincare map $P$ is inherently a proper visualization. During the paper we present a set of examples which demonstrate the usefulness of our techniques.## Additional Files and Images

## Weblinks

No further information available.## BibTeX

@techreport{Loeffelmann-1997-VPM, title = "Visualizing Poincare Maps together with the underlying flow", author = "Helwig L\"{o}ffelmann and Thomas Kucera and Eduard Gr\"{o}ller", year = "1997", abstract = "We present a set of advanced techniques for the visualization of 2D Poincare maps. Since 2D Poincare maps are a mathematical abstraction of periodic or quasiperiodic 3D flows, we propose to embed the 2D visualization with standard 3D techniques to improve the understanding of the Poincare maps. Methods to enhance the representation of the relation $x\leftrightarrow{}P(x)$, 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 Poincare map $P$ is inherently a proper visualization. During the paper we present a set of examples which demonstrate the usefulness of our techniques.", month = mar, number = "TR-186-2-97-06", address = "Favoritenstrasse 9-11/E193-02, A-1040 Vienna, Austria", institution = "Institute of Computer Graphics and Algorithms, Vienna University of Technology ", note = "human contact: technical-report@cg.tuwien.ac.at", keywords = "Poincare maps, dynamical systems, visualization", URL = "https://www.cg.tuwien.ac.at/research/publications/1997/Loeffelmann-1997-VPM/", }