## 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 Meister 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/",
}