Helmut's Page About The Project

"Advanced Fixed Points Visualization"

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This project was carried out by Helmut Doleisch from November 1996 to January 1998 as a computer graphics project.

During this project a lot of different modules for visualization of fixed points, but also other visualization modules, as well as tools, for the visualization in the system DynSys3D have been developed.
But the main interests were in the visualization of fixed points in three-dimensional complex dynamical systems.

Here is now a short Overview, how this document is divided into subsections:

1. Introduction
   
   
2. Fixed Points Visualization: consisting mainly of 5 points, namely:
   
   • IntLenPins: a first, more abstract test.
   • SphereTufts: the first "real" tool, that showed our ideas.
   • Advanced SphereTufts: the further development of the SphereTufts approach, by applying an adaptive algorithmn.
   • CharDirs: a tool for visualizing the characteristic directions of the given fixed point.
   • PlotXYZ: here you can plot the x, y, or z value over time as a functiongraph.
   • Combinations: of the different techniques.
   
   
3. Other Visualization Techniques: Visualization techniques, that can not be used for the visualization of fixed points, but are nevertheless of importance for making visualizations of dynamical systems, parts of that are:
   • Colored Streamline: a colored streamline can be integrated, starting from one point, where the color is given by some attribute mapping.
   • Rake: a Rake is given by a startline, where n uniformly distributed startpoints are chosen, and from each of these startpoints a colored streamline is calculated.
   • Sphere: a Sphere can be generated at a special point in the space.
   
   
4. Tools, that are needed by any of the visualization techniques:
   • ColorMapping: this tool provides the mapping of attributes to colors for the module "ColStreamline".
   • ScaleLines: module, that can scale the x, y, and/or z-values of all lines, that are given as "polylines" in AVS.
   • DistribScales: distributes the values for "ScaleLines" if there are multiple copies of that tool in use at once.
   • DSminScale: calculates the minimal scale of the dynamical system from the given scales of all fixpoints.
   
   
5. Image Gallery: have a look at several results.
   
   
6. Acknowledgments & References