




NDimViewer was developed in the course of my master thesis
"Evaluation and extension of some new techniques
for the visualization of high dimensional dynamical systems"
at the Vienna University of Technology, Institute for Computergraphics in April 1999. Before the implementation an evaluation of a previously existing visualization system using the new techniques was executed. The system of G.Rubik consists of 3 Java applets, each representing one technique. From this system the calculation classes were take and modified slightly.
As a good choice turned out to be the use of the expression parser by David Wanqian Liu, which is used for the numerical approximation of the trajectories and was extended for the use of 25 variables.
In the field of visualization of dynamical system many approaches and techniques exists to represent local characteristics and even larger sections of the phase and parameterspace. But this is only true for low dimensional system. For the case of higher dimensional dynamical systems (D>3), it is hardly possible to visualize all dimension within one view using the common techniques.Especially for this purpose, three new techniques were introduced in the paper "Visualizing the Behavior of Higher Dimensional Dynamical Systems". These techniques are basically designed to visualize high dimensional trajectories, but also sets of trajectories within one view. These techniques are Extruded Parallel Coordinates (EPC), Linking with Wings (LWW) and Threedimensional Parallel Coordinates (TDC), which have all in common that they use the principle of parallel coordinates.
Another characteristic of these techniques is the resulting 3Dgraph. Each graph is drawn into a 3D space, where it can be observed by the user by zooming or rotating. By this the user gets a three dimensional impression of the visualization, which can´t be obtained that easy with a screenshot. It must be noticed that
the visual channel from the visualization system to the human brain is limited to two dimensions (see picture) and the data to be visualized is of much higher dimensionality. So the extention into the third spatial axis is more or less necessary to provide sufficient expressiveness.
The ? marks out the difficulty in providing techniques for high dimensional visualization
As a further point it should be taken into account that the understanding of high dimensional relations naturally requires a high level of abstraction by the observer. The visualization system only can provide a well suited view of the data, but the process of understanding still must be done by the user.




