Java Exploration Tool for Dynamical Systems

by R. Wegenkittl and E. Gröller.

Project Duration: 1997

A detailed description is given in the paper

Fast Oriented Line Integral Convolution for Vector Field Visualization via the Internet
(IEEE Visualization '97 Proceedings)

(Applet Version 1.0)

1) General Features

This Java Applet can be used for the exploration on two-dimensional analytical defined dynamical systems. The system is defined by a set of two differential equations, which will be evaluated within adjustable regions forming a two-dimensional vector field. Basic visualization methods as well as advanced methods can now be applied to the vector field. Each resulting visualization is displayed in an own window allowing easy comparison of different results. Some of the methods also can be animated to give a deeper insight to the systems dynamic. In the following a short description of the tool is given:

2) How to enter a dynamical system

The first two lines of the applet are used for entering the dynamical system (see Fig.1). The state variables are called x and y and only state variables (and no derivatives) can be used on the right hand side of the equations. For each variable a region can be specified, for which the vector field will be calculated. In the Parameter section nine parameter can be entered. This is useful for cleaning up the display of long formulas. Parameters can not only be defined by constants, but can also be made up by difficult calculations, state variables and other parameter (Attention: avoid recursive definition like "a = b" and "b=a" for they will result in a system crash).

Figure 1) The Applet with a dynamical system ready to start the exploration

2.1 Mathematical functions

The formulas for the state variables and for the parameter can consist of the variables x, y and all defined parameter as well as the constants PI and E. Mathematical functions taht are recognized are +, -, *, /, ^, sin(), cos(), tan(), sqrt(), exp(), exp10(), ln(), log(), abs(), ceil(), floor(), round(), asin(), acos(), atan() and actan(). All function have to be followed by parentheses.

2.2 Vector field conversion

The equations are evaluated automatically when a visualization method is applied. A blue progress bar indicates the advance of the conversion progress. The time used for conversion depends on the complexity of the formulas and on the resolution of the vector field (which is equal to the resolution of the visualization windows). The vector field resolution can be specified by the user by changing the values of the "Width" and "Height" fields (Attention: If a visualization window is already open, changing these values and displaying another visualization confuses the original window).

2.3 Input / output of systems

The applet provides a "Load System" and a "Save System" button. Unfortunately Java does not support local file access within a network. So these buttons show no effect except when the applet is viewed local within an applet viewer (and setting correct security options).

3 Visulization

3.1 General features

A visualization method is invoked by pressing the according button. If the vector field has not been evaluated yet (or has been changed) the equations are processed automatically, then the visualization window is displayed. Some techniques show a dialog box to allow changes of some parameter of the visualization technique. Then the visualization is calculated (which is again indicated by the progress bar) and shown in the window. When the user clicks with the mouse at a point within the visualization window according values (position, derivatives, vector length) are displayed in the bottom line of the applet. Each window can be closed separately by using the system menu or hotkey provided by your operating system.

3.2 Available visualization methods

3.2.1 Speed encoding

3.2.2 Directional information

3.2.3 Isoclines

3.2.4 Line Integral Convolution (LIC)

3.2.5 Particle system

3.2.6 Fast rendering of oriented line integral convolution

3.2.7 Optimized placement for fast rendering of oriented line integral convolution

Institute of Computer Graphics - Visualization and Animation Group - Research

This page is maintained by RainerWegenkittl. It was last updated on April 22, 1997.
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