## How to Operate the Applet

This Applet graphs scaling functions and wavelets
with two parameters *even*
and *odd*. If you are interested, check the
mathematics behind the Applet. The applet
shows the graph of the scaling function or wavelet,
which is defined on [0,3], on
top and the parameter space below. The circle and lines in the
parameter space have a specific meaning which you can find in
the mathematical background. The red dot
indicates the current value of the parameters.
You probably already figured out that:

- You can use the slide bar to set the number of iterations of
the algorithm. Use it to find a compromise between quality of
the graph and speed (6 works best for me).
- You can move the red dot in parameter space. In fact, you
can even move it outside the paremeter space.
- The
*Mirror* button flips the function.
- The
*History* radio button allows you to trace the
execution of the program. This originally was a bug in the program, but I now
added it as an option as one can make
pretty pictures with it. How about this as a *multi wavelet* ;-)
Clicking *History* again clears the screan.
By switching history on and changing the level, you can
check the convergence speed of the algorithm. The smoother
the limit function, the faster the convergence.
- The buttons below give you well known functions.
- The buttons on the left allow you to switch between wavelet
and scaling function.
- You only get smooth graphs inside the shaded region.
The closer to the upper right corner (1,1), the more fractal
the function becomes.
- Using the buttons on the bottom left, you can switch between
piecewise linear and piecewise constant drawing. Linear
is best when drawing smooth functions, while constant is
better while outside the region of continuity. With constant
drawing you can see how the function almost falls into two
pieces around the point (1,1). (Try it with the symmetric
constraint on.)
- You can contrain the parameter space using the buttons on
the right. See if you can converge to the Daubechies by
alternating the orthogonality and order 2 constraints.

Some notes on the implementation:

- The Applet uses double buffering to avoid flicker both for
the graph and the parameter space.
- The Applet is fully resizable, so if you would like a larger
canvas, simply adjust the HEIGHT and WIDTH of the APPLET tag.
- The Applet does not rely on garbadge collection and
will never increase memory after initialization.
- In order to increase speed while dragging the mouse,
only every other mouse position is read.

Please feel free to contact me if you
have questions or comments.
**
[
Wavelet Cascade Applet |
Mathematical background |
My home page
]
**

Copyright © 1996 Wim Sweldens. Last modified: Thu Oct 17 17:34:30 EDT 1996