MachBandingApplet - Project Description

MachBandingApplet - Project Description
Overview
This applet is rather simple. Based upon the settings the user has chosen, it draws a sequence of color bands which change color from one extreme to another. The majority of the math is fairly basic and could probably be best understood by looking at the source. The interface is similarly basic - most of the code is involved with laying out the interface.

Areas of Interest

Input Validation - When changes are made or the Repaint button pressed, the applet performs validation on the numerical inputs. If anything is invalid, it is set to a valid value. The applet then updates the display with the corrected values and redraws the bars.

Variable Width Bars - This is done using some simple calculus - an excerpt from the source:

The width of a bar is given by area under the graph:
  Uniform   Non-Uniform
  |           |--
1 |------   1 |  --
  |           |    --
  +------     +------
  0  x  1     0  x  1
Where x (0 to 1) represents the width of the entire Canvas and y
represents the scaling factor that adjusts the individual bar widths.
To determine a bar width, take the area of the trapezoid:

|\
| \
|  \
|   |
|   |
+---+
a   b

Where a represents the current bar position and b represents the next
bar position (if the bars were to be evenly spaced).
NOTE: The function for uniform is simply a constant value (a line
parallel to y=0).  For non-uniform, that line is rotated around
(0.5, 1.0), maintaining constant area from x=0 to x=1 as required.

Smooth Transitions - This is accomplished as follows (also excerpted from the source):

Draw a line at each end of the bar that is 30% of the way
between the color of this bar and the next. This results
in a color change as follows (Bar 1 is on the left):
             Amount of Color
  Bar 1   100%   70%   30%    0%
  Bar 2     0%   30%   70%  100%
Where the columns represent one pixel-wide vertical lines.
This removes the sharp color change between neighboring bars
by smoothing it out somewhat.

Please note that due to the small pixel sizes of most monitors and the subtle color changes involved, this is often difficult to perceive.

Conclusion
I am satisfied that this applet accomplishes its task. People I have spoken with tended to agree that it provided a good demonstration of Mach Banding as well as the effects of separators and colors. There is really nothing that I wish I had done differently (for a change). I suppose the source could be a bit cleaner, but it seems to accomplish its task well and performance is not an issue - so I didn't feel making extensive modifications was justified.

The applet is available.
The source code is available for educational purposes.