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73 How Do I "Anti-Alias" Fractals?




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This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

73 How Do I "Anti-Alias" Fractals?

We can't eliminate aliasing entirely from a fractal but we can
use some tricks to reduce the aliasing present in the fractal. This is
what is called "anti-aliasing." The technique is really quite simple.
We decide what size we want our final image to be, and we take our
samples at a higher resolution than our final size. So if we want a
100x100 image, we use at least 3 times the number of pixels in our
"supersampled" image - 300x300, or 400x400 for even better results.

But wait, we want a 100x100 image, right? Right. So far, we haven't
done anything special. The anti-aliasing part comes in when we take
our supersampled image and use a filter to combine several adjacent
pixels in our supersampled image into a single pixel in our final
image. The choice of the filter is very important if you want the best
results! Most image manipulation and paint programs have a resize with
anti-aliasing option. You can try this and see if you like the
results. Unfortunately, most programs don't tell you exactly what
filter they are applying when they "anti-alias," so you have to
subjectively compare different tools to see which one gives you the
best results.

The most obvious filter is a simple averaging of neighbouring pixels
in the supersampled image. Being the most obvious choice, it is
generally the one most widely implemented in programs. Unfortunately
it gives poor results. However, many fractal programs are now
beginning to incorporate anti-aliasing directly in the fractal
generation process along with a high quality filter. Unless you are a
programmer, your best bet is to take your supersampled image and try
different programs and filters to see which one gives you the best
results.

An example of such filtering in a fractal program can be found on
Dennis C. De Mars' web page on anti-aliasing in his FracPPC program:
http://members.aol.com/dennisdema/anti-alias/anti-alias.html

References

The original submission from Rich Thomson is available from
http://www.mta.ca/~mctaylor/fractals/aliasing.html

To read more about Digital Signal Processing, a good but technical
book is "Digital Signal Processing", by Alan V. Oppenheim and Ronald
W. Schafer, ISBN 0-13-214635-5, Prentice-Hall, 1975.

For more on anti-aliasing filters and their application to computer
graphics, you can read "Reconstruction Filters in Computer Graphics",
Don P. Mitchell, Arun N. Netravali, Computer Graphics, Volume 22,
Number 4, August 1988. (SIGGRAPH 1988 Proceedings).

If you're a programmer type and want to experiment with lots of
different filters on images, or if you're looking for an efficient
sample implementation of digital filtering, check out Paul Heckbert's
zoom program at ftp://ftp.cs.utah.edu/pub/painter/zoom.tar.gz

 

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