Monday, September 10, 2012

Halton sequences, at last

A while ago I posted on generating random point sets, and Sean Gillies suggested Halton sequences as a way of generating nice-looking point distributions.  I finally got around to looking into this idea. Indeed he was correct - Halton sequences provide a very pleasing appearance for point distributions (much better than purely random distributions).
The above shows the first 1000 elements of the Halton sequence with bases (2,3).  Larger bases exhibit progressively more coherence, which may or may not be desirable depending on application. Here's H(7,9):
 The code to generate Halton sequences is pretty trivial - see the Wikipedia article for some pseudo-code.  (Although I have to say that the explanation of their derivation is pretty poor.  I've seen this sad trend on some other Wikipedia mathematical articles as well - in particular the one for Barnes surface interpolation.  I suppose the rejoinder would be to get in there and improve it!)

Keying off something else that Sean showed on his blog, I also played around with using Halton sequences to generate quasi-random sets of polygons.  Here's one example, using a slightly different approach to Sean's:

And the same for H(5,7), which looks slightly nicer I think:

Might come in handy someday for generating test data, or possibly as a visual texture.

1 comment:

city said...

thanks for sharing.