Mark Weyer wrote:
> 
> > First of all there is no 'correct' distribution, you can only try to
> > measure the quality of your sample set and compare it to others.  One
> > measurement of quality would be to measure the distance of each point to
> > its nearest neighbor - if this is very similar for all samples the
> > distribution is quite good (a non uniform distribution is more difficult
> > of course).
> 
> I do not think that would be a good measurement. In the following
> example, the distance to the nearest neighbour is EQUAL for all points
> (it is always 1 because the points are paired), while I expect you to
> agree
> that this is not a good distribution. (The example fills a rectangle,
> not a
> hemisphere, but that is irrelevant.)
> 
> [...]

You are right, this is not a very good measurement.  None the less with
some change it is suited for comparing distributions.  From all
distributions with N points the one with the largest minimum distance
between two points could be considered as the best.  

A different measurement would be calculating the sum of the inverse
distances of every point to all other points.  All this sums together
should be low for a good distribution.

> 
> Proposal for quality measurement: Density. Given a subset A of the
> space you want to fill, the density is the quotient of the number of
> samples inside A and the size (here: area) of A. The density should
> not differ much for different A. As we intend a discrete distribution,
> we have to restrict the quality measurement to A of a suitable minimum
> size.

The problem is that this would not detect anisotropy.  

One important point about radiosity sampling is that the mathematically
best distribution is not necessarily the best for high quality radiosity
results.  As you already mentioned regularity artefacts are a major
problem.  The halton distribution Mael implemented seems to work quite
well at high count values although it is surely not the best in terms of
mathematical quality measurements.  

Christoph

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