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> 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.)
+----------------------------------------+
| * |
| ** * * |
| * ** |
| ** |
| * ** |
| * |
| ** ** |
| ** |
| * ** |
| * |
| |
| |
| |
| |
| |
| |
| |
| |
| |
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+----------------------------------------+
Even if you ,,disallow'' the unevenness depicted here, you are bound
to get grid artefacts, which can be a real killer, if the sample grid
interacts with some object grid in the scene in a moir'e way.
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.
Mark
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