Thomas de Groot wrote:
> "stbenge" <myu### [at] hotmailcom> schreef in bericht 
> news:4c697734@news.povray.org...
>> At first I was really excited by this, but then I started looking it up, 
>> and there appears to be a lot of repetition in Halton point sets... I'll 
>> have to try the code you provided to see how well it distributes the 
>> points.
> 
> How can you tell that, Sam? My tests appear not to overlap but I have no way 
> (yet) to really be sure. What I am pretty sure about is that an additional 
> collision test is necessary if number and size of the objects become too 
> large for a given space, though. Otherwise, the bare locations seem not to 
> repeat themselves within a given sequence, but I may be totally wrong of 
> course.

I haven't tried Edouard's code yet, though I did search for some 
examples with Google's image search. The repetition is often very 
noticeable, as seen in the following images:

http://www.puc-rio.br/marco.ind/imagens/halton_2d.gif
http://www.mathworks.com/matlabcentral/fx_files/17457/1/halton.jpg
http://www.blitzcode.net/images/projects/project_150_big.png

The first and second examples repeat completely in one diagonal 
direction, and partially in another. The third is a bit harder to tell, 
but there is definitely some partial repetition present, even with the 
low number of points.

I typically test for pattern repetition by crossing my eyes at an image 
and seeing if the two images "lock in." Anybody can beat those "how many 
differences can you spot?" picture games in seconds if they would just 
cross their eyes... but what would be the fun in that? :)

>> I usually just test new elements against all other elements and place a 
>> point where there is enough space by evaluating the radii. It's a slow 
>> method, but must only be performed once per-application if the points are 
>> saved to an .inc file.
> 
> Yes, that is slow, but it works :-)

And it works well. It can handle circles of varying radii with 
absolutely no overlaps. I have tried a similar method in raster space, 
which works pretty well and allows for different shapes (like rotated, 
scaled rectangles), but the accuracy goes down because of the granularity.

Sam

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