Christoph Hormann wrote:
> 
> Mark Weyer wrote:
> 
>>I do not see why the quality is better than using repulsion
>>inside the unit circle with a uniform force field before projecting.
> 
> 
> To me it seems fairly obvious that projecting a disc on a hemisphere does
> not maintain the distance relations and therefore reduces the uniformity
> of a distribution.  

The point is that you do not want a uniform distribution on the 
hemisphere ...

> 
> To be precise, the points at the rim of the hemisphere will be quite dense
> in direction of the circumference but will be moved apart in theta
> direction.

Ahh! If you used a unit circle to do the repulsion thing then you are 
quite right - you do not get an even distribution at the edge: all the 
outermost points would be pressed against the rim.

This is why I used a 2 radius circle when I was doing the Delaunay 
triangulation, and adding samples until I had enough in the unit circle. 
That way you get an even distribution right across the unit circle - 
right to the rim of the hemisphere.

You could do the same with a repulsion algorithm - fill a circle of 
greater than 1 radius and keep adding a sample and repelling to 
completion untill you have the right number of samples within the 1 unit 
circle.

> 
> Christoph
> 

Mike Andrews.

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