Hi Christoph,

The cos-theta distribution on the hemisphere is given by creating an 
even distribution on a unit circle and then projecting up or down to a 
unit hemisphere.

You can see this by taking a copy of the radiosity sample array, editing 
it to pov syntax and including it in a small scene which puts a sphere 
at the <X,Y,0> points. If you do an animation which adds 1 or a few 
sample positions each frame you can see how the distribution builds up.

Mike Andrews.

Christoph Hormann wrote:
> Quoting from the source:
> 
> A bit of theory: The goal is to create a set of "random" direction rays
> so that the probability of close-to-normal versus close-to-tangent rolls
> off in a cos-theta curve, where theta is the deviation from normal.
> That is, lots of rays close to normal, and very few close to tangent.
> You also want to have all of the rays be evenly spread, no matter how
> many you want to use.  The lookup array has an array of points carefully
> chosen to meet all of these criteria.
> 
> The problem is similar to the classical "How can I arrange N points evenly
> on a sphere" problem like described in:
> 
> http://www.ogre.nu/sphere.htm
> 
> Just that it is hemispherical, not really uniform and it not only has to
> be good for N points but also for N-X points (X = 1..N-1)
> 
> Christoph
>

Post a reply to this message