Poisson Disk distribution on hemisphere

Question

Hi!

I just implemented Poisson Disk generation in the plane with this simple algorithm: http://people.cs.ubc.ca/~rbridson/docs/bridson-siggraph07-poissondisk.pdf

Now I would like to generate a Poisson Disk distribution on the surface of a hemisphere (or better, on a part of the spherical surface, given a certain angle)

can anyone tell me an algorithm to do that?

Thanks!

Answer 1

I would look at: "Fast Poisson-Disc Sample Generation in n-Dimensional Space by Subdivision Refinement" by Gamito and Maddock. This should be fairly easy to extend to the sphere using "Rendering and managing spherical data with sphere quadtrees" by Fekete.

Answer 2

Thanks thouis for your answer! i already found a solution before, so i'll poste it here for those who are interested:

first i create enough poisson disc samples in the unitsquare (enough means more than n)

then i sort those samples by the smaller coordinate (for example, a point (10,9), the smaller coordinate is 9 - another point (8,50) the smaller coordinate is 8 - the order of the points would be (8,50),(10,9) )

then i take the first n samples in the sorted list. due to the sorting mode, those samples will again lie in a square area. I then scale up the coordinates such that they lie again in the unit square. Now i have exactly n poisson disc samples in the unit square.

then I use the plane to sphere mapping described in http://www.cs.rutgers.edu/~decarlo/readings/mcrt-sg03c.pdf page 23 to get uniformly distributed samples on the spheresegment of an arbitrary area angle

works well for me