From: wskdpl@pukrs12.puk.ac.za (Dirk Laurie)
Newsgroups: sci.math.num-analysis,sci.math
Subject: [FAQ] Well-scattered points on a sphere
Date: 24 Apr 1997 10:52:15 GMT

Question:  Is there an algorithm that generates N well-distributed
  points on a sphere for other values of N than 4, 6, 8, 12 and 20?

Answer:  A thorough but understandable survey appears in
  "Distributing many points on a sphere" by E.B. Saff and A.B.J. Kuijlaars,
  Mathematical Intelligencer 19.1 (1997) 5--11.  The recommended
  algorithm in spherical coordinates (theta, phi) is:

    for k=1 to N do
       h = -1 + 2*(k-1)/(N-1)
       theta[k] = arccos(h)
       if k=1 or k=N then phi[k] = 0
       else phi[k] = (phi[k-1] + 3.6/sqrt(N*(1-h^2))) mod (2*pi)
    endfor

  In Cartesian coordinates the required point on a sphere of radius 1 is
     (cos(theta)*sin(phi), sin(theta)*sin(phi), cos(phi))

Dirk Laurie  (dlaurie@na-net.ornl.gov) 

==============================================================================

From: "Alen Ladavac" <alen@croteam.com>
To: <rusin@math.niu.edu>
Subject: Erratum for spherefaq post on your site
Date: Fri, 17 Sep 2004 16:39:48 -0000

Just wanted to let you know that on this URL:
97/spherefaq
on your site, in the last formula (cos(theta)*sin(phi), sin(theta)*sin(phi),
cos(phi)) phi and theta are reversed. Well, at least with regards to the
meaning of them in the first part of the algorithm.