From rupley!local@cs.arizona.edu  Sat Dec  5 02:18:13 1992
Date: Sat, 5 Dec 92 02:18:13 GMT
From: rupley!local@cs.arizona.edu
Message-Id: <9212050218.AA24053@rupley>
To: arizona!ccl.net!chemistry@cs.arizona.edu
Subject: Re:  distribution of points on a sphere


Bingze Wang writes:
# The original question is:
# >From: Dongchul Lim <lim@rani.chem.yale.edu>
# >Subject: Random Distribution of Points on a Sphere
# > Hi fellow chemists,
# >This may fit better in comp.graphics, but someone in this group
                          ^^^^^^^^^^^^^
Yes, if you want a probably overkill number of responses (:-).
The question is nearly an faq.  And it doesn't lack interest.

# >may have experienced it already. So here it goes.
# >I want to generate points on the surface of a sphere as randomly
# >as possible. These points may be used for drawing van der Waals
# >surface of an atom. I tried with symmetrically distributed points
# >(generated by varying phi and theta, etc), but due to symmetry,
# >the points looked like marching ants at certain angles.
# 
# To Lim:
# There are several ways to get points on a sphere with even distribution.
# For example, vertics and (projects of) face-centers of
# pentakisdodecahedron are 92 points on the sphere. In this way,
# you can have more or less. Please see J.Chem.Phys. 97(1992)4162 for
# 92 points, see J.Compt.Chem.8(1987)778 for 60 points.
# Bingze Wang

There are various and different questions regarding the distribution of
points on the surface of a sphere.  Among these are:

1. How do you get a "uniform" or "even" distribution?  The question
was addressed by Bingze Wang.

2. How do you get a random distribution?  Where each element of the
surface has equal probability of having a point, but probability being
what it is, the points may not be equidistant.

3. How do you get a distribution that is approximately random and
uniform?  I suspect this is what Dongchul Lim was asking about.  One
algorithm for doing this is, put point charges randomly on the surface
of the sphere and minimize the energy.

I will be happy to send interested people a _totally unedited_ collection
of postings from comp.graphics on this thread.

John Rupley
rupley@cs.arizona.edu