From: rusin@washington.math.niu.edu (Dave Rusin) Newsgroups: sci.math Subject: Re: HOW? Equally spaced points on a sphere?? Date: 22 Jan 1995 09:12:25 GMT In article <3fpfkc$mgf@senator-bedfellow.mit.edu>, John C. Carney wrote: > >How do I uniformly space points on a sphere? I have a ball and I'd like >to put X points uniformly spaced on the surface of it. The number X is >not very important (I want it to be about 40 to 80). Is there some way >using a compass and ruler that I can accomplish this? (Sigh) I'll bet I've answered a variant of this question half a dozen times in the past year. Tell you what: I've started writing an FAQ about this issue. I'll put a copy on my gopher/FTP site (math.niu.edu, directory pub/Papers/Rusin) or mail it to whomever wants. Maybe that will cut down on the traffic. The topics that seem to be of interest are below. I'd appreciate it if anyone who works in this area regularly could look it over and send me corrections -- this is not my area of expertise, but I think I have managed accurate statements appropriate for posters like this. By the way, another poster suggested that no regular distribution exists except for a few special N; while I understand the connection to the Platonic solids, it must be conceded that points equally spaced around the equator are as regularly spaced as points at the vertices of those solids! It is even true that electrons so placed will be in equilibrium although of course this equilibrium is unstable. TOPICS ON SPHERE DISTRIBUTIONS [Tentative version of 1/21/95 by Dave Rusin. Send comments & corrections to rusin@math.niu.edu] Current list of questions (suggestions welcome): Q0. Notation Q1. What does it mean to place N points "evenly" on a sphere? Q2. Are there some values of N which are better than others? Q3. How can you describe locations on a sphere, anyway? Q4. Can you give a quick approximation to a good distribution? (*) Q5. How can we improve an approximate solution? (*) Q6. What if I want randomly to place points with a uniform distribution? Q7. Can this be generalized to higher-dimensional spheres? Q8. How is this related to collections of linear subspaces? Q9. Where can I get the coordinates of the vertices of the Platonic solids? (*) (BASIC code provided) So far the list of questions is a little longer than the list of answers but I'll try to polish it up and polish it off in the near future. dave