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From: "Abel Brown" <brown.2179@osu.edu>
Newsgroups: comp.soft-sys.matlab
Subject: Re: evenly distributed subset of points on a sphere
Date: Fri, 30 Oct 2009 17:47:03 +0000 (UTC)
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ImageAnalyst <imageanalyst@mailinator.com> wrote in message <067a12b6-b55b-40b8-8c9c-474d70729e13@p8g2000yqb.googlegroups.com>...
> On Oct 30, 12:09?pm, "Abel Brown" <brown.2...@osu.edu> wrote:
> > LOL, I did not generate this set of 250 points. ?
> >
> > This is a little strange. ?You seem to be avoiding the question. I need a practical solution not a mathematical proof. ?
> >
> > 250 evenly distributed around the earth. ?Need to divide these 250 points into 6 subsets or subnetworks of ~ 250/6 = 40 points each which are themselves evenly distributed around the earth.
> >
> > Indeed, generate 40 evenly distributed points on a sphere and choose closes points in super set. ?Easy enough ... but how to generate 40 evenly distributed points around the earth?
> 
> --------------------------------------------------------------------------------------------------------------------------------------------------
> Abel:
> I would imagine that you'd just take every 6th point in the Z
> direction.  Visualize this:  you have a bunch (say 250) of points more
> or less randomly distributed around the surface of the globe.  Now
> imagine that you take a string and fasten it to the point closest to
> the North Pole.  Now spiral that string around the globe such that it
> traverses every point, say as the string is going from east to west as
> you wind the string around the globe clockwise (looking down from the
> top).  So now every point on the globe is ordered as to its location
> on the string.  Now assuming your initial set was fairly randomly and
> uniformly distributed, I think you could get one set which consists of
> points
> 1, 7, 13, 19, 25, etc.
> The second set would be one over from that:
> 2, 8, 14, 20, 26, etc.
> and the third set would consist of points
> 3, 9, 15, 21, 27, etc.
> and so on.  Imagine that each set was identified by different colored
> beads on the surface of the globe.  It seems like the set of (say) red
> beads (taken starting with location 1) would be approximately just as
> uniformly scattered as the (say) green beads (take starting with
> location 2), and so on.  Every set of different colored beads would be
> about as randomly and uniformly positioned as any other set.
> 
> Because we picked up the points by spiraling down, subsequent points
> have decreasing Z values (latitude).  So all you need to do is to sort
> your array of x,y,z coordinates by the z value and then take every nth
> point.  Other sets just start at a different point before taking every
> nth point, like my example above.  Does that make sense - do you
> follow me?  Does that seem like it will work well enough for you?
> Might be worth a try and see how it goes.
> Regards,
> ImageAnalyst

Brilliant!  I really like this idea!  Nice and simple.  I'll give it a try and let you know how it works out.  

Fetterman:  Thanks for your reply!  Indeed, I did some reading/googling before posting and pretty much all of the algorithms I found were overkill.  Many folks on the forum have tremendous practical experience.  It's always interesting to see what solutions come up!

Thanks again!