Comments on: Points on a sphere

By: Anton Sherwood

Anton Sherwood — Mon, 13 Oct 2008 00:30:51 +0000

Neil Sloane has some info on spherical arrangements in higher dimensions.

By: Will

Will — Wed, 13 Aug 2008 14:43:25 +0000

Do any of you think you’d be able to expand this to higher dimensions?

I’m looking to find a way to give me a set of the most unique vectors. This kind of thing would do it i think. the most seperated points on the 10D equivalent of a sphere should be the most unique set of vectors with 10 elements right?

By: Anton Sherwood

Anton Sherwood — Thu, 07 Aug 2008 22:40:29 +0000

a possibly useful reference page (heavily rewritten by me last September)

By: Joe Wheeler

Joe Wheeler — Tue, 05 Aug 2008 15:50:04 +0000

Thanks Patrick, this is really useful. I’ve ported your golden spiral version to ActionScript.

public function pointsOnSphere ( num:uint, radius:Number=1.0 ) :Array
{
var pts:Array, inc:Number, off:Number, i:uint, y:Number, r:Number, phi:Number;

num = uint( num );
pts = new Array( num );
inc = Math.PI * ( 3 - Math.sqrt( 5 ) );
off = 2 / num;
i = num;
while ( i– ) {

y = i*off - 1 + ( off / 2 );
r = Math.sqrt( 1 - y*y );
phi = i*inc;
pts[ i ] = { x:Math.cos( phi )*r*radius, y:y*radius, z:Math.sin( phi )*r*radius };
}

return pts;
}

By: Jeremy

Jeremy — Tue, 01 May 2007 04:56:46 +0000

Hi guys, great article and discussion. I wonder does anyone have a link or comparison of the various techniques using the voronoi cell area? I am particularly interested in how close to equal area the various combinations of the Rubin’s Disco Ball area. Thanks again!

By: Michal

Michal — Mon, 20 Nov 2006 23:19:22 +0000

Thanks, great article. Just want I needed! Really helpful, thanks again.

By: Anton Sherwood

Anton Sherwood — Sat, 07 Oct 2006 06:20:05 +0000

Felix, a set of nodes spaced equally on a great circle as you have them — or indeed on any circle — would have congruent Voronoi cells, so how is the Voronoi-area measure better than the nearest-neighbor measure? (Anyway I used the nearest-neighbor distance primarily as a measure of packing efficiency, rather than evenness.)

By: Andy Nicholas

Andy Nicholas — Thu, 05 Oct 2006 12:07:04 +0000

Brilliant, I”ve not seen that paper. Thanks for finding it!

By: Patrick Boucher

Patrick Boucher — Wed, 04 Oct 2006 18:59:51 +0000

Andy, I googled really quickly and don”t know if this is one of the techniques you mention but this paper in the ACM’’s repository seems interesting…

http://portal.acm.org/citation.cfm?id=122749

I gotta get me an account.

By: Andy Nicholas

Andy Nicholas — Wed, 04 Oct 2006 17:22:06 +0000

Great article Patrick. I love all this sort of stuff.

BTW, I don”t suppose you or anyone else knows of any papers or links for methods that can generate evenly spaced points on an arbitrary mesh, rather than just a sphere?

Obviously the relaxation method is still valid and also I”ve seen various other things to do with conformal mapping and texture synthesis. Are there any other methods out there that are a little easier to implement?