 | | | Random points on a unit sphere without biasing | Random points on a unit sphere without biasing 2005-06-14 - By Alan Jones
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I finally hit the right combination of keywords in my google. They key
was to add "Open Sesame" to the end.
http://mathworld.wolfram.com/SpherePointPicking.html
Cheers,
Alan.
On 6/14/05, Alan Jones <skyphyr@(protected)> wrote:
> Thanks Kim. I'll pass a little more info on what I'm trying to
> achieve. It's a shader (surprize surprize) and I want to be able to
> generate X normals given X and a seed. So I can reproduce the same
> normals again and again.... While it doesn't matter if the
> distribution of these points is even or not (actually it kindof kills
> the point of randomly generating them from a seed if it is) I don't
> want it to bias towards the poles because this will look ugly.
>
> Cheers,
>
> Alan.
>
> On 6/14/05, kim aldis <kim@(protected)> wrote:
> > But of course, this won't give you absolute control over exactly how many
> > points. You'd be stuck whatever the subd gave you.
> >
> > Relaxation?
> >
> >
> > > -- --Original Message-- --
> > > From: owner-xsi@(protected)
> > > [mailto:owner-xsi@(protected)] On Behalf Of kim aldis
> > > Sent: 14 June 2005 16:08
> > > To: XSI@(protected)
> > > Subject: RE: Random points on a unit sphere without biasing
> > >
> > > Geodesic dome. Infact there's no such thing as a perfectly
> > > even distribution of points over a sphere greater than the
> > > number of points on an icosahedron (20 faces) but Buckminster
> > > Fuller got pretty close with his domes by splitting the
> > > icosahedron across it's faces. He did it by putting points in
> > > the middle of each face then triangulating the new points,
> > > omitting the old. You can get a good way into complexities by
> > > doing this recursively.
> > >
> > > If you can't use the xsi primitive as a starting point then
> > > you can generate the starting icosahedron but I remember it
> > > proved fiddly when I last tried it.
> > >
> > > None of the XSI subdees give the results you need.
> > >
> > >
> > >
> > > > -- --Original Message-- --
> > > > From: owner-xsi@(protected)
> > > > [mailto:owner-xsi@(protected)] On Behalf Of Alan Jones
> > > > Sent: 14 June 2005 15:55
> > > > To: xsi@(protected)
> > > > Subject: Random points on a unit sphere without biasing
> > > >
> > > > Hi All,
> > > >
> > > > This is to the maths geniuses in the room. I want to
> > > generate X number
> > > > of points on a unit sphere, but be sure I won't have any biasing
> > > > involved.
> > > >
> > > > My first thought was just to use a couple of random numbers (let's
> > > > assume they don't have any bias) and then use those with a
> > > few sin and
> > > > cos function etc to generate the points.
> > > > Though I have a feeling that would give me more points around the
> > > > poles.
> > > >
> > > > Anyone have some good suggestions?
> > > >
> > > > Cheers,
> > > >
> > > > Alan.
> > > >
> > > > ---
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