 | | | 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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Thanks Kim. :-) How many beers is that now?
On 6/14/05, kim aldis <kim@(protected)> wrote:
> Mathworld is back on line. Excelent. I thought they were going to die for a
> while.
>
> Ah .. You want a uniform random distribution rather than a random number,
> evenly distributed.
>
> Generate a cube of random points in space then project onto the sphere
> surface (normalise then mult by radius)
>
> > -- --Original Message-- --
> > From: owner-xsi@(protected)
> > [mailto:owner-xsi@(protected)] On Behalf Of Alan Jones
> > Sent: 14 June 2005 16:49
> > To: XSI@(protected)
> > Subject: Re: Random points on a unit sphere without biasing
> >
> > 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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