[Papervision3D] distributing planes evenly within a spherical bound

[Nathaniel Warner]

Did you figure this out?  If not I'll throw together a quick demo.

On 1/15/08, Makc <makc.the.great at gmail.com> wrote:
> good idea. maybe you would need random^(1/3) in 3D
>
> On 1/16/08, Roy Wiggins <bungadunga at gmail.com> wrote:
> > Keith Peters' Making Things Move had a formula for distributing points more
> > or less evenly inside a circular bound. I think it was a matter of just
> > taking the square root of a random multiple of the radius:
> >
> > var radius:Number = Math.sqrt(Math.random()) * maxRadius;
> > var angle:Number = Math.random() * (Math.PI * 2);
> >
> > I'm not sure how that would work in a sphere. It doesn't guarantee that the
> > points are spread out, just that they don't bunch up in the middle (radii
> > are a lot closer in the center). The easiest way is to just generate a
> > cube-shaped space full of planes and get rid of all the ones beyond the
> > radius you want.
> >
> >
> > On Jan 14, 2008 4:34 AM, Makc <makc.the.great at gmail.com> wrote:
> > > In fact, I've got interested if smth like this would actually work,
> > > and made quick 2d test (will try to attach). Result is not as
> > > expected, seems like no balance could be ever reached, but it is
> > > interesting in itself; I wonder how this would look like in 3d...
> > >
> > >
> > >
> > >
> > > On 1/14/08, Makc <makc.the.great at gmail.com> wrote:
> > > > there is no much theory, I wrote that out of my head. the idea was to
> > > > separate closer objects more than distant ones every time (hence 1/r),
> > > > so that in the end there should be some kind of balance achieved. this
> > > > all assumes you have some random positions to start with.
> > > >
> > > > On 1/14/08, Lukasz Karluk <julapy at googlemail.com> wrote:
> > > > > hi Makc, thx for ur response.
> > > > > im not entirely familiar with the theory there, i get some parts but
> > not the
> > > > > whole.
> > > > > do u know where i could read up about it further?
> > > > >
> > > > >
> > > > > On Jan 14, 2008 6:01 PM, Makc < makc.the.great at gmail.com > wrote:
> > > > > >
> > > > > > you can run few iterations of simple procedure, such as: for every
> > two
> > > > > > planes a) find distance r (vector), b) displace one of them by
> > vector
> > > > > > proportional to 1/|r| (like dr = 0.1 * r / (r dot r) for example),
> > and
> > > > > > then apply uniform scale to all their coordinates to get them within
> > > > > > sphere of given radius.
> > > > > >
> > > > > >
> > > > > >
> > > > > >
> > > > > > On 1/13/08, Lukasz Karluk <julapy at googlemail.com> wrote:
> > > > > > > hi,
> > > > > > >
> > > > > > > would anyone know a method of distributing planes evenly within a
> > > > > spherical
> > > > > > > bound?
> > > > > > > essentially the paper cloud example although i wanted to ensure
> > that the
> > > > > > > planes don't overlap and are spaced out.
> > > > > > > if anyone could point me in the right direction that would be
> > great.
> > > > > > >
> > > > > > > cheers
> > > > > > > julaps
> > > > > > >
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