[Papervision3D] distributing planes evenly within a spherical bound

[Roy Wiggins]

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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