 | | | Random points on a unit sphere without biasing | Random points on a unit sphere without biasing 2005-06-14 - By Alan Jones
Back
X, Y, Z ones would be the same as doing a cube getting more in the
corners. Apparently gaussian is special... At least that's what I
assume from what I read on the mathworld page.
Cheers,
Alan.
On 6/14/05, kim aldis <kim@(protected)> wrote:
> Why Gaussian? Wouldn't normalising x/y/z random numbers work?
>
>
>
> > -- --Original Message-- --
> > From: owner-xsi@(protected)
> > [mailto:owner-xsi@(protected)] On Behalf Of Alan Jones
> > Sent: 14 June 2005 21:42
> > To: XSI@(protected)
> > Subject: Re: Random points on a unit sphere without biasing
> >
> > Thanks Andy. After looking at the options I think I'm going
> > to go with the one at the bottom of the mathworld page. It
> > suggested 3 gaussian random numbers for X, Y and Z in a
> > vector and normalizing the vector (at least that's what I
> > think it said from my limited math). I managed to track down
> > an apparently fast way to generate gaussian random numbers
> > from evenly distributed ones so with any luck I'm set.
> >
> > Thanks again,
> >
> > Alan.
> >
> > On 6/14/05, Andy Jones <andy@(protected)> wrote:
> > > The mathworld article answers this perfectly. Basically,
> > you pick one
> > > angle (theta) at random and a height (h) on the sphere at
> > random. You
> > > can check this by calculating the approximated surface area (width *
> > > radius) of the bands around the sphere at different heights
> > along the
> > > sphere, and take the limit as dh -> 0. At the poles, the
> > width of the
> > > band is larger for a given height, and at the equator, the
> > radius of
> > > the band is obviously larger. In the limit, they have a perfectly
> > > inverse relationship such that each band has the same area. More
> > > generally, a good way to randomly sample vectors within a
> > given angle
> > > of an average vector is to restrict the height range to
> > [cos(angle), 1].
> > >
> > > I think you can't pick points in a cube and normalize
> > because you'll
> > > bias more points at the corners and fewer points in the
> > middles of the
> > > faces, since a cube has more and less volume in those
> > directions. The
> > > same problem occurs if you sample on a cube's surface area.
> > The cube
> > > method is especially problematic because the biasing isn't
> > determined
> > > by the original vector direction. Of course, that doesn't mean it
> > > doesn't work okay in practice for many applications.
> > >
> > > -Andy
> > >
> > > Alan Jones wrote:
> > >
> > > >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.
> > > >
> > > >---
> > > >Unsubscribe? Mail Majordomo@(protected) with the
> > following text in body:
> > > >unsubscribe xsi
> > > >
> > > >
> > > >
> > >
> > > ---
> > > Unsubscribe? Mail Majordomo@(protected) with the
> > following text in body:
> > > unsubscribe xsi
> > >
> >
> > ---
> > Unsubscribe? Mail Majordomo@(protected) with the following
> > text in body:
> > unsubscribe xsi
> >
> >
>
> ---
> Unsubscribe? Mail Majordomo@(protected) with the following text in body:
> unsubscribe xsi
>
---
Unsubscribe? Mail Majordomo@(protected) with the following text in body:
unsubscribe xsi
|
|
|