Re: Converting spherical to elliptical distribution Bradley Lucier 04 Aug 2020 02:35 UTC
That's a very good concern.

I'm including a test program here that shows that the points on an
ellipse generated by (make-sphere-generator '#(10 2)) from sphere.scm
are not distributed uniformly around the ellipse.  In other words,
Arvydas's concerns are valid.

If I generate 10,000 points on the ellipse, then on the top of the
ellipse I find for points on the "top" of the ellipse, with y > 1.5,
that the average distance between adjacent points is

 > (average-distance top)
.003781294690450104

and on the "right" of the ellipse, with x > 8, the average distance
between adjacent points is

 > (average-distance right)
.004584542133993673

So I don't think (make-sphere-generator '#(10 2)) generates points
uniformly on the ellipse.

Brad

On 7/16/20 4:14 PM, Arvydas Silanskas wrote:
> Yes, that's how I'm picturing implementing it. But what I'm not sure of
> is the quality of spacing between the points. Maybe unneededly, if you
> say it's ok then it's ok, I just want to confirm you understand my
> question. I attach a picture of my concern.
>
> 2020-07-16, kt, 21:33 Lucier, Bradley J <xxxxxx@purdue.edu
> <mailto:xxxxxx@purdue.edu>> rašė:
>
>     Sorry, you meant standard deviation, not variance.
>
>      > On Jul 16, 2020, at 2:28 PM, Lucier, Bradley J <xxxxxx@purdue.edu
>     <mailto:xxxxxx@purdue.edu>> wrote:
>      >
>      > I think you mean sqrt(A), etc. Brad
>      >
>      >> On Jul 16, 2020, at 2:14 PM, Linas Vepstas
>     <xxxxxx@gmail.com <mailto:xxxxxx@gmail.com>> wrote:
>      >>
>      >> So, if the ellipse major axis lengths are A,B,C... then generate
>     X,Y,Z with widths A,B,C..
>