POV-Ray : Newsgroups : povray.binaries.images : Elliptical torus : Re: Elliptical torus Server Time
28 Mar 2023 17:24:14 EDT (-0400)
  Re: Elliptical torus  
From: William F Pokorny
Date: 4 May 2020 03:56:00
Message: <5eafca90$1@news.povray.org>
On 5/3/20 4:30 PM, Bald Eagle wrote:
> William F Pokorny <ano### [at] anonymousorg> wrote:
>> :-) Thanks for pushing here. Does this all work only when the major axis
>> is 1.0 or something?
> Unfortunately, I thought, nay - believed (at 1am) that I had gotten it
> sufficiently worked out so that I could just get it prettied up and all would be
> fine, but of course it has proven to be a bit more challenging than that.
> I have been trying to get it re-worked out myself, but how exactly the
> z-parameter gets adjusted to compensate for the x and y stretching in the
> implicit form is unclear.
> I too have been trying to get it to be consistent with POV-Ray's torus in the
> xz-plane - I just need to hit upon the proper form.
> On the plus side, after a few dozen experiments, I have at least one function
> that's sufficiently interesting to pursue at some other point.
> It's maddening to be this tantalizingly close and still not _have_ it.

FYI. I've not recently looked at it, but back in 2006 Bruno Cabasson 
worked up some code for elliptical tori implemented with sphere_sweeps 
and blobs. Perhaps useful to review that work as we look for an 
f_elliptical_torus() or complete parametric solution.

Given we can use blobs as potential patterns in functions/isosurfaces in 
v38, perhaps this a path to something practical for Cousin Ricky?

The sphere_sweep as a general solution is not very attractive in v37 and 
prior due bugs. Situations is better in v38 - and still better in povr 
but the sphere_sweep probably not the fastest.

With both approaches expect tolerances to any math ideal, but perhaps we 
are stuck with a fuzzy result in any case?

I captured his code in my sphere_sweep test cases, let me see if small 
enough to just attach it - yep. Warning! Some chance I hacked on the 
scene file a little from what was originally posted - I didn't check.

Bill P.

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