On 5/3/20 12:04 AM, Bald Eagle wrote:
> "Bald Eagle" <cre### [at] netscapenet> wrote:
> 
>>> "I couldn't resist trying it..."
>>
>> lol - well of course not.  :D
> 
> And I couldn't resist implicitizing it.
> I mussssst ... do..... the math..... yesss....
>                                                       my Precious........!
> 
> And here is The One Elliptical Ring.
> The gradient is only about 4.5    :)
> 
> However, you will notice that it doesn't render correctly when axis-aligned.
> If I rotate it by 1 degree (0.5 isn't enough), then it becomes fully visible.
> 
> Do we smell a root-finding problem?  Ugh.
> 
> Martijn does some interesting little tweaks that I haven't thought out
> completely to fix holes and other artifacts:
> https://www.youtube.com/watch?v=-adHIyjIYgk   (14 min mark)
> No idea if any of that is related to POV-Ray isosurface issues.
> I think he might address some similar issues either earlier or in Part 2.
> 
> Anyway, I'm off to bed, but had to post this for Ricky.
> 
> Maybe tomorrow I will be able to better parameterize it.
> 
> Boo-Ya!
> 
:-) Thanks for pushing here. Does this all work only when the major axis 
is 1.0 or something?

I grabbed what you did and tried it after a little re-work to align it 
with the f_torus behavior and on testing the constant sphere width was 
not maintained when a != b - or when I changed the major axis to other 
than one. The last was relatively easy to fix. I had no luck with a!=b 
across all testing - though I could get some subsets of parameters to work.

Might be I screwed something up in reworking it. Will come back to it 
later, but if there are assumptions with the implicit form use,it would 
be helpful to know.

Bill P.

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