On 5/8/20 9:29 PM, Cousin Ricky wrote:
> On 2020-05-02 9:27 AM (-4), Bald Eagle wrote:
....
> 

> appears to be exact, but the max_gradient is a nightmare, and I don't 

> > https://news.povray.org/4409cd2a%40news.povray.org

Ah... Thanks. I would probably not have jumped in knowing all that 
ahead. I was only aware of Bruno's work and his only because I was 
looking for sphere_sweep and blob test cases for my solver work.

I've captured all the information in my f_torus working directory.

My gut when I first read your list of requirements was that there was 
probably no exact solution. That the requirements force some 
discontinuity / fuzz. Is this thinking proven wrong somewhere?

I was on a path that solutions like Bruno's were OK / useful enough... 
If I run at this again I'll probably try and implement the blob like 
solution on the fly as a solution for something I can use.

Sebastian's images mention compares to a mesh. Of what mesh was he 
speaking? Something created from an exact solution? Something in your 
package somewhere?

Did you see my recent post to povray.general on the parametric 
performance being better than we've thought all these years? Default 
gradient of 1.0 should be more like 0.001.

Supposing there is an exact solution for the elliptical tori you want. 
Any 8th order equation will be somewhat sloppy with respect to solutions 
(165 terms were mentioned in the one post. If not sparse...).

My personal interests lean toward something with good gradients in a 
range which will play well with all the other stuff I'm doing. Solutions 
a little sloppy, but fast, and good enough are OK with me. :-)

Bill P.

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