IIRC, Mike Williams addressed this very thing in his isosurface tutorial.

I can send you a copy - seeing all of the functions converted to POV-Ray scenes
would be great!   :)


- Bill

"Droj" <803### [at] drojde> wrote:
> I was interested to see how can a 2D curve get a more interesting life in a 3D
> world.
> And I found a promising approach in the Internet on B. Frassek's website
> https://www.frassek.org (sorry, the site is in German but an automatic
> translation is available). Look for 'function graph as pipe/tube'.
> The steps are outlined here:
>
>  - take the parametric function of a circle as cross section for the tube
>  - determin the gradient of the 2D curve you want to use (derivatives must
> exist)
>  - let the center of the cross section travel along the 2D curve (e.g. like
> insulation on a copper wire)
>
> Alas, that's it.
>
> So I started to adapt all the functions to Povray. I am aware that using atan2
> is an unexplicable mystery but what the heck.
>
> The result was sort of sobering as the tube was flatend in some parts and bulgy
> in others.
> I upload the POV-Script I generated to show the problem.
>
> Any suggestions (if there are any) on how to get a perfectly round tube are
> welcome but I need the parametric approach as I want to use the .inc/.obj output
> for more things to come.

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