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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Attachments:
Download 'tube_heartcurve.zip' (1 KB)