Extract two longitudinal isocurves from Birk’s surface at opposing quads, tween the resulting curves and rebuild the tween curve to something less horrendous. You’ll then see that his curve is so close to three circular arcs you can substitute them without anyone noticing. 
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Here’s my final GH script:
PipeLamp2.gh (34.4 KB)
I didn’t post it earlier because it was a total mess due to my trying different methods to resolve the non-horizontal end situation.
As you will see I’ve adapted a number of methods provided by postings here. The script is the way it is because I think of things strictly in terms of geometry that I can visualize mentally. Many years ago (late 1960’s)I worked in the Loft Lines department of an aircraft manufacturer where I was in the group that managed the Fortran programs that produced the code (now called GCode) for milling machines that cut out airplane parts. I was one of 3 people who built the very first graphical 3D design software that actually worked.
When I started with 3D printing about 7 years ago I realized I needed a design software that was parametric, and at that time Rhino and GH was the only product I could find that worked like that. Needless to say Rhino just blew my mind, but I got GH right away and just stuck with that since then. Consequently I am unaware of many of Rhino’s capabilities that are accessible from GH.
I didn’t use Volker’s approach for dealing with the non-horizontal surfaces because I simply could not visualize how it worked. The method I did use is, at least in my opinion, easy to visualize and easy to implement. So that’s why my GH file is the way it is.
The good news is the GH file works. The bad news is I’ve got a 3D printer firmware problem I have to tweak due to the latest update in the printer controller Klipper firmware. I’ll post a few pics of the printed part in a few days.
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Damn there are some pioneers on that forum
My printer firmware problem was more annoying than anticipated, but I finally got it fixed. Here are a couple of pics of the final results:
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Cool. Is this your last attempt? I feel like you could finesse it alot (and in the process learn alot by doing so) to make the form look less primitive geometrically and more organic.
I don’t mean this disparagingly.
Yes and no.
It is my latest (not necessarily last) attempt at making a design that will work - meaning that it is printable. It is also my first complete print resulting from this and all previous versions - of which there were many.
Well…I get your meaning, but I’m not sure I’ll want to do that. Remember, I think of things in terms of fairly standard geometry, and not in terms of what Rhino (or Blender or MeshMixer) can do. I get the interest and appeal of organic stuff - my introduction to that was years ago when I was in Barcelona and saw Gaudi’s structures. My reaction was that his designs were clearly unique and interesting, but are buildings really supposed to look like that? To this day I’m still undecided about that.
Of course you don’t. You just don’t know that I was growing up when the first B/W TV sets came out, so I tend to have a rather old-fashioned view/perception of things.
Thanks again for your interest and help.