I would like to move the seam of this Möbius Surface component from LunchBox. Preferably, the seam needs to be on the opposite side of where it is now. Any help is greatly appreciated.
Move Seam.gh (1.7 KB)
This is great, thank you.
This looks interesting, would love to try an idea but don’t have Lunchbox. Too bad the Möbius surface is not internalized. 
The white group creates the Möbius surface without a plugin, the purple group moves the seam.
Möbius_2024_Jul16a.gh (15.5 KB)
The purple group might work on the Lunchbox Möbius surface?
P.S. I just realized that my “Möbius surface” twists the strip 360 degrees (2 * Pi) instead of 180 degrees (Pi) and why it fails if you try ‘Pi’ instead of ‘2 * Pi’…
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Another great solution.
But it is not a Möbius strip with 360 degrees twist instead of 180 degrees, right?
I am not sure, that is a good question.
A Möbius strip has only one “face” and one edge. That’s its “magic”.
I would say it can have an infinite amount of twists, but it depends on the semantics.
Möbius strip From Wikipedia
In mathematics, a Möbius strip, Möbius band, or Möbius loop is a surface that can be formed by attaching the ends of a strip of paper together with a half-twist. As a mathematical object, it was discovered by Johann Benedict Listing and August Ferdinand Möbius in 1858, but it had already appeared in Roman mosaics from the third century CE.
I think it would make sense to define it as what you said earlier, a surface that only has one face and one naked edge, otherwise you would have to give the ones that have a full-twist and more individual names, or set them apart from the one that has a half-twist.
When the number of half twists is odd, you can call it a Möbius strip, though this is a brep not a surface. See the green section to cheat?
Möbius_2024_Jul16c.gh (24.2 KB)
5 half twists:
When the number of half twists is even, it’s just a twisted surface.
twistSrf_2024_Jul16a.gh (25.4 KB)
6 half twists:
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I have much to learn. They look so similar yet are so different.
thanks @Joseph_Oster for showing method of creating it
i have attached another one a little modified version of @Joseph_Oster
it works only in odd number multiplication with pi
as @i3f8b6r5l2 said here i am not able to move the seam
twistSrf_2024_Jul16a_modified.gh (19.7 KB)
Very cool! Thanks. I had considered something similar but of course it won’t work with a closed loft. Took me awhile to understand what you did but I’ve got it now. Modified my code to work with both odd (Möbius) and even half twists. Still working on moving that seam but need a break.
twistSrf_2024_Jul17a.gh (18.0 KB)
To summarize the method in my previous post (‘17a’), a closed loft is used when the number of half twists is even. When the number of half twists is odd (Möbius), an unclosed loft is used with a flipped copy of the first section inserted at the end (thanks again @Rajeev2 for that).
The seam moving solution in my first post (version ‘16a’) still works when the number of half twists is even, but fails when it is odd. Still working on that, but I have two questions:
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Should I add it as a feature to creating the twisted surface or separate it?
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Does the surface produced by LunchBox follow the same convention regarding even and odd half twists? Per my first question, should moving the seam work on LunchBox output?
This became way, WAY more complicated than I had hoped. The white group at the top generates twisted surfaces with odd (Möbius) and even half twists. The orange group at the bottom has a ‘Seam’ slider (blue group) that moves the surface seam. Numbered isocurves are used and left visible. One detail from the white group is used in the orange group: ‘odd’ (0 or 1)
twistSrf_2024_Jul17b.gh (34.2 KB)
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Thank you again, this is plentiful.
This is the third and final time I will ask.
Posting a GH file that begins with a plugin I don’t have or want is functionally the same as posting no file at all. 
I was getting exasperated yesterday trying to get version ‘17a’ to work. Then I tried enabling the loft option ‘Align sections’ (‘Adjust seams’) and voila! Success! So I quickly posted it, then realized later that my efforts to flip the last section curve (when ‘odd’) weren’t needed. So I removed those bits in this version.
Then wrote a little cluster (yellow group) to count half twists (odd or even), trying to eliminate the dependency of the orange group for that bit from the white group. Alas, more code re-org is needed to avoid a “cyclical data stream” so I skipped that for now.
twistSrf_2024_Jul18a.gh (40.4 KB)
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