Selfintersecting Moebius Band

Continuing to explore the work of Rinus Roelufs, I had some progress with the selfintersecting Moebius band.

The holes that permits the surface to weave into itself are now circular. The definition is not all that parametric yet, meaning you can only change the size of the moebius, the size of the holes and whether the moebius band should be twisted once or three times.

This last part, that you can control the number of twists is thanks to Lorenz Lachauer. This possibility never occurred to me before, but it's really cool.

MoebiusConnectedHoles.ghx

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Comment by MillieJordon on October 17, 2022 at 10:22am: A self intersecting Moebius band is a version of the Moebius band with no ends and no start. The surface area of this shape is unchanged by rotations, but its boundary determines which direction it can be rotated.The topologically simplest example of such a surface is the sphere (in fact, if you draw lines tangent to all points on the surface, they will cross each other). If we consider this object as a circle instead, then its interior would look like a cylinder with two holes in it. Well, I have decided to hire a law research paper writer because I have no idea about how to write a good research paper.

Comment by Sahara on August 5, 2010 at 5:26am: hi there,
for some reason I cannot open the ghx file!!!!it opens,but there is nothing inside???could you plaease help!!!!it give me a message like IQ generated 34 messages...something like that???thx

Comment by Daniel Xiong on August 1, 2009 at 10:13am: Amazing! I really learned a lot from you guys:)
I would try to make some of my own later.

Comment by Vicente Soler on August 1, 2009 at 8:06am: That's probably due to the nurbs interpolation, if you increase the number of points it should go away.
Btw, now i remember that thread, my memory is failing me misserably lately, i didn't even remember i had it with you.

Comment by Lars Renklint on August 1, 2009 at 7:41am: Anyway, it was thanks to your enormous willingness to share and help people that I got started with GH, and the Moebius definition you posted kept me occupied for a long time, trying out different options. Thanks!

Comment by Lars Renklint on August 1, 2009 at 7:14am: Hi Vicente, yes I remember that thread, it is very good that the forum moved here, so files don't dissapear all the time.

Found that def - doublemobius.ghx just flattened one input and now it works.

I actually look at it the other way around and prefer the holes in the finished model to be round. One thing I never did understand with the definition above is why the surface didn't meet nicely, since it was constructed from a mathematical function it should have.

Comment by Vicente Soler on August 1, 2009 at 6:41am: Hi Lars, it's a shame many files have been deleted from the old forum. I posted something similar in december of last year. I don't have the definition, just the screenshot i posted:

The downside of orienting circles directly onto the mobius band is that if you were to unroll the band and flatten it out, the holes won't be circular. This definition uses another method so this doesen't happen.