Twisting curve / loft issue for Mobius Strip

Hello all

I'm currently trying to loft a series of lines along a continuous curve which loops back on itself. I was hoping that if the curve is periodic, the lofted shape would finish in the same orientation as it started, however this is not the case and a 'kink' forms at the start/end of the curve.

I've been trying to solve this (as part of a larger project I'm working on) for ages now, and can't seem to sort it out. My approach to the loft has been to put a series of perpendicular aligned frames along the curve, and then construct lines on these planes and loft.

If anyone has any insight it would be greatly appreciated

Attachments:

Replies to This Discussion

Permalink Reply by Hyungsoo Kim on July 28, 2016 at 11:38am

Hi.

Some adjustment of your "Perp Frames" may be necessary.

Attachments:

MobiusStrip_re.gh, 15 KB

Permalink Reply by James Dalessandro on July 28, 2016 at 11:56am

I dont have a solution, but I noticed that while you solved the kink, it is no longer a mobius strip, just a regular 2-sided strip.

Permalink Reply by Pirouz Nourian on July 28, 2016 at 12:14pm

Hi, I have a mesh solution attached. Note that a Mobius strip is inherently non-orientable; that is there will be always two adjacent faces that cannot be oriented in the same way towards back/front. That is probably why the loft method fails.

Attachments:

Mobius.gh, 7 KB

Permalink Reply by Max Alexander on July 29, 2016 at 3:44am

Hi all, little update

Thankyou for all your answers so far, Hyungsoo your method is simple yet useful for what I need (having a Mobius strip is not my priority, rather removing the kink is)

Pirouz you raise a great point about the non orientable nature of a mobius strip which seems obvious now you've pointed it out.

A weird thing I've noticed, which I hope someone could help me figure out, is in the file attached. If I use a curve which loops twice, rather than once, and loft using only the first half, it creates a full Mobius strip (although admittedly its ends don't connect, but I don't think that is vital for my use). Anyone have any ideas why the twist of the curve differs like this? If of interest, the base curve I am using traces the surface of a torus.

Attachments: