Curvature match ends of moebius strip?

[eobet]

I’m trying to figure out how to build a moebius strip with Grasshopper, but I’m having trouble making it a nicely flowing seamless surface:

It’s the fact that the beginning and end is rotated 180 degrees that prevents me from using the “closed” loft option, so does anyone have any ideas how to get around this?

Note, the input curve is a circle in this case, but I might want to use a different closed curve…

moebius.gh (13.0 KB)

[Joseph_Oster]

Riccardo Majewski ( @maje90 ) produced this five years ago and we had some good fun with it:

Unrolling mobius strip

Also here:

SAMPLE Interlaced Möbius-like strip

[davidcockey]

Split the edge curve into two open curves. Loft using the pair of open curves and then match the edges of the surface.

[eobet]

Thanks, but I want a different type of control for my strip:

However, after reversing the vector of the rotation axis (because I wanted the rotation to start in the other direction), I’m getting weird “flips” that I don’t know the source of…

Even if I skip reversing the axis, and instead go from 0 to -180 I get the same flip result…

moebius2.gh (15.4 KB)

[Joseph_Oster]

[eobet]

They’re free you know. And nobody should use Grasshopper without Pufferfish.

[Joseph_Oster]

I do.

[Joseph_Oster]

I believe the only difference between the two Rotate components in the yellow group is that you reversed the Z vector on the first one. The smaller one simply rotates the pFrames around each planes normal Z axis.

moebius2_2020May07a.gh (17.5 KB)

[eobet]

Thank you!

Interesting to see your reduction in the number of nodes. I started out with the perpendicular frames node, but I wasn’t able to get any result from it at all (but now it obviously works)… perhaps it’s the order of things I do it in, because at first, when I replaced the input curves with the curves from my file, I got errors as well, but after a few tries it now works.

Super interesting to see how you achieve a complete strip as well! Seems like a much better method than mine. As usual with Grasshopper, I’m going to have to digest this a bit.

[Joseph_Oster]

Here are a few changes:

• It uses any closed curve as a guide, doesn’t have to be a circle.
• It has a “seam” adjustment for that curve (moves start/end point).
• It generates its own width line (doesn’t require the second curve input, cyan group).
• It generates a “solid” with thickness (“Closed Brep”, white group).

I’m not convinced of the value of using a Graph Mapper but left it in.

Möbius_2020May08b.gh (27.1 KB)

Still working on the twice-around feature we had five years ago…

[Joseph_Oster]

Here is a “twice around” version:

Möbius_2020May08a.gh (31.5 KB)