Hi Mike

1. Load the .3dm file of a 2D pair of curves into Moi. Front view is good.

2. Start the script. I am using Max's custom UI, having run short of shortcut keys :-)

3. Select the upper curve as Kappa curvature. Select the lower curve as Tau Torsion.
Selection in reverse will create a different curve.

4. Adjust the values appropriately.
PI length is the maximum x value of the 2D curves, and also will be the arclength of the new 3D curve, Currently the script starts running at x=0.
numpoints +1 is the the number of points used to create the 3D curve and lines. The start point accounts for the +1.
The Project command is used about 2 X 8 times per point, to get Kappa and Tau.
Checkboxes are for creating BiNormal lines and/or Normal lines.
Bothsides uses the line factory to extend the lines to the other side of the 3D curve.
User Loft of the lines creates a Ribbon effect.

5. Press the Update pushbutton. It is from the Pipe2 command.

6. Depending upon the Style setup, if there are Normal lines, they will change color a couple of seconds after completion, to the next color.

The Moebius papers talk of using an "anti-Frenet" frame where Kappa is zero. This term does not appear in google searches.
I think that this is an "isolated inflection point." Maybe B and N can be negated there? http://arxiv.org/abs/1302.3175

So there is a lot of room for improvement.

Using a formula for Kappa and Tau would be faster, but I do not have a formula for the Moebius strip centerline.

- Brian

Added an Update button.
The GetValue( name ) function does not include .integerValue nor .value

- Brian

Found one more paper on a physical Moebius Strip, a thesis by Coilin P. Boylan Jeritslev.
He uses cubic B-Splines. Page 42 may be helpful, and also shows 3-fold information.

www.coilin.dk/RapportFinal.pdf

- Brian

Updated script to version 03.
Added start point and end point selection. Did not add check that startpoint < endpoint. startpoint = (0,0,0) typically.
Deleted cLength.
Deleted second half of Kappa and Tau curves.
Adjusted initial values of T, N, and B.
Added an alternate selection of values for T, N, and B, called antiFrenet.
The color g_style_index is not being used correctly. (It is better not to use the second color, usually red, when running the script.)

Running the script, without anti, can create half of a Moebius strip of width 1.6 units.
Rotating the results in top view, from the origin, by 180 degrees, produces the other half of the Moebius strip.
Alternatively, re-run the script with the anti checkbox, will produce the same second half. So anti is not needed.

Loft(s) creates the ribbon(s).

The curves do not quite match up at the inflection point, because the source curves are not quite right,
so a little bit can be deleted from each end, and the ends of the lofted ribbons Blended with G2 curvature.
The centerline can also be blended G2. The Blended strip can have a few points arrayed on its centerline, and isolines added.
The result is not quite perfect.

- Brian