Irina inspired me to go home and work out this problem for creating mobius strips. Deconstructing the problems in its simplest terms yields a line rotated about a closed circular path 180 degrees from start to finish. Thankfully Maya has two powerful commands that can be used to accomplish this easily.
Attach to Motion Paths> allows you to attach a curve to a path. It also alows you to generates keyframes for the curve's orientation as it moves aling the path. In this case the rotation at 90 degrees and at 180 degrees. Once completed you can then use Create Animated Sweep> to generate the lofted surface for your mobius strip. You can create output as Nurbs or as a Polygonal Object, and that's where the fun begins. This solution was inspired by a Jose Sanchez tutorial: The Mobius Strip from GSAPPonline at Columbia University. It provides a good start. A similar technique can also be used to generate shell forms. I have extended some of the concepts covered in the tutorial which will be explained in an upcoming tutorial video on using animation for modeling in Maya.
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