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Flat band that procedurally twists and bends

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I've been trying to procedurally model the path of a flat band (think a flexible metal tape) as it moves through space.

I need the the two outer rails to start at a fixed location and arrive at a second fixed location and direction in 3 dimensional space ( not flat on the ground like rail tracks etc.).

Similar to how a metal tape measure would start at one point (at the housing) and one might hold the tip at another pointed in a different direction.

The two outer edges will bend and twist together but will remain the same distance from each other as well as have the same over all length.

This is also what contributes to the twisting affect which is giving me the problems.

I need to find a procedural way to generate the shortest path between the two ends accounting for the twisting etc.

Remember, in a true band there is no actual "turning", just twisting and bending under tension to create a "turn".

I've experimented with "growing" the two ends towards each other in segments using a coordinate system that steers each segment in iterations towards the other by only bending from the middle , twisting from an outer edge or twisting from center.

This kind of works but ultimately could never meet the other end.

I wonder if there is a simpler approach or solution using curves etc. that someone has already figured out as I'm sure I'm not the first to procedurally model a rigid, yet bendable, surface in such a manner.
















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If your band needs to be the same width along the entire length, why treat it as 2 rails? Would it not be easier to find the midpoint of the band and then manipulate up-vector along the length to get your different twists, then Sweep? If you need it to line up at the end, you can precompute the end's up-vector and smooth out the transition towards the end to meet it.

Edit: attached naive solve


Edited by Fenolis
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