Unbending wire

Hi all,

I'm working on a project which involves some fairly complicated geometry issues with bending and unbending metal wire and I'd like to ask for your help.

What I'd like to achieve is a definition which would take a closed 3d curve as input and unbend it so that it would form a 2d curve, keeping as much of the original planar curvature as possible and avoiding twisting in the process.

I imagine it would work like this:

What I've come up with so far is a way to identify the "planarity" of the curvature, thus finding the parts of the curve to which (i think) the unbending should apply:

and a mini-tool for the visual display of the curve's twists and bends:

...but I'm kind of stuck here and can't figure out a way how to move on.

I'd be very thankful for any ideas and thoughts on how to approach this problem.

Many thanks,
JJ

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Permalink Reply by Daniel Piker on June 6, 2010 at 9:07am

I've actually just been working recently on some functions for spatial elastica in Kangaroo.
At the moment it just relaxes rods with zero intrinsic curvature, but I think it should be possible to make it work with a wire does have some intrinsic curvature and apply a force to pull it onto a plane. This will only work if you don't have any intrinsic torsion though (ie you've not bent the wire into a loop, given it a twist and reconnected it). (http://math.arizona.edu/~goriely/res-michel.html)

But maybe this is overkill - there might be a simpler geometric solution in your case - if you can fit your curve to a developable surface then unroll it.

Permalink Reply by Jacek Jaskólski on June 10, 2010 at 3:38pm