Unwrapping surfaces from a polysurface accurately for sheet metal forming

Hello all. I have a puzzle for all the smart people in the group:

Last year, my colleague and I set a challenge to design a round or oval signet ring in Rhino, then unwrap the surfaces into something flat for manufacturing in sheet copper or silver.

We tried Unroll Surface. We tried Create UV. We tried Squish. And we tried Smash (which gave us the least worst result).

The problem was every single command we tried gave distorted and inaccurate results for the unrolled surfaces. In particular, if I used the templates made by Rhino to cut out metal, the short sides would not come together on the upper parts of these signet rings. While I suspect some of this was due to surface thickness discrepancies, I don’t think that covers all of it.

What can I do to minimise this inaccuracy?

To help, I’ve enclosed some examples of the exercise I’ve used to run this test.
round signet ring size T 002.3dm (1.9 MB)



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You’re dealing with double curved surfaces. There’s no way to unwrap them into something flat that is completely correct. It’s the same reason why flat world maps are not an accurate representation of the world/globe either.