If you are talking about space curves, you can sample points and try to find a minimal-distance point-to-point mapping, threshoding it afterwards. If you are talking about arbitrary shapes with holes and stuff or a textures even, that is much harder.
Also, you can adapt the sampling based on local derivatives. The higher the first/second drivative, the denser sampling. You can also incude non-differentiable points by default.
Yes, of course. You could either put them into a grid like suggested or generate pixel matrices then calculate the difference of those two matrices with something like Levenshtein distance
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