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Taking this purely as an engineering task, how is this remotely possible? I can barely begin to imagine how restrictions on what can be printed could be set. Am I missing something obvious? Some kind of contextual understanding of the object seems to be necessary... please don't tell me their proposed solution is AI.
In any case it will never work because 3D printing is so easy for makers to do from scratch, so any solution will fail to prevent printed guns from being made.
Again, this is just the pragmatic engineering angle. Please don't respond with political arguments.
Just spitballing but you'd have to align the desired shape somehow, perhaps with a singular value decomposition. Once its transform was normalized you could compare its shape, or perhaps its convex hull, with a database of banned shapes.
The problem is this is pretty easy to defeat (by adding extra sprues and spikes to the object, breaking it into two shapes, etc) and the more aggressive you get with the check the more you risk false positives.
An AI training set would involve creating a dataset of all the banned shapes, then generating tens of thousands of permutations of them however you believe people might try to trick it. Ultimately the AI would lock onto some small feature of the shape that scores it as positive, perhaps something trivial. That also leads to weird false positives. This also creates an arms race as people figure out what that feature is subvert it.
This problem is much harder in 3D than in 2D (currency). Since you can also cut, file, and glue shit that comes out of a 3D printer later I don't think this is a solvable problem. Like most gun control measures in the USA it appears to be aesthetics.
You could also just aggressively go false positive all over the place and say "fuck the users", with exceptions for cops. This is basically the USA's approach to drones.
That would be an even more interesting solution for finding new gun-designs for mass-manufacture. Kalashnikov, Winchester, Glock, and Colt watch out!