Approximations, precision and design constraints

[winksaville]

I'm a noob so I ask bots questions. They generalls give answers that sound authoritative, but they almost always have errors. Anyway, I asked 2 bots the same question about "Approximations, precision and design constraints"; Claude Opus 4.5 and ChatGPT 5.1. They produced reasonable sounding responses that I thought I'd share. Human thoughts :)

[hannobraun]

Claude's reply seems reasonable, with the possible exception of the "Your 3D Printing Use Case" bit. I can't tell if there's any substance behind that, and didn't take a lot of time to think about it. GPT mentions some more stuff that I can't verify is true. It also outright hallucinates/speculates about the specific problems that I ran into with Fornjot, and I stopped reading after that.

What's definitely true is that approximations are required anyway for graphics, export to some file formats, usually CAM (as far as I know), and mathematical edge cases. In my latest experiments, I decided to go a step further and use these approximations as a uniform intermediate representation, meaning I won't even try to compute a mathematically exact intersection (for example), even where that is possible.

My hypothesis here is that it won't matter. In any realistic use case, you're going to have some acceptable tolerance. And unless you throw away your model and only keep your STL export (which you shouldn't do), you can always go back and re-create your output with higher precision.

There's the open question of how STEP export is going to work under that model. I came to the conclusion that I'm not going to think about that for now. I already have a million problems, and I won't make progress by trying to keep them all in my head at once.