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Overview:
I have a simple plastic sandbox represented by a 3D polygonal mesh. I need to be able to determine the water level after pouring a specific amount of water into the sandbox.
- The water is distributed evenly from above when poured
- No fluid simulation, the water is poured very slowly
- It needs to be fast
Question:
What kind of techniques/algorithms could I use for this problem?

I'm not looking for a program or similar that can do this, just algorithms - I'll do the implementation.