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You are right there is a field of optimization dedicated to solving this problem to guaranteed optimality.

However, Multi dimensional bin packing problems are the some of the hardest non linear optimization problems.

Early in my generative art, I spent a lot of time packing various small shapes together, it was a fun process to figure out how to maximize the coverage without leaving large gaps. For example, a piece with almost every shape I was using: https://digcon.art/details.html?key=river-in-the-woods

Depends on the shape. Irregular shape packing and optimisation is still being advanced. Newer approaches are using ai. Lots of GitHub repositories with different approaches.