How to know whether a polyhedron fits within another?

Question

I need to know whether a sofa fits within an elevator.

I know their dimensions, and I found this topic.

However, does it check the fitting regardless of the orientation of the contained solid ? Or does it only try translating the moving object inside the container without changing its orientation ?

I know a bit about linear algebra but pretty much nothing about convex optimization.

Answer 1

This is a difficult problem in its full generality. There is actually a paper entitled, "On Moving a Sofa Around a Corner," discussed at this MO question. See also Sofa in a snaky 3D corridor:

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          ^{Hammerslay's "sofa" in a corridor.}

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