How could I calculate if a rectangular cuboid fits in an other rectangular cuboid, it may rotate or be placed in any way inside the bigger one.
For example would, (650,220,55) fit in (590,290,160), they are all mm.
[Math] How to check if a box fits in a box
discrete geometrymg.metric-geometry
Best Answer
There are several algorithms in polynomial time to decide if a convex polytope contains another polytope, see e.g. for Martin, Stephenson, "Containment algorithms for objects in rectangular boxes" (1989).
Let me invoke @Joseph O'Rourke, a regular contributor to mathoverflow, and also the author of one of these algorithms. He will probably show up soon and give a definitive answer for the case at hand.