Yes, Dr. Mu's concept is exact, but it need to solve collisions, too - generally, problems related with real dimensions of pieces.
Ad intermediate points - imho, my concept of occupied squares is better (but not exhausting collision problems), of course, when it is possible to split every piece into set of square-unit.

In reply to Re^4: Closed geometry: a train track problem by pajout
in thread Closed geometry: a train track problem by SamCG

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