Interesting, but not practical. All real furniture movers would make use of the third dimension. The difficulty of extending the definition to 3 dimensions is

Interesting, but not practical. All real furniture movers would make use of the third dimension. The difficulty of extending the definition to 3 dimensions is that the restriction to 2 separates two classes of constraint: being able to move the sofa round the corner, and the shape of the sofa being comfortable to sit on.