The detection and response to collisions with the cushion and the pockets is much easier to calculate if the coordinate system is alligned with the table and hence the cushions.
Within this coordinate system the position of each ball is given by the position of its centre of mass.
The centre cannot get within the balls radius (r) of the cushion therfore the effective boundary, for the centre of mass of the ball, is an imaginary line a distance of r inside the real cushon.
This is mostly 2D except for some effects like backspin or miscuing, etc. Therefore it might allow a lot of simplification if we model in 2D but with a few additional parameters to allow for these effects.