If while distributing particles to their corresponding nodes, two particles comes closer to a level smaller than the machine precision (or $\Delta d \to 0$), how is the situation to be treated? Should the recursive distribution stop and both of them be added to a single node?
This happens because of treating particles as point objects rather than 2D objects. Imagine a machine having a precision level of 3 decimal points (mm in SI) and a situation in which the bodies come within $10^{-6}$ (micro level) of one another.