compute overlap

Dear all,

I was trying to understand how the overlap can be measured in LIGGGHTS if we have two spheres in collision. I know that I can find the value of the overlap through this equation (from the positions):
Overlap= d-r ;

But actually I am looking for the original equation that has been used in the source to compute the overlap for any collision.

I would be very grateful if you could provide me with any information (equation or paper or book) about computing the overlap in DEM .

Many thanks,
Abdul