Statistical mechanics of hard ellipsoids. I. Overlap algorithm and the contact function

A contact function for two arbitrary ellipsoids is derived. The numerical value of the contact function is less than 1 if they overlap, and greater than 1 if they do not. This extends previous work by Vieillard-Baron, who derived an overlap criterion for spheroids without use of a contact function. The equivalence of the two criteria has been checked by extensive numerical test with spheroids. It is shown that the use of the contact function greatly facilitates the calculation of the pressure in Monte Carlo simulations.