Finding the Minimum Distance Between Two Convex Polygons

suppose that a provisional path of coordinated motion has been planned for two rigid polyhedral bodies B1 and B2 in 3-space. Then there will exist functions RI(t), R*(t), x1(t), x2(t) of a parameter t designating time such that the set of points occupied by Bj at time t is Rj(t)Bj + xj(t). TO verify the validity of the proposed motion, one can proceed as follows: find the minimum distance 6 between the convex sets Rl(t)B1 + x1(t) and R*(t) 13s + x2(t) for t = 0. Let L be the diameter of the set BZ, and from the known form of the functions RI, R2, xl, and x2 find an e sufficiently small so that