Given a pair of objects A and B, we define new measures called touching distances that determine how much A should be moved from a nonintersecting/deeply intersecting position so that it just touches the boundary of B (assumed to be static). Our distance measures evaluate to zero only when the objects are just touching. We show that the touching distances are continuous with respect to rotation and translation of A when both objects are convex polygons or convex polyhedra. Usefulness of this property in the context of collision detection is indicated. © 1998 Elsevier Science Ltd. All rights reserved.