SEPARATING AN OBJECT FROM ITS CAST

Abstract

In casting, liquid is poured into a cast that has a cavity with the shape of the object to be manufactured. The liquid then hardens. after which the cast is removed. We consider the case where the cast consists of two parts and address the following problems. (1) Given a cast for an object and a direction (d) over right arrow, can the cast be partitioned into two parts such that the parts can be removed in directions and (d) over right arrow and -(d) over right arrow, respectively. without colliding with the object or the other cast part? (2) How can one find a direction (d) over right arrow such that the above cast partitioning can be done? We give necessary and sufficient conditions for both problems, as well as algorithms to decide them for polyhedral objects. We also give some evidence that the case where the cast parts need not be removed in opposite directions is considerably harder. (C) 2002 Elsevier Science Ltd. All rights reserved.