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, can the cast be partitioned into two parts such that the parts can be removed in directions d and -d, respectively, without colliding with the object or the other cast part? (2) How to find a direction d 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 present a surprising result on the case where the cast parts need not be removed in opposite directions.

Proceedings of the 1997 13th Annual Symposium on Computational Geometry
School of Computer Science

Ahn, Hee-Kap (Hee Kap), de Berg, Mark (Mark), Bose, P, Cheng, Siu-Wing (Siu Wing), Halperin, Dan (Dan), Matousek, Jiri (Jiri), & Schwarzkopf, Otfried (Otfried). (1997). Separating an object from its cast. In Proceedings of the Annual Symposium on Computational Geometry (pp. 221–230).