Separating an object from its cast

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 can one nd a direction ~ d such that the above cast partitioning can be done? We give necessary and su cient 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.

[1]  Ketan Mulmuley,et al.  Computational geometry : an introduction through randomized algorithms , 1993 .

[2]  R. Elliott.  Cast iron technology , 1988 .

[3]  David Rappaport,et al.  Moldable and Castable Polygons , 1994, Comput. Geom..

[4]  Jirí Matousek,et al.  Efficient partition trees , 1991, SCG '91.

[5]  K. C. Hui,et al.  Geometric aspects of the mouldability of parts , 1997, Comput. Aided Des..

[6]  G. Toussaint,et al.  Geometric and Computational Aspects of Injection Molding , 1992 .

[7]  Bernard Chazelle.  Triangulating a simple polygon in linear time , 1991, Discret. Comput. Geom..

[8]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[9]  Godfried T. Toussaint,et al.  Feasability of Design in Stereolithography , 1993, FSTTCS.

[10]  Jean-Claude Latombe,et al.  Geometric Reasoning About Mechanical Assembly , 1994, Artif. Intell..

[11]  Godfried T. Toussaint,et al.  Geometric and computational aspects of manufacturing processes , 1996, Comput. Graph..

[12]  Prosenjit Bose,et al.  Determining the castability of simple polyhedra , 1994, SCG '94.

[13]  Eric L. Buckleitner,et al.  Molds for Reaction Injection, Structural Foam and Expandable Styrene Molding , 1987 .

[14]  Shuo-Yan Chou,et al.  Parting directions for mould and die design , 1993, Comput. Aided Des..

[15]  Leonidas J. Guibas,et al.  Primitives for the manipulation of general subdivisions and the computation of Voronoi diagrams , 1983, STOC.

[16]  Otfried Cheong,et al.  Immobilizing polygons against a wall , 1995, SCG '95.

[17]  鄺建華.  Computer-aided parting line and parting surface generation in mould design , 1992 .

[18]  Prosenjit Gupta,et al.  Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design , 1996, Comput. Geom..

[19]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

[20]  Godfried T. Toussaint,et al.  Movable Separability of Sets , 1985 .

[21]  Prosenjit Bose,et al.  Feasibility of Design in Stereolithography , 1997, Algorithmica.

[22]  Prosenjit Bose,et al.  Determining the Castability of Simple Polyhedra , 1997, Algorithmica.

[23]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[24]  Jack Snoeyink,et al.  Two-dimensional Computation of the Three-dimensional Reachable Region for a Welding Head , 1993, CCCG.

[25]  K. C. Hui,et al.  Mould design with sweep operations - a heuristic search approach , 1992, Comput. Aided Des..

[26]  Prosenjit Bose,et al.  Filling Polyhedral Molds , 1993, WADS.

[27]  Martin Held,et al.  On the Computational Geometry of Pocket Machining , 1991, Lecture Notes in Computer Science.