Casting with Skewed Ejection Direction
Casting is a manufacturing process in which liquid is poured into a cast (mould)that has a cavity with the shape of the object to be manufactured. The liquid then hardens, after which the cast is removed. We address geometric problems concerning the removal of the cast. A cast consists of two parts, one of which retracts in a given direction carrying the object with it. Afterwards, the object will be ejected from the retracted cast part. In this paper, we give necessary and sufficient conditions to test the feasibility of the cast part retraction and object ejection, where retraction and ejection directions need not be the same. For polyhedral objects, we show that the test can be performed in O(n3log n) time and the cast parts can be constructed within the same time bound. We also give a polynomial time algorithm for finding a feasible pair of retraction and ejection directions for a given polyhedral object.
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- 1.Pankaj K. Agarwal and J. Matoušek. Ray shooting and parametric search.In Proc. 24th Annu. ACM Sympos. Theory Comput., pages 517–526, 1992.Google Scholar
- 2.H.K. Ahn, M. de Berg, P. Bose, W. Cheng, D. Halperin, J. Matoušek, and O. Schwarzkopf. eparating an object from its cast. In Proc. 13th Annu. ACM Sympos. Comput. Geom., 1997.Google Scholar
- 3.B. Asberg, G. Blanco, P. Bose, J. Garcia, M. Overmars, G. Toussaint, G. Wilfong, and B. Zhu. Feasibility of design in stereolithography. In Proc. 13th Symp. on FST & TCS volume 761 of Lecture Notes in Computer Science pages 228–237. pringer-Verlag, 1993. To appear in Algorithmica.Google Scholar
- 4.P. Bose. Geometric and Computational Aspects of Manufacturing Processes. PhD thesis, McGill University, 1994. Also available as UBC Tech Rep 95-02, Dept. of Comp. Sci, Univ. of British Columbia,1995.Google Scholar
- 5.P. Bose, D. Bremner, and M. van Kreveld. Determining the castability of simple polyhedra. In Proc. 10th Annu. ACM Sympos. Comput. Geom., pages 123–131, 1994. To appear in Algorithmica.Google Scholar
- 7.Prosenjit Bose, Marc van Kreveld, and Godfried Toussaint. Filling polyhedral molds. In Proc. 3rd Workshop Algorithms Data Struct., volume 709 of Lecture Notes Comput. Sci., pages 210–221. Springer-Verlag, 1993.Google Scholar
- 9.R. Elliot. Cast Iron Technology Butterworths, London, 1988.Google Scholar
- 10.Sándor P. Fekete and Joseph S.B. Mitchell. Geometric aspects of injection molding. Workshop on Geometric and Computational Aspects of Injection Molding, Bellairs Research Institute, February 5–12, 1993.Google Scholar
- 13.K.K. Kwong. Computer-aided parting line and parting surface generation in mould design, PhD thesis, The University of Hong Kong, Hong Kong, 1992.Google Scholar
- 14.J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.Google Scholar
- 15.A. Rosenbloom and D. Rappaport. Moldable and castable polygons. In Proc. 4th Canad. Conf. Comput. Geom., pages 322–327, 1992.Google Scholar
- 16.C.F. Walton and T.J. Opar, editors. Iron Castings Handbook, Ironcastingsociety, Inc., 1981.Google Scholar