Abstract
In casting, molten material is poured into the cavity of the cast and allowed to solidify. The cast has two main parts to be removed in opposite parting directions. To manufacture more complicated objects, the cast may also have a side core to be removed in a direction skewed to the parting directions. In this paper, given an object and the parting and side core directions, we give necessary and sufficient conditions to verify whether a cast can be constructed for these directions. In the case of polyhedral objects, we develop a discrete algorithm to perform the test in O(n 3log n) time, where n is the object size. If the test result is positive, a cast with complexity O(n 3) can be constructed within the same time bound. We also present an example to show that a cast may have Θ(n 3) complexity in the worst case. Thus, the complexity of our cast is worst-case optimal.
Work by Ahn, Bae and Chwa was supported by the Brain Korea 21 Project, The School of Information Technology, KAIST, in 2005. Work by Cheng was supported by Research Grant Council, Hong Kong, China (DAG04/05.EG21).
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References
Ahn, H.K., Cheng, S.W., Cheong, O.: Casting with skewed ejection direction. In: Chwa, K.-Y., Ibarra, O.H. (eds.) ISAAC 1998. LNCS, vol. 1533, pp. 139–148. Springer, Heidelberg (1998)
Ahn, H.K., Cheng, S.W., Cheong, O., Snoeyink, J.: The reflex-free hull. International Journal of Computational Geometry and Applications 14(6), 453–474 (2004)
Ahn, H.K., Cheong, O., van Oostrum, R.: Casting a polyhedron with directional uncertainty. Computational Geometry: Theory and Applications 26(2), 129–141 (2003)
Ahn, H.K., de Berg, M., Bose, P., Cheng, S.W., Halperin, D., Matoušek, J., Schwarzkopf, O.: Separating an object from its cast. Computer-Aided Design 34, 547–559 (2002)
Bose, P., Toussaint, G.: Geometric and computational aspects of gravity casting. Computer-Aided Design 27(6), 455–464 (1995)
Chen, L.L., Chou, S.Y., Woo, T.C.: Parting directions for mould and die design. Computer-Aided Design 25, 762–768 (1993)
Elliot, R.: Cast Iron Technology. Butterworths, London (1988)
Hui, K.: Geometric aspects of mouldability of parts. Computer Aided Design 29(3), 197–208 (1997)
Hui, K.C., Tan, S.T.: Mould design with sweep operations—a heuristic search approach. Computer-Aided Design 24, 81–91 (1992)
Kwong, K.K.: Computer-aided parting line and parting surface generation in mould design. PhD thesis, The University of Hong Kong, Hong Kong (1992)
Majhi, J., Gupta, P., Janardan, R.: Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design. Computational Geometry: Theory and Applications 13, 229–252 (1999)
Pribble, W.I.: Molds for reaction injection, structural foam and expandable styrene molding. In: DuBois, J.H., Pribble, W.I. (eds.) Plastics Mold Engineering Handbook. Van Nostrand Reinhold Company, New York (1987)
Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Communications of the ACM 29, 669–679 (1986)
Walton, C.F., Opar, T.J. (eds.): Iron Castings Handbook. Iron casting society, Inc. (1981)
Zuppann, E.C.: Castings made in sand molds. In: Bralla, J.G. (ed.) Handbook of Product Design for Manufacturing, pp. 5.3–5.22. McGraw-Hill, New York (1986)
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Ahn, HK., Bae, S.W., Cheng, SW., Chwa, KY. (2005). Casting an Object with a Core. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_6
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DOI: https://doi.org/10.1007/11602613_6
Publisher Name: Springer, Berlin, Heidelberg
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