ISAAC 2005: Algorithms and Computation pp 40-49

# Casting an Object with a Core

• Hee-Kap Ahn
• Sang Won Bae
• Siu-Wing Cheng
• Kyung-Yong Chwa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3827)

## 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.

## Keywords

Cast Part Parting Direction Monotonicity Test Boundary Facet Side Core
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
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)
2. 2.
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)
3. 3.
Ahn, H.K., Cheong, O., van Oostrum, R.: Casting a polyhedron with directional uncertainty. Computational Geometry: Theory and Applications 26(2), 129–141 (2003)
4. 4.
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)
5. 5.
Bose, P., Toussaint, G.: Geometric and computational aspects of gravity casting. Computer-Aided Design 27(6), 455–464 (1995)
6. 6.
Chen, L.L., Chou, S.Y., Woo, T.C.: Parting directions for mould and die design. Computer-Aided Design 25, 762–768 (1993)
7. 7.
Elliot, R.: Cast Iron Technology. Butterworths, London (1988)Google Scholar
8. 8.
Hui, K.: Geometric aspects of mouldability of parts. Computer Aided Design 29(3), 197–208 (1997)
9. 9.
Hui, K.C., Tan, S.T.: Mould design with sweep operations—a heuristic search approach. Computer-Aided Design 24, 81–91 (1992)
10. 10.
Kwong, K.K.: Computer-aided parting line and parting surface generation in mould design. PhD thesis, The University of Hong Kong, Hong Kong (1992)Google Scholar
11. 11.
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)
12. 12.
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)Google Scholar
13. 13.
Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Communications of the ACM 29, 669–679 (1986)
14. 14.
Walton, C.F., Opar, T.J. (eds.): Iron Castings Handbook. Iron casting society, Inc. (1981)Google Scholar
15. 15.
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)Google Scholar

## Authors and Affiliations

• Hee-Kap Ahn
• 1
• Sang Won Bae
• 1
• Siu-Wing Cheng
• 2
• Kyung-Yong Chwa
• 1
1. 1.Division of Computer ScienceKorea Advanced Institute of Science and TechnologyDaejonKorea
2. 2.Dept. of Computer ScienceHong Kong University of Science and TechnologyHong KongChina