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Casting an Object with a Core

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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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

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  5. Bose, P., Toussaint, G.: Geometric and computational aspects of gravity casting. Computer-Aided Design 27(6), 455–464 (1995)

    Article  MATH  Google Scholar 

  6. Chen, L.L., Chou, S.Y., Woo, T.C.: Parting directions for mould and die design. Computer-Aided Design 25, 762–768 (1993)

    Article  MATH  Google Scholar 

  7. Elliot, R.: Cast Iron Technology. Butterworths, London (1988)

    Google Scholar 

  8. Hui, K.: Geometric aspects of mouldability of parts. Computer Aided Design 29(3), 197–208 (1997)

    Article  Google Scholar 

  9. Hui, K.C., Tan, S.T.: Mould design with sweep operations—a heuristic search approach. Computer-Aided Design 24, 81–91 (1992)

    Article  MATH  Google Scholar 

  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. 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)

    MATH  MathSciNet  Google Scholar 

  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. Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Communications of the ACM 29, 669–679 (1986)

    Article  MathSciNet  Google Scholar 

  14. Walton, C.F., Opar, T.J. (eds.): Iron Castings Handbook. Iron casting society, Inc. (1981)

    Google Scholar 

  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 

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Author information

Authors and Affiliations

  1. Division of Computer Science, Korea Advanced Institute of Science and Technology, Daejon, Korea

    Hee-Kap Ahn, Sang Won Bae & Kyung-Yong Chwa

  2. Dept. of Computer Science, Hong Kong University of Science and Technology, Hong Kong, China

    Siu-Wing Cheng

Authors
  1. Hee-Kap Ahn
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  2. Sang Won Bae
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  3. Siu-Wing Cheng
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  4. Kyung-Yong Chwa
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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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

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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