, Volume 54, Issue 1, pp 72–88 | Cite as

Casting an Object with a Core

  • Hee-Kap Ahn
  • Sang Won Bae
  • Siu-Wing Cheng
  • Kyung-Yong Chwa


This paper addresses geometric problems in manufacturing objects by casting. In casting, molten material is poured into the cavity of the cast and allowed to solidify, after which the cast is removed. The cast has two cast parts to be removed in opposite directions. To manufacture more complicated objects, the cast may also have a side core to be removed in a direction skewed to the removal directions for the cast parts. We address the following problem: Given an object and the removal directions for the cast parts and the side core, can a cast be constructed such that the cast parts and the side core can be removed in the directions specified without colliding with the object or each other? We give necessary and sufficient conditions for the problem, as well as a discrete algorithm to perform the test in O(n 3log n) time for polyhedral objects, where n is the number of vertices, edges, and facets. 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 Ω(n 3) complexity in the worst case.


Manufacturing Casting Core Discrete algorithms 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ahn, H.K., de Berg, M., Bose, P., Cheng, S.W., Halperin, D., Matoušek, J., Schwarzkopf, O.: Separating an object from its cast. Comput. Aided Des. 34, 547–559 (2002) CrossRefGoogle Scholar
  2. 2.
    Ahn, H.K., Cheong, O., van Oostrum, R.: Casting a polyhedron with directional uncertainty. Comput. Geom. Theory Appl. 26(2), 129–141 (2003) zbMATHGoogle Scholar
  3. 3.
    Ahn, H.K., Cheng, S.W., Cheong, O., Snoeyink, J.: The reflex-free hull. Int. J. Comput. Geom. Appl. 14(6), 453–474 (2004) zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Ahn, H.K., Cheng, S.W., Cheong, O.: Casting with skewed ejection direction. Algorithmica 44(4), 325–342 (2006) zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Bose, P., Bremner, D., van Kreveld, M.: Determining the castability of simple polyhedra. Algorithmica 19, 84–113 (1997) zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chen, L.L., Chou, S.Y., Woo, T.C.: Parting directions for mould and die design. Comput. Aided Des. 25, 762–768 (1993) zbMATHCrossRefGoogle Scholar
  7. 7.
    Elliot, R.: Cast Iron Technology. Butterworths, London (1988) Google Scholar
  8. 8.
    Gastrow, H.: Injection Molds. Hanser, Munich (1983) Google Scholar
  9. 9.
    Halperin, D., Kavraki, L., Latombe, J.-C.: Robot algorithms. In: Attalah, M. (ed.) CRC Algorithms and Theory of Computation Handbook. CRC Press, Boca Raton (1999) Google Scholar
  10. 10.
    Hui, K.: Geometric aspects of mouldability of parts. Comput. Aided Des. 29(3), 197–208 (1997) CrossRefGoogle Scholar
  11. 11.
    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
  12. 12.
    Majhi, J., Gupta, P., Janardan, R.: Computing a flattest, undercut-free parting line for a convex polyhedron, with application to mold design. Comput. Geom. Theory Appl. 13, 229–252 (1999) zbMATHMathSciNetGoogle Scholar
  13. 13.
    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
  14. 14.
    Sarnak, N., Tarjan, R.E.: Planar point location using persistent search trees. Commun. ACM 29, 669–679 (1986) CrossRefMathSciNetGoogle Scholar
  15. 15.
    Walton, C.F., Opar, T.J. (eds.): Iron Castings Handbook. Iron Casting Society (1981) Google Scholar
  16. 16.
    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

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Sang Won Bae
    • 2
  • Siu-Wing Cheng
    • 3
  • Kyung-Yong Chwa
    • 2
  1. 1.Department of Computer Science and EngineeringPOSTECHPohangRepublic of Korea
  2. 2.Division of Computer ScienceKAISTDaejeonRepublic of Korea
  3. 3.Department of Computer Science and EngineeringHKUSTPohangHong Kong

Personalised recommendations