Casting with Skewed Ejection Direction

  • Hee-Kap Ahn
  • Siu-Wing Cheng
  • Otfried Cheong
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1533)

Abstract

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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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. 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. 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. 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. 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
  6. 6.
    P. Bose and G. Toussaint. Geometric and computational aspects of manufacturing processes. Comput. & Graphics, 18:487–497, 1994.CrossRefGoogle Scholar
  7. 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
  8. 8.
    L.L. Chen, S.Y. Chou, and T.C. Woo. Parting directions for mould and die design. Computer-Aided Design 25:762–768, 1993.MATHCrossRefGoogle Scholar
  9. 9.
    R. Elliot. Cast Iron Technology Butterworths, London, 1988.Google Scholar
  10. 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
  11. 11.
    K. Hui. Geometric aspects of mouldability of parts. Computer Aided Design, 29(3):197–208, 1997.CrossRefGoogle Scholar
  12. 12.
    K.C. Hui and S.T. Tan. Mould design with sweep operations-a heuristic search approach. Computer-Aided Design 24:81–91, 1992.MATHCrossRefGoogle Scholar
  13. 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. 14.
    J.-C. Latombe. Robot Motion Planning. Kluwer Academic Publishers, Boston, 1991.Google Scholar
  15. 15.
    A. Rosenbloom and D. Rappaport. Moldable and castable polygons. In Proc. 4th Canad. Conf. Comput. Geom., pages 322–327, 1992.Google Scholar
  16. 16.
    C.F. Walton and T.J. Opar, editors. Iron Castings Handbook, Ironcastingsociety, Inc., 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Hee-Kap Ahn
    • 1
  • Siu-Wing Cheng
    • 1
  • Otfried Cheong
    • 1
  1. 1.Department of Computer ScienceHKUSTHong Kong

Personalised recommendations