Casting an Object with a Core

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


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.


Cast Part Parting Direction Monotonicity Test Boundary Facet Side Core 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

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

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