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Algorithmica

, Volume 55, Issue 4, pp 666–702 | Cite as

Clamshell Casting

  • Prosenjit Bose
  • Pat Morin
  • Michiel Smid
  • Stefanie Wuhrer
Article
  • 71 Downloads

Abstract

A popular manufacturing technique is clamshell casting, where liquid is poured into a cast and the cast is removed by a rotation once the liquid has hardened. We consider the case where the object to be manufactured is modeled by a polyhedron with combinatorial complexity n of arbitrary genus. The cast consists of exactly two parts and is removed by a rotation around a line in space. The following two problems are addressed: (1) Given a line of rotation l in space, we determine in O(nlog n) time whether there exists a partitioning of the cast into exactly two parts, such that one part can be rotated clockwise around l and the other part can be rotated counterclockwise around l without colliding with the interior of P or the cast. If the problem is restricted further, such a partitioning is only valid when no reflex edge or face of P is perpendicular to l, the algorithm runs in O(n) time. (2) An algorithm running in O(n 4log n) time is presented to find all the lines in space that allow a cast partitioning as described above. If we restrict the problem further and find all the lines in space that allow a cast partitioning as described above, such that no reflex edge or face of P is perpendicular to l, the algorithm’s running time becomes O(n 4 α(n)). All of the running times are shown to be almost optimal.

Keywords

Simple Polygon Event Point Black Region Valid Region Cast Removal 
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.

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Pat Morin
    • 1
  • Michiel Smid
    • 1
  • Stefanie Wuhrer
    • 1
  1. 1.School of Computer ScienceCarleton UniversityOttawaCanada

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