Clamshell Casting |
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Authors: | Prosenjit Bose Pat Morin Michiel Smid Stefanie Wuhrer |
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Affiliation: | 1.School of Computer Science,Carleton University,Ottawa,Canada |
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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. |
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