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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Research partially supported by NSERC. An extended abstract of this paper appeared in CAD&A [,??].
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Bose, P., Morin, P., Smid, M. et al. Clamshell Casting. Algorithmica 55, 666–702 (2009). https://doi.org/10.1007/s00453-007-9160-0
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DOI: https://doi.org/10.1007/s00453-007-9160-0