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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.
KeywordsSimple Polygon Event Point Black Region Valid Region Cast Removal
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- 5.Bartsch, H.: Taschenbuch Mathematischer Formeln, 18. Auflage. Fachbuchverlag, Leipzig (1999) Google Scholar
- 6.Bose, P.: Geometric and computational aspects of manufacturing processes. PhD thesis, McGill University (1994) Google Scholar
- 26.van Kreveld, M.: New results on data structures in computational geometry. PhD dissertation, Utrecht University (1992) Google Scholar
- 27.Wang, C., Schubert, L.: An optimal algorithm for constructing the Delaunay triangulation of a set of line segments. In: Proceedings of the Third Annual ACM Symposium on Computational geometry, pp. 223–232 (1987) Google Scholar
- 28.Wuhrer, S., Bose, P., Morin, P., Smid, M.: Algorithms for designing clamshell molds (extended abstract). Comput.-Aided Des. Appl. 4, 1–10 (2007) Google Scholar