Planar point location using persistent search trees
Communications of the ACM
Computational Geometry: Theory and Applications
Casting with Skewed Ejection Direction
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Casting a polyhedron with directional uncertainty
Computational Geometry: Theory and Applications
Computer-Aided Design
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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(n3log n) time, where n is the object size. If the test result is positive, a cast with complexity O(n3) can be constructed within the same time bound. We also present an example to show that a cast may have Θ(n3) complexity in the worst case. Thus, the complexity of our cast is worst-case optimal.