Ray shooting and parametric search
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Determining the castability of simple polyhedra
SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Geometric and computational aspects of manufacturing processes
Geometric and computational aspects of manufacturing processes
Separating an object from its cast
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
Robot Motion Planning
WADS '93 Proceedings of the Third Workshop on Algorithms and Data Structures
Feasability of Design in Stereolithography
Proceedings of the 13th Conference on Foundations of Software Technology and Theoretical Computer Science
Casting a Polyhedron with Directional Uncertainty
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation
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Casting is a manufacturing process in which liquid is poured into a cast (mould) that has a cavity with the shape of the object to be manufactured. The liquid then hardens, after which the cast is removed. We address geometric problems concerning the removal of the cast. A cast consists of two parts, one of which retracts in a given direction carrying the object with it. Afterwards, the object will be ejected from the retracted cast part. In this paper, we give necessary and sufficient conditions to test the feasibility of the cast part retraction and object ejection, where retraction and ejection directions need not be the same. For polyhedral objects, we show that the test can be performed in O(n3 log n) time and the cast parts can be constructed within the same time bound. We also give a polynomial time algorithm for finding a feasible pair of retraction and ejection directions for a given polyhedral object.