Ahn, HK Cheong, O van Oostrum, R 2024-01-21T08:09:19Z 2024-01-21T08:09:19Z 2021-09-03 2003-10 0925-7721 https://pubs.kist.re.kr/handle/201004/138198 Casting is a manufacturing process in which molten material is poured into a cast (mould), which is opened after the material has solidified. As in all applications of robotics, we have to deal with imperfect control of the casting machinery. In this paper, we consider directional uncertainty: given a 3-dimensional polyhedral object, is there a polyhedral cast such that its two parts can be removed in opposite directions with uncertainty a without inflicting damage to the object or the cast parts? We give a necessary and sufficient condition for castability, and a randomized algorithm that verifies castability and produces two polyhedral cast parts for a polyhedral object of arbitrary genus. Its expected running time is O(n log n). The resulting cast parts have O(n) vertices in total. We also consider the case where the removal direction is not specified in advance, and give an algorithm that finds all feasible removal directions with uncertainty a in expected time O(n(2) log n/alpha(2)). (C) 2003 Elsevier B.V. All rights reserved. English Elsevier BV Casting a polyhedron with directional uncertainty Article 10.1016/S0925-7721(02)00167-0 1 Computational Geometry: Theory and Applications, v.26, no.2, pp.129 - 141 Computational Geometry: Theory and Applications 26 2 129 141 N scopus 000184681800003 2-s2.0-84867932273 Mathematics, Applied Mathematics Mathematics Article RANDOMIZED INCREMENTAL CONSTRUCTION computational geometry casting uncertainty Voronoi diagram