TY - GEN
T1 - On translational motion planning in 3-space
AU - Aronov, Boris
AU - Sharir, Micha
PY - 1994
Y1 - 1994
N2 - Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1,....,Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free placements) of B can be represented as the complement of the union of the Minkowski sums Pi Ai ⊕ (-B), for i = l,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log2 k), where n is the total complexity of the individual Minkowski sums P1,..., Pk. The bound is almost tight in the worst case. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log3 k).
AB - Let B be a convex polyhedron translating in 3-space amidst k convex polyhedral obstacles A1,....,Ak with pairwise disjoint interiors. The free configuration space (space of all collision-free placements) of B can be represented as the complement of the union of the Minkowski sums Pi Ai ⊕ (-B), for i = l,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log2 k), where n is the total complexity of the individual Minkowski sums P1,..., Pk. The bound is almost tight in the worst case. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log3 k).
UR - http://www.scopus.com/inward/record.url?scp=0028015213&partnerID=8YFLogxK
U2 - 10.1145/177424.177445
DO - 10.1145/177424.177445
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AN - SCOPUS:0028015213
SN - 0897916484
SN - 9780897916486
T3 - Proceedings of the Annual Symposium on Computational Geometry
SP - 21
EP - 30
BT - Proceedings of the Annual Symposium on Computational Geometry
PB - Association for Computing Machinery (ACM)
T2 - Proceedings of the 10th Annual Symposium on Computational Geometry
Y2 - 6 June 1994 through 8 June 1994
ER -