TY - JOUR
T1 - On translational motion planning of a convex polyhedron in 3-space
AU - Aronov, Boris
AU - Sharir, Micha
PY - 1997/12
Y1 - 1997/12
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 = 1,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log k), and that it can be Ω(nkα(k)) in the worst case, where n is the total complexity of the individual Minkowski sums P1,...,Pk. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log k log n).
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 = 1,...,k. We show that the combinatorial complexity of the free configuration space of B is O(nk log k), and that it can be Ω(nkα(k)) in the worst case, where n is the total complexity of the individual Minkowski sums P1,...,Pk. We also derive an efficient randomized algorithm that constructs this configuration space in expected time O(nk log k log n).
KW - Algorithmic motion planning
KW - Combinatorial complexity
KW - Combinatorial geometry
KW - Computational geometry
KW - Convex polyhedra
KW - Geometric algorithms
KW - Randomized algorithms
UR - http://www.scopus.com/inward/record.url?scp=0001404144&partnerID=8YFLogxK
U2 - 10.1137/S0097539794266602
DO - 10.1137/S0097539794266602
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AN - SCOPUS:0001404144
SN - 0097-5397
VL - 26
SP - 1785
EP - 1803
JO - SIAM Journal on Computing
JF - SIAM Journal on Computing
IS - 6
ER -