TY - JOUR
T1 - Combinatorial complexity of translating a box in polyhedral 3-space
AU - Halperin, Dan
AU - Yap, Chee Keng
PY - 1998/2
Y1 - 1998/2
N2 - We study the space of free translations of a box amidst polyhedral obstacles with n vertices. We show that the combinatorial complexity of this space is O(n2α(n)), where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n3). For the case of a convex polygon of fixed (constant) size translating in the same setting (namely, a two-dimensional polygon translating in three-dimensional space), we show a tight bound Θ(n2α(n)) on the complexity of the free space.
AB - We study the space of free translations of a box amidst polyhedral obstacles with n vertices. We show that the combinatorial complexity of this space is O(n2α(n)), where α(n) is the inverse Ackermann function. Our bound is within an α(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n3). For the case of a convex polygon of fixed (constant) size translating in the same setting (namely, a two-dimensional polygon translating in three-dimensional space), we show a tight bound Θ(n2α(n)) on the complexity of the free space.
KW - Computational geometry
KW - Minkowski sums
KW - Motion planning
UR - https://www.scopus.com/pages/publications/0037764554
U2 - 10.1016/S0925-7721(97)00030-8
DO - 10.1016/S0925-7721(97)00030-8
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AN - SCOPUS:0037764554
SN - 0925-7721
VL - 9
SP - 181
EP - 196
JO - Computational Geometry: Theory and Applications
JF - Computational Geometry: Theory and Applications
IS - 3
ER -