TY - JOUR
T1 - Computing farthest neighbors on a convex polytope
AU - Cheong, Otfried
AU - Shin, Chan Su
AU - Vigneron, Antoine
N1 - Funding Information:
This research was partially supported by the Hong Kong Research Grants Council and partially by grant No. R05-2002-000-00780-0 from the Korea Science & Engineering Foundation. Part of it was done when the 1rst two authors were at HKUST. ∗Corresponding author. E-mail addresses: [email protected] (O. Cheong), [email protected] (C.-S. Shin), [email protected] (A. Vigneron).
PY - 2003
Y1 - 2003
N2 - Let N be a set of n points in convex position in R3. The farthest point Voronoi diagram of N partitions R3 into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expected O(nlog2n) time. More precisely, we compute the combinatorial structure of G(N), the coordinates of its vertices, and the equation of the plane defining each edge of G(N). The algorithm allows us to solve the all-pairs farthest neighbor problem for N in expected time O(nlog2n), and to perform farthest-neighbor queries on N in O(log2n) time with high probability.
AB - Let N be a set of n points in convex position in R3. The farthest point Voronoi diagram of N partitions R3 into n convex cells. We consider the intersection G(N) of the diagram with the boundary of the convex hull of N. We give an algorithm that computes an implicit representation of G(N) in expected O(nlog2n) time. More precisely, we compute the combinatorial structure of G(N), the coordinates of its vertices, and the equation of the plane defining each edge of G(N). The algorithm allows us to solve the all-pairs farthest neighbor problem for N in expected time O(nlog2n), and to perform farthest-neighbor queries on N in O(log2n) time with high probability.
KW - 3D
KW - Computational geometry
KW - Farthest neighbors
KW - Farthest-point Voronoi Diagram
KW - Polytope
UR - http://www.scopus.com/inward/record.url?scp=0037265307&partnerID=8YFLogxK
U2 - 10.1016/S0304-3975(02)00431-0
DO - 10.1016/S0304-3975(02)00431-0
M3 - Conference article
AN - SCOPUS:0037265307
SN - 0304-3975
VL - 296
SP - 47
EP - 58
JO - Theoretical Computer Science
JF - Theoretical Computer Science
IS - 1
T2 - Computing and Combinatorics
Y2 - 20 August 2001 through 23 August 2001
ER -