TY - JOUR
T1 - Voronoi Diagrams of Lines in 3-Space under Polyhedral Convex Distance Functions
AU - Chew, L. Paul
AU - Kedem, Klara
AU - Sharir, Micha
AU - Tagansky, Boaz
AU - Welzl, Emo
N1 - Funding Information:
*Work by Paul Chew and Klara Kedem was supported by AFOSR Grant AFOSR-91-0328 and by the US–Israeli Binational Science Foundation. Work by Paul Chew was also supported by ONR Grant N00014-89-J-1946 and ARPA under ONR contract N00014-88-K-0591. Work by Micha Sharir and Emo Welzl was supported by the G.I.F.}the German Israeli Foundation for Scientific Research and Development (work by Boaz Tagansky was also supported by this grant), and by Max Planck Researach Award. Work by Micha Sharir was also supported by National Science Foundation Grants CCR-91-22103 and CCR-93-11127, and by grants from the US–Israeli Binational Science Foundation, and the Israel Science Fund administered by the Israeli Academy of Sciences. Work by Emo Welzl was also supported by the EC Basic Research Action, Project ALCOM II. ²E-mail address: [email protected]. ³E-mail address: [email protected]. §E-mail address: [email protected]. 5E-mail address: [email protected]. ¶E-mail address: [email protected].
PY - 1998/11
Y1 - 1998/11
N2 - The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n2α(n)log n), where α(n) is a slowly growing inverse of the Ackermann function. There are arrangements of n lines where this complexity can be as large as Ω(n2α(n)).
AB - The combinatorial complexity of the Voronoi diagram of n lines in three dimensions under a convex distance function induced by a polytope with a constant number of edges is shown to be O(n2α(n)log n), where α(n) is a slowly growing inverse of the Ackermann function. There are arrangements of n lines where this complexity can be as large as Ω(n2α(n)).
UR - https://www.scopus.com/pages/publications/0000671228
U2 - 10.1006/jagm.1998.0957
DO - 10.1006/jagm.1998.0957
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AN - SCOPUS:0000671228
SN - 0196-6774
VL - 29
SP - 238
EP - 255
JO - Journal of Algorithms
JF - Journal of Algorithms
IS - 2
ER -