Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions (0)
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| Venue: | J. Algorithms |
| Citations: | 19 - 5 self |
BibTeX
@ARTICLE{Chew_voronoidiagrams,
author = {L. Paul Chew and Klara Kedem and Micha Sharir and Boaz Tagansky and Emo Welzl},
title = {Voronoi Diagrams of Lines in 3-Space Under Polyhedral Convex Distance Functions},
journal = {J. Algorithms},
year = {},
volume = {29},
pages = {pages}
}
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Abstract
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(n 2 ff(n) log n), where ff is a slowly growing inverse of the Ackermann function. There are arrangements of n lines where this complexity can be as large as \Omega\Gamma n 2 ff(n)). 1 Introduction Statement of result. Let P be a closed convex polytope in 3-space which contains the origin. Given any point w 2 IR 3 , its distance from a line (or any other object) `, as induced by P , is d P (w; `) = inf ft 0 : (w + tP ) " ` 6= ;g ; Work by Paul Chew and Klara Kedem has been supported by AFOSR Grant AFOSR-91-0328 and by the U.S.--Israeli Binational Science Foundation. Work by Paul Chew has also been supported by ONR Grant N00014-89-J-1946 and ARPA under ONR contract N00014-88-K-0591. Work by Micha Sharir and Emo Welzl has been supported by the G.I.F. --- the German Israeli Foundation for Sc...
