Authors
Citation
M. Sharir, ON JOINTS IN ARRANGEMENTS OF LINES IN-SPACE AND RELATED PROBLEMS, J COMB TH A, 67(1), 1994, pp. 89-99
Citations number
9
Categorie Soggetti
Mathematics, Pure",Mathematics
Journal title
JOURNAL OF COMBINATORIAL THEORY SERIES A
ISSN journal
00973165
→ ACNP
Volume
67
Issue
1
Year of publication
1994
Pages
89 - 99
Database
ISI
SICI code
0097-3165(1994)67:1<89:OJIAOL>2.0.ZU;2-D
Abstract
Let L = {l1 ..., l(n)} be a collection of n lines in three-dimensional
space. A joint of L is a point incident to three noncoplanar lines of
L. We prove that the number of joints of L is O(n23/14 log31/14 n), w
hich is O(n1.643). This improves a previous bound of O(n7/4) due to Ch
azelle et al. The proof makes use of recent range searching techniques
and of a structural analysis of the pattern of intersections between
n lines in space. (C) 1994 Academic Press, Inc.