An Improved Bound for Joints in Arrangements of Lines in Space

Authors:
Sharona Feldman;Micha Sharir
Affiliations:
School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel;School of Computer Science, Tel Aviv University, Tel Aviv 69978, Israel and Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA
Venue:
Discrete & Computational Geometry
Year:
2005

Citing 0
Cited 5

On the number of tetrahedra with minimum, unit, and distinct volumes in three-space

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the number of tetrahedra with minimum, unit, and distinct volumes in three-space

Combinatorics, Probability and Computing
On a question of bourgain about geometric incidences

Combinatorics, Probability and Computing
Guest column: from randomness extraction to rotating needles

ACM SIGACT News
On lines, joints, and incidences in three dimensions

Journal of Combinatorial Theory Series A

Quantified Score

Hi-index	0.00

Visualization

Abstract

Let L be a set of n lines in space. A joint of L is a point in R3 where at least three non-coplanar lines meet. We show that the number of joints of L is O(n112/69 log6/23n)=O(n1.6232), improving the previous bound O(n1.643) of Sharir.