COUNTING TRIANGLE CROSSINGS AND HALVING PLANES

Authors
DEY TK EDELSBRUNNER H
Citation
Tk. Dey et H. Edelsbrunner, COUNTING TRIANGLE CROSSINGS AND HALVING PLANES, Discrete & computational geometry, 12(3), 1994, pp. 281-289
Citations number
9
Categorie Soggetti
Computer Sciences, Special Topics","Mathematics, General","Computer Science Theory & Methods",Mathematics
Journal title
Discrete & computational geometry → ACNP
ISSN journal
01795376
Volume
12
Issue
3
Year of publication
1994
Pages
281 - 289
Database
ISI
SICI code
0179-5376(1994)12:3<281:CTCAHP>2.0.ZU;2-#
Abstract
Every collection of t greater than or equal to 2n(2) triangles with a total of n vertices in R(3) has Omega(t(4)/n(6)) crossing pairs. This implies that one of their edges meets Omega(t(3)/n(6)) of the triangle s. From this it follows that n points in R(3) have only O(n(8/3)) halv ing planes.