Order types and cross-sections of line arrangements in ℝ3

Oswin Aichholzer; Ruy Fabila-Monroy; Ferran Hurtado; Pablo Pérez-Lantero; Andres J. Ruiz-Vargas; Jorge Urrutia; Birgit Vogtenhuber

Order types and cross-sections of line arrangements in ℝ³

Oswin Aichholzer
, Ruy Fabila-Monroy
, Ferran Hurtado
, Pablo Pérez-Lantero
, Andres J. Ruiz-Vargas
, Jorge Urrutia
, Birgit Vogtenhuber

Institute of Software Engineering and Artificial Intelligence (7160)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

We consider sets 葦 = {ℓ₁;.,ℓ_n} of n labeled lines in general position in ℝ³, and study the order types of point sets {p₁;.; p_n} that stem from the intersections of the lines in L with (directed) planes II not parallel to any line of 葦, i.e., the proper cross-sections of 葦. As a main result we show that the number of diérent order types that can be obtained as cross-sections of L is O(n⁹), and that this bound is tight.

Original language	English
Title of host publication	26th Canadian Conference on Computational Geometry, CCCG 2014
Publisher	Canadian Conference on Computational Geometry
Pages	267-272
Number of pages	6
Publication status	Published - 2014
Event	26th Canadian Conference on Computational Geometry: CCCG 2014 - Halifax, Canada Duration: 11 Aug 2014 → 13 Aug 2014

Conference

Conference	26th Canadian Conference on Computational Geometry
Country/Territory	Canada
City	Halifax
Period	11/08/14 → 13/08/14

ASJC Scopus subject areas

Geometry and Topology
Computational Mathematics

Fields of Expertise

Information, Communication & Computing

Cite this

Aichholzer, O, Fabila-Monroy, R, Hurtado, F, Pérez-Lantero, P, Ruiz-Vargas, AJ, Urrutia, J & Vogtenhuber, B 2014, Order types and cross-sections of line arrangements in ℝ³. in 26th Canadian Conference on Computational Geometry, CCCG 2014. Canadian Conference on Computational Geometry, pp. 267-272, 26th Canadian Conference on Computational Geometry, Halifax, Canada, 11/08/14.

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title = "Order types and cross-sections of line arrangements in ℝ3",

abstract = "We consider sets 葦 = \{ℓ1;.,ℓn\} of n labeled lines in general position in ℝ3, and study the order types of point sets \{p1;.; pn\} that stem from the intersections of the lines in L with (directed) planes II not parallel to any line of 葦, i.e., the proper cross-sections of 葦. As a main result we show that the number of di{\'e}rent order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.",

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author = "Oswin Aichholzer and Ruy Fabila-Monroy and Ferran Hurtado and Pablo P{\'e}rez-Lantero and Ruiz-Vargas, \{Andres J.\} and Jorge Urrutia and Birgit Vogtenhuber",

year = "2014",

language = "English",

pages = "267--272",

booktitle = "26th Canadian Conference on Computational Geometry, CCCG 2014",

publisher = "Canadian Conference on Computational Geometry",

note = "26th Canadian Conference on Computational Geometry : CCCG 2014 ; Conference date: 11-08-2014 Through 13-08-2014",

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TY - GEN

T1 - Order types and cross-sections of line arrangements in ℝ3

AU - Aichholzer, Oswin

AU - Fabila-Monroy, Ruy

AU - Hurtado, Ferran

AU - Pérez-Lantero, Pablo

AU - Ruiz-Vargas, Andres J.

AU - Urrutia, Jorge

AU - Vogtenhuber, Birgit

PY - 2014

Y1 - 2014

N2 - We consider sets 葦 = {ℓ1;.,ℓn} of n labeled lines in general position in ℝ3, and study the order types of point sets {p1;.; pn} that stem from the intersections of the lines in L with (directed) planes II not parallel to any line of 葦, i.e., the proper cross-sections of 葦. As a main result we show that the number of diérent order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.

AB - We consider sets 葦 = {ℓ1;.,ℓn} of n labeled lines in general position in ℝ3, and study the order types of point sets {p1;.; pn} that stem from the intersections of the lines in L with (directed) planes II not parallel to any line of 葦, i.e., the proper cross-sections of 葦. As a main result we show that the number of diérent order types that can be obtained as cross-sections of L is O(n9), and that this bound is tight.

KW - Order types

UR - https://www.scopus.com/pages/publications/84926063092

M3 - Conference paper

AN - SCOPUS:84926063092

SP - 267

EP - 272

BT - 26th Canadian Conference on Computational Geometry, CCCG 2014

PB - Canadian Conference on Computational Geometry

T2 - 26th Canadian Conference on Computational Geometry

Y2 - 11 August 2014 through 13 August 2014

ER -