Quadrangles which cannot be separated with two hands

Michael E. Houle, Godfried Toussaint

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A set of objects O is said to be separable with two hands if some proper subset of O can be simultaneously displaced by some rigid motion to infinity without disturbing its complement. It is shown that for all n ≥ 7 there exist configurations of n quadrangles in the plane, which cannot be separated by translation with two hands. Furthermore, no single quadrangle can be separated from the others by means of translation and rotation.

Original languageEnglish (US)
Title of host publicationInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
PublisherAmerican Institute of Physics Inc.
Volume1738
ISBN (Electronic)9780735413924
DOIs
StatePublished - Jun 8 2016
EventInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 - Rhodes, Greece
Duration: Sep 23 2015Sep 29 2015

Other

OtherInternational Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015
CountryGreece
CityRhodes
Period9/23/159/29/15

Fingerprint

complement
infinity
set theory
configurations

Keywords

  • Algorithms
  • Artificial Intelligence
  • Collision Avoidance
  • Computational Geometry
  • Discrete Geometry
  • Interlocking Polygons
  • Object Mobility
  • Robotics
  • Spatial Planning

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Houle, M. E., & Toussaint, G. (2016). Quadrangles which cannot be separated with two hands. In International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015 (Vol. 1738). [480021] American Institute of Physics Inc.. https://doi.org/10.1063/1.4952257

Quadrangles which cannot be separated with two hands. / Houle, Michael E.; Toussaint, Godfried.

International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738 American Institute of Physics Inc., 2016. 480021.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Houle, ME & Toussaint, G 2016, Quadrangles which cannot be separated with two hands. in International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. vol. 1738, 480021, American Institute of Physics Inc., International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015, Rhodes, Greece, 9/23/15. https://doi.org/10.1063/1.4952257
Houle ME, Toussaint G. Quadrangles which cannot be separated with two hands. In International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738. American Institute of Physics Inc. 2016. 480021 https://doi.org/10.1063/1.4952257
Houle, Michael E. ; Toussaint, Godfried. / Quadrangles which cannot be separated with two hands. International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015. Vol. 1738 American Institute of Physics Inc., 2016.
@inproceedings{5225c78bcf6a4fde9e7afda5b7a06e8a,
title = "Quadrangles which cannot be separated with two hands",
abstract = "A set of objects O is said to be separable with two hands if some proper subset of O can be simultaneously displaced by some rigid motion to infinity without disturbing its complement. It is shown that for all n ≥ 7 there exist configurations of n quadrangles in the plane, which cannot be separated by translation with two hands. Furthermore, no single quadrangle can be separated from the others by means of translation and rotation.",
keywords = "Algorithms, Artificial Intelligence, Collision Avoidance, Computational Geometry, Discrete Geometry, Interlocking Polygons, Object Mobility, Robotics, Spatial Planning",
author = "Houle, {Michael E.} and Godfried Toussaint",
year = "2016",
month = "6",
day = "8",
doi = "10.1063/1.4952257",
language = "English (US)",
volume = "1738",
booktitle = "International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015",
publisher = "American Institute of Physics Inc.",

}

TY - GEN

T1 - Quadrangles which cannot be separated with two hands

AU - Houle, Michael E.

AU - Toussaint, Godfried

PY - 2016/6/8

Y1 - 2016/6/8

N2 - A set of objects O is said to be separable with two hands if some proper subset of O can be simultaneously displaced by some rigid motion to infinity without disturbing its complement. It is shown that for all n ≥ 7 there exist configurations of n quadrangles in the plane, which cannot be separated by translation with two hands. Furthermore, no single quadrangle can be separated from the others by means of translation and rotation.

AB - A set of objects O is said to be separable with two hands if some proper subset of O can be simultaneously displaced by some rigid motion to infinity without disturbing its complement. It is shown that for all n ≥ 7 there exist configurations of n quadrangles in the plane, which cannot be separated by translation with two hands. Furthermore, no single quadrangle can be separated from the others by means of translation and rotation.

KW - Algorithms

KW - Artificial Intelligence

KW - Collision Avoidance

KW - Computational Geometry

KW - Discrete Geometry

KW - Interlocking Polygons

KW - Object Mobility

KW - Robotics

KW - Spatial Planning

UR - http://www.scopus.com/inward/record.url?scp=84984535910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84984535910&partnerID=8YFLogxK

U2 - 10.1063/1.4952257

DO - 10.1063/1.4952257

M3 - Conference contribution

AN - SCOPUS:84984535910

VL - 1738

BT - International Conference of Numerical Analysis and Applied Mathematics 2015, ICNAAM 2015

PB - American Institute of Physics Inc.

ER -