Separation of two monotone polygons in linear time

Godfried Toussaint, Hossam A. El Gindy

Research output: Contribution to journalArticle

Abstract

Let P = (p1, p2, …, pn) and Q = (q1 q2, …, qm) be two simple polygons monotonic in directions θ and ϕ, respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: θ + π/2, ϕ + π/2. Furthermore, a direction for carrying out such a 2 translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.

Original languageEnglish (US)
Pages (from-to)215-220
Number of pages6
JournalRobotica
Volume2
Issue number4
DOIs
StatePublished - Jan 1 1984

Fingerprint

Polygon
Linear Time
Monotone
Robotics
Simple Polygon
Monotonic

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Mathematics(all)
  • Computer Science Applications

Cite this

Separation of two monotone polygons in linear time. / Toussaint, Godfried; El Gindy, Hossam A.

In: Robotica, Vol. 2, No. 4, 01.01.1984, p. 215-220.

Research output: Contribution to journalArticle

Toussaint, Godfried ; El Gindy, Hossam A. / Separation of two monotone polygons in linear time. In: Robotica. 1984 ; Vol. 2, No. 4. pp. 215-220.
@article{db815d80d6bf4165acd31ccab108afee,
title = "Separation of two monotone polygons in linear time",
abstract = "Let P = (p1, p2, …, pn) and Q = (q1 q2, …, qm) be two simple polygons monotonic in directions θ and ϕ, respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: θ + π/2, ϕ + π/2. Furthermore, a direction for carrying out such a 2 translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.",
author = "Godfried Toussaint and {El Gindy}, {Hossam A.}",
year = "1984",
month = "1",
day = "1",
doi = "10.1017/S0263574700008924",
language = "English (US)",
volume = "2",
pages = "215--220",
journal = "Robotica",
issn = "0263-5747",
publisher = "Cambridge University Press",
number = "4",

}

TY - JOUR

T1 - Separation of two monotone polygons in linear time

AU - Toussaint, Godfried

AU - El Gindy, Hossam A.

PY - 1984/1/1

Y1 - 1984/1/1

N2 - Let P = (p1, p2, …, pn) and Q = (q1 q2, …, qm) be two simple polygons monotonic in directions θ and ϕ, respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: θ + π/2, ϕ + π/2. Furthermore, a direction for carrying out such a 2 translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.

AB - Let P = (p1, p2, …, pn) and Q = (q1 q2, …, qm) be two simple polygons monotonic in directions θ and ϕ, respectively. It is shown that P and Q are separable with a single translation in at least one of the directions: θ + π/2, ϕ + π/2. Furthermore, a direction for carrying out such a 2 translation can be determined in O(m + n) time. This procedure is of use in solving the FIND-PATH problem in robotics.

UR - http://www.scopus.com/inward/record.url?scp=0021504531&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021504531&partnerID=8YFLogxK

U2 - 10.1017/S0263574700008924

DO - 10.1017/S0263574700008924

M3 - Article

AN - SCOPUS:0021504531

VL - 2

SP - 215

EP - 220

JO - Robotica

JF - Robotica

SN - 0263-5747

IS - 4

ER -