Translating polygons in the plane

Jӧrg R. Sack, Godfried Toussaint

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

Abstract

Let P = (p1,..,pn) and Q = (ql,..,qm) be two simple polygons with nonintersecting interiors in the plane specified by their cartesian coordinates in order. Given a direction d we can ask whether P can be translated an arbitrary distance in direction d without colliding with Q. It has been shown that this problem can be solved in time proportional to the number of vertices in P and Q. Here we present a new and efficient algorithm for determining all directions in which such movement is possible. In designing this algorithm a partitioning technique is developed which might find applications when solving other geometric problems. The algorithm utilizes several tools and concepts (e.g. convex hulls, point-location, weakly edge-visible polygons) from the area of computational geometry.

Original languageEnglish (US)
Title of host publicationSTACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science
PublisherSpringer-Verlag
Pages310-321
Number of pages12
ISBN (Print)9783540139126
DOIs
StatePublished - Jan 1 1985
Event2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985 - Saarbrucken, Germany
Duration: Jan 3 1985Jan 5 1985

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume182 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985
CountryGermany
CitySaarbrucken
Period1/3/851/5/85

Fingerprint

Polygon
Computational geometry
Point Location
Simple Polygon
Computational Geometry
Cartesian
Convex Hull
Partitioning
Interior
Efficient Algorithms
Directly proportional
Arbitrary
Concepts
Movement

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Sack, J. R., & Toussaint, G. (1985). Translating polygons in the plane. In STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science (pp. 310-321). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 182 LNCS). Springer-Verlag. https://doi.org/10.1007/BFb0024019

Translating polygons in the plane. / Sack, Jӧrg R.; Toussaint, Godfried.

STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag, 1985. p. 310-321 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 182 LNCS).

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

Sack, JR & Toussaint, G 1985, Translating polygons in the plane. in STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 182 LNCS, Springer-Verlag, pp. 310-321, 2nd Annual Symposium on Theoretical Aspects of Computer Science, STACS 1985, Saarbrucken, Germany, 1/3/85. https://doi.org/10.1007/BFb0024019
Sack JR, Toussaint G. Translating polygons in the plane. In STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag. 1985. p. 310-321. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/BFb0024019
Sack, Jӧrg R. ; Toussaint, Godfried. / Translating polygons in the plane. STACS 85 - 2nd Annual Symposium on Theoretical Aspects of Computer Science. Springer-Verlag, 1985. pp. 310-321 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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