Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 7
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Houle, Michael E. and Toussaint, Godfried T. 2016. Vol. 1738, Issue. , p. 480021.

    Toussaint, G. 1989. On separating two simple polygons by a single translation. Discrete & Computational Geometry, Vol. 4, Issue. 3, p. 265.

    Toussaint, Godfried T. 1988. Pattern Recognition and Artificial Intelligence - Towards an Integration.

    Dehne, Frank and Sack, Jörg-Rüdiger 1987. Translation separability of sets of polygons. The Visual Computer, Vol. 3, Issue. 4, p. 227.

    Sack, Jörg-Rüdiger and Toussaint, Godfried T. 1987. Separability of pairs of polygons through single translations. Robotica, Vol. 5, Issue. 01, p. 55.

    Woo, Tony C. 1987. SAE Technical Paper Series. Vol. 1, Issue. ,

    Avis, David Gum, Teren and Toussaint, Godfried 1986. Visibility between two edges of a simple polygon. The Visual Computer, Vol. 2, Issue. 6, p. 342.


Separation of two monotone polygons in linear time

  • Godfried T. Toussaint (a1) and Hossam A. El Gindy (a1)
  • DOI:
  • Published online: 01 March 2009

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

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

T. Ottman and P. Widmayer , “On translating a set of line segmentsComputer Vision, Graphics and Image Processing24, 382389 (1983).

G.T. Toussaint , “The complexity of movement” IEEE International Symposium on Information Theory, St Jovite, Canada (09, 1983).

R. Dawson , “On removing a ball without disturbing the othersMathematics Magazine 57, No. 1, 2730 (01, 1984).

F.P. Preparata and K. Supowit , “Testing a simple polygon for monotonicityInformation Processing Letters 12, 161164 (1981).

H. ElGindy and D. Avis , “A linear algorithm for computing the visibility polygon from a pointJ. Algorithms 2, 186197 (1981).

D.T. Lee , Visibility of a simple polygon Computer Vision, Graphics and Image Processing 22, 207221 (1983).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
Please enter your name
Please enter a valid email address
Who would you like to send this to? *