Skip to main content
    • Aa
    • Aa

Separation of two monotone polygons in linear time

  • Godfried T. Toussaint (a1) and Hossam A. El Gindy (a1)

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.

Hide All
Guibas L.J. and Yao F.F., “On translating a set of rectangles,” Proc. Twelfth Annual ACM Symposium on Theory of Computing 154160 (1980).
Ottman T. and Widmayer P., “On translating a set of line segmentsComputer Vision, Graphics and Image Processing 24, 382389 (1983).
Toussaint G.T., “The complexity of movement” IEEE International Symposium on Information Theory, St Jovite, Canada (09, 1983).
Sack J.-R. and Toussaint G.T., “Movability of objects” IEEE International Symposium on Information Theory, St. Jovite, Canada (09, 1983).
Toussaint G.T. and Sack J-.R., “Some new results on moving polygons in the plane” Proc. Robotic Intelligence and Productivity Conference” Detroit, Michigan158163, (11 18–19, 1983),.
Chazelle B. et al. , “The complexity and decidability of SEPARATION” Technical Report CS-83–34, University of Waterloo (11, 1983).
Toussaint G.T., “On translating a set of Polyhedra” Conference on Polyhedra, Smith College, Northampton, Mass. (04 6–8, 1984).
Dawson R., “On removing a ball without disturbing the othersMathematics Magazine 57, No. 1, 2730 (01, 1984).
Post K., “Six interlocking cylinders with respect to all directions” internal manuscript, University of Eindhoven (12, 1983).
Moser W., Research Problems in Discrete Geometry (Department of Mathematics, McGill University, 1981).
Toussaint G.T., “On translating a set of spheres” Technical Report SOCS-84.4, School of Computer Science, McGill University (03, 1984).
Van-Duc Nguyen, “The Find-Path Problem in the Plane” A.I. Memo No. 160, Artificial Intelligence Laboratory, M.I.T. (02, 1984).
Bruce R. Donald, “Hypothesizing Channels Through Free-Space In Solving the Findpath Problem” A.I. Memo No. 736, Artificial Intelligence Laboratory, M.I.T. (06, 1983).
David Marr and Lucia Vaina, “Representation and Recognition of the Movement of Shapes” A.I. Memo No. 597, Artificial Intelligence Laboratory, M.I.T. (10, 1980).
Preparata F.P. and Supowit K., “Testing a simple polygon for monotonicityInformation Processing Letters 12, 161164 (1981).
ElGindy H. and Avis D., “A linear algorithm for computing the visibility polygon from a pointJ. Algorithms 2, 186197 (1981).
Lee D.T., Visibility of a simple polygon Computer Vision, Graphics and Image Processing 22, 207221 (1983).
Shamos M.I. and Hoey D., “Geometric intersections problems” Seventeenth Annual IEEE Symposium on Foundations of Computer Science 208215 (10, 1976).
Guibas L.J. and Stolfi J., Notes on Computational Geometry (XEROX PARK and Stanford University, 1982).
Toussaint G.T., “Pattern recognition and geometrical complexity” Proc. Fifth International Conference on Pattern Recognition Miami Beach13241347 (12, 1980).
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? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 2 *
Loading metrics...

Abstract views

Total abstract views: 90 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 23rd October 2017. This data will be updated every 24 hours.