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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.

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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).

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  • ISSN: 0263-5747
  • EISSN: 1469-8668
  • URL: /core/journals/robotica
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