On separating two simple polygons by a single translation

Godfried Toussaint

    Research output: Contribution to journalArticle

    Abstract

    Let P and Q be two disjoint simple polygons having n sides each. We present an algorithm which determines whether Q can be moved by a single translation to a position sufficiently far from P, and which produces all such motions if they exist. The algorithm runs in time O(t(n)) where t(n) is the time needed to triangulate an n-sided polygon. Since Tarjan and Van Wyk have recently shown that t(n)=O(n log log n) this improves the previous best result for this problem which was O(n log n) even after triangulation.

    Original languageEnglish (US)
    Pages (from-to)265-278
    Number of pages14
    JournalDiscrete & Computational Geometry
    Volume4
    Issue number1
    DOIs
    StatePublished - Dec 1 1989

    Fingerprint

    Simple Polygon
    Triangulate
    Triangulation
    Polygon
    Disjoint
    Motion

    ASJC Scopus subject areas

    • Theoretical Computer Science
    • Geometry and Topology
    • Discrete Mathematics and Combinatorics
    • Computational Theory and Mathematics

    Cite this

    On separating two simple polygons by a single translation. / Toussaint, Godfried.

    In: Discrete & Computational Geometry, Vol. 4, No. 1, 01.12.1989, p. 265-278.

    Research output: Contribution to journalArticle

    Toussaint, Godfried. / On separating two simple polygons by a single translation. In: Discrete & Computational Geometry. 1989 ; Vol. 4, No. 1. pp. 265-278.
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