The common exterior of convex polygons in the plane

Boris Aronov, Micha Sharir

    Research output: Contribution to journalArticlepeer-review


    We establish several combinatorial bounds on the complexity (number of vertices and edges) of the complement of the union (also known as the common exterior) of k convex polygons in the plane, with a total of n edges. We show: (1) The maximum complexity of the entire common exterior is Θ(na(k) + k2). 2 (2) The maximum complexity of a single cell of the common exterior is Θ(na(k)). (3) The complexity of m distinct cells in the common exterior is O(m2/3k2/3log1/3(k2/m) + n log k) and can be Ω(m2/3k2/3 + na(k)) in the worst case.

    Original languageEnglish (US)
    Pages (from-to)139-149
    Number of pages11
    JournalComputational Geometry: Theory and Applications
    Issue number3
    StatePublished - Aug 1997


    • Arrangements
    • Combinatorial complexity
    • Common exterior
    • Convex polygons

    ASJC Scopus subject areas

    • Computer Science Applications
    • Geometry and Topology
    • Control and Optimization
    • Computational Theory and Mathematics
    • Computational Mathematics


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