The union of convex polyhedra in three dimensions

Boris Aronov, Micha Sharir, Boaz Tagansky

    Research output: Contribution to journalArticlepeer-review


    We show that the number of vertices, edges, and faces of the union of k convex polyhedra in 3-space, having a total of n faces, is O(k3 + kn log k). This bound is almost tight in the worst case, as there exist collections of polyhedra with Ω(k3 + knα(k)) union complexity. We also describe a rather simple randomized incremental algorithm for computing the boundary of the union in O(k3 + kn log k log n) expected time.

    Original languageEnglish (US)
    Pages (from-to)1670-1688
    Number of pages19
    JournalSIAM Journal on Computing
    Issue number6
    StatePublished - Dec 1997


    • Combinatorial complexity
    • Combinatorial geometry
    • Computational geometry
    • Convex polyhedra
    • Geometric algorithms
    • Randomized algorithms

    ASJC Scopus subject areas

    • General Computer Science
    • General Mathematics


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