Point location in zones of k-flats in arrangements

M. Berg, de, M.J. Kreveld, van, O. Schwarzkopf, J. Snoeyink

    Research output: Contribution to journalArticleAcademicpeer-review


    Let A(H) be the arrangement of a set H of n hyperplanes in d-space. A k-flat is a k-dimensional affine subspace of d-space. The zone of a k-flat f with respect to H is the set of all faces in A(H) that intersect f. this paper we study some problems on zones of k-flats. Our most important result is a data structure for point location in the zone of a k-flat. This structure uses O(nd/2++nk+) preprocessing time and space and has a query time of O(log2 n). We also show how to test efficiently whether two flats are visible from each other with respect to a set of hyperplanes. Then point location in m faces in arrangements is studied. Our data structure for this problem has size O(nd/2+md/2/d) and the query time is O(log2 n).
    Original languageEnglish
    Pages (from-to)131-143
    Number of pages13
    JournalComputational Geometry
    Issue number3
    Publication statusPublished - 1996

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