On the zone of a surface in a hyperplane arrangement

  • Boris Aronov
  • Micha Sharir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 519)


Let H be a collection of n hyperplanes in ℝ d , let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(nd−1 log n).


Convex Body General Position Algebraic Surface Hyperplane Arrangement Simple Arrangement 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Boris Aronov
    • 1
  • Micha Sharir
    • 2
    • 1
  1. 1.Department of Computer SciencePolytechnic UniversityBrooklynUSA
  2. 2.Courant Institute of Mathematical SciencesNew York UniversityUSA

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