On the zone of the boundary of a convex body

Orit E. Raz*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


We consider an arrangement A of n hyperplanes in ℝd and the zone Z in A of the boundary of an arbitrary convex set in Rd in such an arrangement. We show that, whereas the combinatorial complexity of Z is known only to be O(nd-1 log n) [3], the outer part of the zone has complexity O(nd-1) (without the logarithmic factor). Whether this bound also holds for the complexity of the inner part of the zone is still an open question (even for d=2).

Original languageAmerican English
Pages (from-to)333-341
Number of pages9
JournalComputational Geometry: Theory and Applications
Issue number4
StatePublished - May 2015
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2014, Elsevier B.V. All rights reserved.


  • Hyperplane arrangements
  • Zone theorem


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