On the zone of a surface in a hyperplane arrangement
type: Item
instance of: scholarly article
title: On the zone of a surface in a hyperplane arrangement
zbMATH Open document ID: 0773.52007
DOI: 10.1007/BF02189317
author: Boris Aronov
author: Micha Sharir
author: Marco Pellegrini
published in: Discrete \& Computational Geometry
publication date: 1993-05-16T00:00:00Z
full work available at URL: https://eudml.org/doc/131243
review text: For a collection of \(n\) hyperplanes in \(\mathbb{R}^ d\) the complex of all open cells and their lower dimensional faces is called an arrangement. The collection of all those cells which are met by a set \(\sigma\) is called its zone and its complexity is the number of all the faces. Asymptotic estimates for the complexity are given the simplest, for the case that \(\sigma\) is the boundary of a convex set or an algebraic surface, is \(O(n^{d-1}\log n)\).
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 52B05
Mathematics Subject Classification ID: 68U05
zbMATH DE Number: 168601
zbMATH Keywords: hyperplane arrangement
zbMATH Keywords: zone theorem
zbMATH Keywords: algebraic surface
reviewed by: Erhard Heil
MaRDI profile type: Publication
cites work: On range searching with semialgebraic sets
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OpenAlex ID: W2080052061
description: scientific article; zbMATH DE number 168601