The complexity of cells in three-dimensional arrangements

✍ Scribed by H. Edelsbrunner; D. Haussler

• Publisher: Elsevier Science
• Year: 1986
• Tongue: English
• Weight: 439 KB
• Volume: 60
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(86)90008-7

✦ Synopsis

A set of m planes dissects E3 into cells, facets, edges and vertices. Letting deg(c) be the number of facets that bound a cell c, we give exact and asymptotic bounds on the maximum of Crincdeg(c), if C is a family of cells of the arrangement with fixed cardinality. * Research reported in the paper was conducted while the second author was visiting the Technical University of Graz. Support provided by the Technical University for this visit is gratefully acknowledged. ' An arrangements in E2 is a dissection induced by a finite set of lines. a In general, a finite set of hyperplanes in Ed defines an arrangement.