---
res:
bibo_abstract:
- |-
A finite set of lines partitions the Euclidean plane into a cell complex. Similarly, a finite set of $(d - 1)$-dimensional hyperplanes partitions $d$-dimensional Euclidean space. An algorithm is presented that constructs a representation for the cell complex defined by $n$ hyperplanes in optimal $O(n^d )$ time in $d$ dimensions. It relies on a combinatorial result that is of interest in its own right. The algorithm is shown to lead to new methods for computing $\lambda $-matrices, constructing all higher-order Voronoi diagrams, halfspatial range estimation, degeneracy testing, and finding minimum measure simplices. In all five applications, the new algorithms are asymptotically faster than previous results, and in several cases are the only known methods that generalize to arbitrary dimensions. The algorithm also implies an upper bound of $2^{cn^d } $, $c$ a positive constant, for the number of combinatorially distinct arrangements of $n$ hyperplanes in $E^d $.
© 1986 Society for Industrial and Applied Mathematics@eng
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Herbert Edelsbrunner
foaf_surname: Edelsbrunner
foaf_workInfoHomepage: http://www.librecat.org/personId=3FB178DA-F248-11E8-B48F-1D18A9856A87
orcid: 0000-0002-9823-6833
- foaf_Person:
foaf_givenName: Joseph
foaf_name: O'Rourke, Joseph
foaf_surname: O'Rourke
- foaf_Person:
foaf_givenName: Raimund
foaf_name: Seidel, Raimund
foaf_surname: Seidel
bibo_doi: 10.1137/0215024
bibo_issue: '2'
bibo_volume: 15
dct_date: 1986^xs_gYear
dct_publisher: SIAM@
dct_title: Constructing arrangements of lines and hyperplanes with applications@
...