---
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 $.\r\n© 1986 Society for Industrial and Applied Mathematics@eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Herbert
foaf_name: Edelsbrunner, Herbert
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_isPartOf:
- http://id.crossref.org/issn/0097-5397
- http://id.crossref.org/issn/1095-7111
dct_language: eng
dct_publisher: SIAM@
dct_title: Constructing arrangements of lines and hyperplanes with applications@
...