Arrangements of curves in the plane - topology, combinatorics, and algorithms Journal Article


Author(s): Edelsbrunner, Herbert; Guibas, Leonidas; Pach, János; Pollack, Richard; Seidel, Raimund; Sharir, Micha
Article Title: Arrangements of curves in the plane - topology, combinatorics, and algorithms
Affiliation
Abstract: Arrangements of curves in the plane are fundamental to many problems in computational and combinatorial geometry (e.g. motion planning, algebraic cell decomposition, etc.). In this paper we study various topological and combinatorial properties of such arrangements under some mild assumptions on the shape of the curves, and develop basic tools for the construction, manipulation, and analysis of these arrangements. Our main results include a generalization of the zone theorem of Edelsbrunner (1986) and Chazelle (1985) to arrangements of curves (in which we show that the combinatorial complexity of the zone of a curve is nearly linear in the number of curves) and an application of that theorem to obtain a nearly quadratic incremental algorithm for the construction of such arrangements.
Keywords: Algorithms; topology; Computer Programming; Mathematical Techniques
Journal Title: Theoretical Computer Science
Volume: 92
Issue 2
ISSN: 0304-3975
Publisher: Elsevier  
Date Published: 1992-01-01
Start Page: 319
End Page: 336
DOI: 10.1016/0304-3975(92)90319-B
Open access: no
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