ISSN:
1432-0541
Keywords:
Computational geometry
;
Lines in space
;
Plücker coordinates
;
ε-Nets
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Questions about lines in space arise frequently as subproblems in three-dimensional computational geometry. In this paper we study a number of fundamental combinatorial and algorithmic problems involving arrangements ofn lines in three-dimensional space. Our main results include: 1. A tight Θ(n 2) bound on the maximum combinatorial description complexity of the set of all oriented lines that have specified orientations relative to then given lines. 2. A similar bound of Θ(n 3) for the complexity of the set of all lines passing above then given lines. 3. A preprocessing procedure usingO(n 2+ɛ) time and storage, for anyε〉0, that builds a structure supportingO(logn)-time queries for testing if a line lies above all the given lines. 4. An algorithm that tests the “towering property” inO(n 2+ɛ) time, for anyε〉0; don given red lines lie all aboven given blue lines? The tools used to obtain these and other results include Plücker coordinates for lines in space andε-nets for various geometric range spaces.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01955043
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