BibTeX
@MISC{Agarwal95combinatorialgeometry,
author = {P. K. Agarwal},
title = {Combinatorial Geometry},
year = {1995}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
Abstract. Let P be a set of n points in ~d (where d is a small fixed positive integer), and let F be a collection of subsets of ~d, each of which is defined by a constant number of bounded degree polynomial inequalities. We consider the following F-range searching problem: Given P, build a data structure for efficient answering of queries of the form, "Given a 7 ~ F, count (or report) the points of P lying in 7." Generalizing the simplex range searching techniques, we give a solution with nearly linear space and preprocessing time and with O(n 1- x/b+~) query time, where d < b < 2d- 3 and ~> 0 is an arbitrarily small constant. The acutal value of b is related to the problem of partitioning arrangements of algebraic surfaces into cells with a constant description complexity. We present some of the applications of F-range searching problem, including improved ray shooting among triangles in ~3 1.
Keyphrases
combinatorial geometry constant number data structure small fixed positive integer constant description complexity small constant acutal value bounded degree polynomial inequality algebraic surface linear space ray shooting query time following f-range simplex range efficient answering preprocessing time
