Linear data structures for fast ray-shooting amidst convex polyhedra

Haim Kaplan, Natan Rubin, Micha Sharir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


We consider the problem of ray shooting in a three-dimensional scene consisting of k (possibly intersecting) convex polyhedra with a total of n facets. That is, we want to preprocess them into a data structure, so that the first intersection point of a query ray and the given polyhedra can be determined quickly. We describe data structures that require Õ(npoly(k)) preprocessing time and storage, and have polylogarithmic query time, for several special instances of the problem. These include the case when the ray origins are restricted to lie on a fixed line ℓ0, but the directions of the rays are arbitrary, the more general case when the supporting lines of the rays pass through ℓ0, and the case of rays orthogonal to z-axis with arbitrary origins. In all cases, this is a significant improvement over previously known techniques (which require Ω(n2) storage, even when A: ≪ n).

Original languageEnglish
Title of host publicationAlgorithms - ESA 2007 - 15th Annual European Symposium, Proceedings
PublisherSpringer Verlag
Number of pages12
ISBN (Print)9783540755197
StatePublished - 1 Jan 2007
Externally publishedYes
Event15th Annual European Symposium on Algorithms, ESA 2007 - Eilat, Israel
Duration: 8 Oct 200710 Oct 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4698 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference15th Annual European Symposium on Algorithms, ESA 2007

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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