ON RAY SHOOTING FOR TRIANGLES IN 3-SPACE AND RELATED PROBLEMS

Esther Ezra, Micha Sharir

Research output: Contribution to journalArticlepeer-review

Abstract

We consider several problems that involve lines in three dimensions, and present improved algorithms for solving them. The problems include (i) ray shooting amid triangles in R3, (ii) reporting intersections between query lines (segments, or rays) and input triangles, as well as approximately counting the number of such intersections, (iii) computing the intersection of two nonconvex polyhedra, (iv) detecting, counting, or reporting intersections in a set of lines in R3, and (v) output-sensitive construction of an arrangement of triangles in three dimensions. Our approach is based on the polynomial partitioning technique. For example, our ray-shooting algorithm processes a set of n triangles in R3 into a data structure for answering ray shooting queries amid the given triangles, which uses O(n3/2+ε) storage and preprocessing, and answers a query in O(n1/2+ε) time, for any ε>0.

Original languageEnglish
Pages (from-to)1065-1095
Number of pages31
JournalSIAM Journal on Computing
Volume51
Issue number4
DOIs
StatePublished - 2022

Keywords

  • Polynomial partitioning
  • Ray shooting
  • Three dimensions
  • Tradeoff

Fingerprint

Dive into the research topics of 'ON RAY SHOOTING FOR TRIANGLES IN 3-SPACE AND RELATED PROBLEMS'. Together they form a unique fingerprint.

Cite this