Algorithmica

, Volume 11, Issue 2, pp 116–132 | Cite as

Algorithms for bichromatic line-segment problems and polyhedral terrains

  • Bernard Chazelle
  • Herbert Edelsbrunner
  • Leonidas J. Guibas
  • Micha Sharir
Article
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Revised:

Abstract

We consider a variety of problems on the interaction between two sets of line segments in two and three dimensions. These problems range from counting the number of intersecting pairs between m blue segments andn red segments in the plane (assuming that two line segments are disjoint if they have the same color) to finding the smallest vertical distance between two nonintersecting polyhedral terrains in three-dimensional space. We solve these problems efficiently by using a variant of the segment tree. For the three-dimensional problems we also apply a variety of recent combinatorial and algorithmic techniques involving arrangements of lines in three-dimensional space, as developed in a companion paper.

Key words

Computational geometry Line-segment intersection Segment trees Lines in space Polyhedral terrains Deterministic and randomized algorithms 
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Copyright information

© Springer-Verlag New York Inc. 1994

Authors and Affiliations

  • Bernard Chazelle
    • 1
  • Herbert Edelsbrunner
    • 2
  • Leonidas J. Guibas
    • 3
    • 4
  • Micha Sharir
    • 5
    • 6
  1. 1.Department of Computer SciencePrinceton UniversityPrincetonUSA
  2. 2.Department of Computer ScienceUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.DEC Systems Research CenterPalo AltoUSA
  4. 4.Computer Science DepartmentStanford UniversityUSA
  5. 5.Courant Institute of Mathematical SciencesNew York UniversityNew YorkUSA
  6. 6.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael

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