Algorithms for bichromatic line-segment problems and polyhedral terrains

Bernard Chazelle, Herbert Edelsbrunner, Leonidas J. Guibas, Micha Sharir

Research output: Contribution to journalArticlepeer-review

83 Scopus citations


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 and n 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.

Original languageEnglish (US)
Pages (from-to)116-132
Number of pages17
Issue number2
StatePublished - Feb 1994
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • Computer Science Applications
  • Applied Mathematics


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


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