A tight bound for the number of different directions in three dimensions

János Pach, Rom Pinchasi, Micha Sharir

Research output: Contribution to conferencePaperpeer-review

Abstract

Let P be a set of n points in ℝ3, not all of which are in a plane and no three on a line. We partially answer a question of Scott (1970) by showing that the connecting lines of P assume at least 2n -3 different directions if n is even and at least 2n - 2 if n is odd. These bounds are sharp. The proof is based on a far-reaching generalization of Ungar's theorem concerning the analogous problem in the plane.

Original languageEnglish
Pages106-113
Number of pages8
DOIs
StatePublished - 2003
EventNineteenth Annual Symposium on Computational Geometry - san Diego, CA, United States
Duration: 8 Jun 200310 Jun 2003

Conference

ConferenceNineteenth Annual Symposium on Computational Geometry
Country/TerritoryUnited States
Citysan Diego, CA
Period8/06/0310/06/03

Keywords

  • Directions
  • Slope Problem
  • Ungar's Theorem

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