Generalized Voronoi diagrams for a ladder

II. Efficient construction of the diagram

Colm Ó'Dúnlaing, Micha Sharir, Chee Yap

Research output: Contribution to journalArticle

Abstract

We present a collection of algorithms, all running in time O(n2 log n α (n)o(α(n)3)) for some fixed integer s(where α(n) is the inverse Ackermann's function), for constructing a skeleton representation of a suitably generalized "Voronoi diagram" for a ladder moving in a two-dimensional space bounded by polygonal barriers consisting of n line segments. This diagram, which is a two-dimensional subcomplex of the dimensional configuration space of the ladder, is introduced and analyzed in a companion paper by the present authors. The construction of the diagram described in this paper yields a motion-planning algorithm for the ladder which runs within the same time bound given above.

Original languageEnglish (US)
Pages (from-to)27-59
Number of pages33
JournalAlgorithmica (New York)
Volume2
Issue number1
DOIs
StatePublished - Mar 1987

Fingerprint

Voronoi Diagram
Ladders
Diagram
Inverse function
Motion Planning
Line segment
Skeleton
Configuration Space
Motion planning
Integer

Keywords

  • Configuration space
  • Motion planning
  • Moving ladder
  • Robotics
  • Voronoi diagram

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Safety, Risk, Reliability and Quality
  • Applied Mathematics

Cite this

Generalized Voronoi diagrams for a ladder : II. Efficient construction of the diagram. / Ó'Dúnlaing, Colm; Sharir, Micha; Yap, Chee.

In: Algorithmica (New York), Vol. 2, No. 1, 03.1987, p. 27-59.

Research output: Contribution to journalArticle

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