Operations preserving global rigidity of generic direction-length frameworks

Bill Jackson, T. Jordán

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

A two-dimensional direction-length framework is a pair (G, p), where G = (V; D, L) is a graph whose edges are labeled as 'direction' or 'length' edges, and a map p from V to 2. The label of an edge uv represents a direction or length constraint between p(u) and p(v). The framework (G, p) is called globally rigid if every other framework (G, q) in which the direction or length between the endvertices of corresponding edges is the same, is 'congruent' to (G, p), i.e. it can be obtained from (G, p) by a translation and, possibly, a dilation by -1. We show that labeled versions of the two Henneberg operations (0-extension and 1-extension) preserve global rigidity of generic direction-length frameworks. These results, together with appropriate inductive constructions, can be used to verify global rigidity of special families of generic direction-length frameworks.

Original languageEnglish
Pages (from-to)685-706
Number of pages22
JournalInternational Journal of Computational Geometry and Applications
Volume20
Issue number6
DOIs
Publication statusPublished - Dec 2010

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Keywords

  • direction and length constraints
  • Globally rigid frameworks
  • rigid graphs

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Applied Mathematics
  • Geometry and Topology
  • Computational Mathematics

Cite this

Operations preserving global rigidity of generic direction-length frameworks. / Jackson, Bill; Jordán, T.

In: International Journal of Computational Geometry and Applications, Vol. 20, No. 6, 12.2010, p. 685-706.

Research output: Contribution to journalArticle

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