Discrete & Computational Geometry

, Volume 40, Issue 1, pp 31–46 | Cite as

Enumerating Constrained Non-crossing Minimally Rigid Frameworks

  • David Avis
  • Naoki Katoh
  • Makoto Ohsaki
  • Ileana Streinu
  • Shin-ichi Tanigawa
Article

Abstract

In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints, which we call constrained non-crossing Laman frameworks, on a given set of n points in the plane. Our algorithm is based on the reverse search paradigm of Avis and Fukuda. It generates each output graph in O(n4) time and O(n) space, or, with a slightly different implementation, in O(n3) time and O(n2) space. In particular, we obtain that the set of all the constrained non-crossing Laman frameworks on a given point set is connected by flips which preserve the Laman property.

Keywords

Geometric enumeration Rigidity Constrained non-crossing minimally rigid frameworks Constrained Delaunay triangulation 

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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  • David Avis
    • 1
  • Naoki Katoh
    • 2
  • Makoto Ohsaki
    • 2
  • Ileana Streinu
    • 3
  • Shin-ichi Tanigawa
    • 2
  1. 1.School of Computer ScienceMcGill UniversityMcGillCanada
  2. 2.Department of Architecture and Architectural EngineeringKyoto University KatsuraKyotoJapan
  3. 3.Dept. of Comp. ScienceSmith CollegeNorthamptonUSA

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