Enumerating Constrained Non-Crossing Minimally Rigid Frameworks

Authors

David Avis, McGill University
Naoki Katoh, Kyoto University
Makoto Ohsaki, Kyoto University
Ileana Streinu, Smith CollegeFollow
Shin-Ichi Tanigawa, Kyoto University

Document Type

Article

Publication Date

7-2008

Publication Title

Discrete & Computational Geometry

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

Volume

40

Issue

1

First Page

31

Last Page

46

DOI

dx.doi.org/10.1007/s00454-007-9026-x

ISSN

1432-0444

Comments

Peer reviewed accepted manuscript.

Recommended Citation

Avis, David; Katoh, Naoki; Ohsaki, Makoto; Streinu, Ileana; and Tanigawa, Shin-Ichi, "Enumerating Constrained Non-Crossing Minimally Rigid Frameworks" (2008). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/19