A characterisation of the generic rigidity of 2-dimensional point-line frameworks
Metric Geometry
2016-05-26 v2 Combinatorics
Abstract
A 2-dimensional point-line framework is a collection of points and lines in the plane which are linked by pairwise constraints that fix some angles between pairs of lines and also some point-line and point-point distances. It is rigid if every continuous motion of the points and lines which preserves the constraints results in a point-line framework which can be obtained from the initial framework by a translation or a rotation. We characterise when a generic point-line framework is rigid. Our characterisation gives rise to a polynomial algorithm for solving this decision problem.
Keywords
Cite
@article{arxiv.1407.4675,
title = {A characterisation of the generic rigidity of 2-dimensional point-line frameworks},
author = {Bill Jackson and J. C. Owen},
journal= {arXiv preprint arXiv:1407.4675},
year = {2016}
}