Double-distance frameworks and mixed sparsity graphs
Abstract
A rigidity theory is developed for frameworks in a metric space with two types of distance constraints. Mixed sparsity graph characterisations are obtained for the infinitesimal and continuous rigidity of completely regular bar-joint frameworks in a variety of such contexts. The main results are combinatorial characterisations for (i) frameworks restricted to surfaces with both Euclidean and geodesic distance constraints, (ii) frameworks in the plane with Euclidean and non-Euclidean distance constraints, and (iii) direction-length frameworks in the non-Euclidean plane.
Cite
@article{arxiv.1709.06349,
title = {Double-distance frameworks and mixed sparsity graphs},
author = {Anthony Nixon and Stephen Power},
journal= {arXiv preprint arXiv:1709.06349},
year = {2019}
}
Comments
Revised version, 23 pages, 6 figures. The analysis of the projective plane frameworks (whose proofs were incomplete) has been removed for discussion elsewhere. This double-distance context is defined in the final section of the revision together with other settings with underlying (2,1)-sparsity