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Double-distance frameworks and mixed sparsity graphs

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>31/03/2020
<mark>Journal</mark>Discrete and Computational Geometry
Issue number2
Volume63
Number of pages25
Pages (from-to)294-318
Publication statusPublished
Early online date18/12/19
Original languageEnglish

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.