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arXiv · 1807.01050

Constructing isostatic frameworks for the $\ell^\infty$ plane

K. Clinch·D. Kitson
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Abstract

We use a new coloured multi-graph constructive method to prove that every 2-tree decomposition can be realised in the plane as a bar-joint framework which is minimally rigid (isostatic) with respect to $\ell^1$ or $\ell^\infty$ distance constraints. We show how to adapt this technique to incorporate symmetry and indicate several related open problems on rigidity, redundant rigidity and forced symmetric rigidity in normed spaces.

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K. Clinch, D. Kitson. 2018-07-03. Constructing isostatic frameworks for the $\ell^\infty$ plane. https://arxiv.org/abs/1807.01050

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