String-node nets and meshes
Abstract
New classes of distance-constrained structures are introduced, namely string-node nets and meshes, a mesh being a string-node net for which the nodes are dense in the strings. Various construction schemes are given including the minimal extension of a (countable) line segment net by an arbitrary countable scaling group. A linear mesh has strings that are straight lines and nodes given by the intersection points of these lines. Classes of linear meshes, such as the regular linear meshes in R^2 and R^3, are defined and classified. Contrasting flexing and rigidity properties are obtained for some fundamental meshes in the plane with respect to noncrossing motions in the space of smooth meshes.
Cite
@article{arxiv.1601.04539,
title = {String-node nets and meshes},
author = {S. C. Power and B. Schulze},
journal= {arXiv preprint arXiv:1601.04539},
year = {2016}
}
Comments
Further references added and some minor reorganisation. 27 pages, 9 figures