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String-node nets and meshes

Research output: Contribution to journalJournal article

Forthcoming
<mark>Journal publication date</mark>7/09/2017
<mark>Journal</mark>Discrete and Computational Geometry
<mark>State</mark>Accepted/In press
<mark>Original language</mark>English

Abstract

New classes of infinite bond-node 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 a countable scaling group. A linear mesh has strings that are straight lines and nodes given by the intersection points of these lines. Classes of meshes, such as the regular meshes in R2 and R3, are defined and classified. String-length preserving motions are also determined for a number of fundamental examples and contrasting flexing and rigidity properties are obtained with respect to noncrossing motions in the space of smooth meshes.