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arXiv · 1601.04539

String-node nets and meshes

S. C. Power·B. Schulze
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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.

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S. C. Power, B. Schulze. 2016-01-18. String-node nets and meshes. https://arxiv.org/abs/1601.04539

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