  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.
