Final published version
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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - String-node nets and meshes
AU - Power, Stephen Charles
AU - Schulze, Bernd
PY - 2018/1
Y1 - 2018/1
N2 - 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.
AB - 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.
KW - periodic net
KW - string-node net
KW - Rigidity
KW - flexibility
KW - Sierpinski mesh
U2 - 10.1007/s00454-017-9941-4
DO - 10.1007/s00454-017-9941-4
M3 - Journal article
VL - 59
SP - 31
EP - 58
JO - Discrete and Computational Geometry
JF - Discrete and Computational Geometry
SN - 0179-5376
IS - 1
ER -