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String-wrapped rotating disks. (English) Zbl 1374.68669
Márquez, Alberto (ed.) et al., Computational geometry. XIV Spanish meeting on computational geometry, EGC 2011, dedicated to Ferran Hurtado on the occasion of his 60th birthday, Alcalá de Henares, Spain, June 27–30, 2011. Revised selected papers. Berlin: Springer (ISBN 978-3-642-34190-8/pbk). Lecture Notes in Computer Science 7579, 65-78 (2012).
Summary: Let the centers of a finite number of disjoint, closed disks be pinned to the plane, but with each free to rotate about its center. Given an arrangement of such disks with each labeled \(+\) or \(-\), we investigate the question of whether they can be all wrapped by a single loop of string so that, when the string is taut and circulates, it rotates by friction all the \(\oplus\)-disks counterclockwise and all the \(\circleddash\)-disks clockwise, without any string-rubbing conflicts. We show that although this is not always possible, natural disk-separation conditions guarantee a solution. We also characterize the hexagonal “penny-packing” arrangements that are wrappable.
For the entire collection see [Zbl 1253.68016].
MSC:
68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
52C15 Packing and covering in \(2\) dimensions (aspects of discrete geometry)
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