Abstract
We present filling as a type of spatial subdivision problem similar to covering and packing. Filling addresses the optimal placement of overlapping objects lying entirely inside an arbitrary shape so as to cover the most interior volume. In -dimensional space, if the objects are polydisperse -balls, we show that solutions correspond to sets of maximal -balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of disks as . We note an analogy with energy landscapes.
- Received 19 January 2012
DOI:https://doi.org/10.1103/PhysRevLett.108.198304
© 2012 American Physical Society
Synopsis
Thinking Inside the Box
Published 10 May 2012
Finding the optimal solution to filling a volume with spheres could be useful for modeling nanoparticles.
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