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Optimal Filling of Shapes

Carolyn L. Phillips, Joshua A. Anderson, Greg Huber, and Sharon C. Glotzer
Phys. Rev. Lett. 108, 198304 – Published 10 May 2012
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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 n-dimensional space, if the objects are polydisperse n-balls, we show that solutions correspond to sets of maximal n-balls. For polygons, we provide a heuristic for finding solutions of maximal disks. We consider the properties of ideal distributions of N disks as N. We note an analogy with energy landscapes.

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  • Received 19 January 2012

DOI:https://doi.org/10.1103/PhysRevLett.108.198304

© 2012 American Physical Society

Synopsis

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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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Authors & Affiliations

Carolyn L. Phillips1,*, Joshua A. Anderson2, Greg Huber3,4,5, and Sharon C. Glotzer1,2,6,†

  • 1Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 2Department of Chemical Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 3Center for Cell Analysis and Modeling, University of Connecticut Health Center, Farmington, Connecticut 06032, USA
  • 4Department of Cell Biology, University of Connecticut Health Center, Farmington, Connecticut 06032, USA
  • 5Department of Mathematics, University of Connecticut, Storrs, Connecticut 06032, USA
  • 6Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109, USA

  • *Present address: Computation Institute, Argonne National Laboratory, Lemont, IL, USA.
  • Corresponding author. sglotzer@umich.edu

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Issue

Vol. 108, Iss. 19 — 11 May 2012

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