title: Optimal filling of shapes.
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.
authors.affiliation: Applied Physics Program, University of Michigan, Ann Arbor, Michigan 48109, USA.
authors.forename: Carolyn L
authors.initials: CL
authors.lastname: Phillips
authors.forename: Joshua A
authors.initials: JA
authors.lastname: Anderson
authors.forename: Greg
authors.initials: G
authors.lastname: Huber
authors.forename: Sharon C
authors.initials: SC
authors.lastname: Glotzer
mesh_terms: D008962:Models, Theoretical