Optimal Filling of Shapes

Details Optimal Filling of Shapes Optimal Filling of Shapes

2012-02-11

arxiv.org/abs/1202.2450v1

Physics

Condensed Matter

Soft Condensed Matter

5 pages

Scientific paper

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 discs. We consider the properties of ideal distributions of N discs as N approaches infinity. We note an analogy with energy landscapes.

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