最佳填充量
Optimal Filling of Shapes
摘要：
我们提出填充作为一种类似于覆盖和包装的空间细分问题。填充解决了完全位于任意形状内的重叠对象的最佳放置，以便覆盖大多数内部体积。在n维空间中，如果对象是多分散的n-球，我们表明，解决方案对应于集的最大n-球。对于多边形，我们提供了一个启发式的最大磁盘的解决方案。当N趋于无穷大时，我们考虑了N个圆的理想分布的性质。我们注意到一个与能源景观的类比。
英文摘要：
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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