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LANS Informal Seminar: Carolyn Phillips
March 14, 2012 @ 15:00 CDT
Seminar Title: Optimal Filling of Shapes
Speaker: Carolyn Phillips, Aneesur Rahman Postdoctoral Fellow, CI
Date/Time: 2012-03-14 15:00
Location: Building 240, 1404-1405
Description:
We present filling as a new type of spatial subdivision problem that is related 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 and the solutions space can reduced to the medial axis of a shape. We consider the structure of the solution space in two-dimensions. For polygons, we provide a detailed description of a heuristic and genetic algorithm for finding solutions of maximal discs. We also consider the properties of ideal distributions of $N$ discs in polygons as $N$ goes to infinity.