Abstract

Geometric Disks Covering (GDC) is one of the most typical and well studied problems in computational geometry. Geometric disks are well known 2-D objects which have surface area with circular boundaries but differ from polygons whose surfaces area are bounded by straight line segments. Unlike polygons covering with disks is a rigorous task because of the circular boundaries that do not tessellate. In this paper, we investigate an area approximate polygon to disks that facilitate tiling as a guide to disks covering with least overlap difference. Our study uses geometry of tessellable regular polygons to show that hexagonal tiling is the most efficient way to tessellate the plane in terms of the total perimeter per area coverage.

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