The visible perimeter of an arrangement of disks (Q390363)

The paper deals with the one-to one assignment of stacking order to the given collection of opaque distinct overlapping unit disks in the \((x,y)\) plane so that the visible perimeter of disks is maximized. The map corresponding to the determined stacking order is the 2-dimensional view of the disks arrangement from the point at negative infinity of the \(z\)-axis, i.e., the direction of visibility is considered from below. At the same time, the amount of disks overlap is minimized. In the presented work, the cases where the centers of disks form a dense point set and the centers of disks are centered at the points of a uniform grid are discussed. The results of this paper can be used in cartography and data visualization where similar copies of a symbols have to be placed on a map or a figure at given locations.