Coverage Diameters of Polygons

Abstract

This paper formalizes and proposes an algorithm to compute coverage diameters of polygons in 2D. Roughly speaking, the coverage diameter of a polygon is the longest possible distance between two points through which the polygon cannot pass in between. The primary use of coverage diameter is to form a cage for transporting an object, not necessarily convex, with multiple disc-shaped robots. The main idea of the computation of coverage diameter is to convert the problem into a graph structure, then perform the search for a solution path in that graph. The proposed algorithm runs in O(n <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> log n) time for the input polygon with n vertices