Covering an Arbitrary Shaped Domain by Identical Circles

Abstract

The problem of covering a bounded disconnected arbitrary shaped area (domain) by identical circles is considered. To describe analytically the coverage conditions we use special continuous and everywhere defined functions for modelling relations between circles and the border of the area. A new function for modelling the relations between three circles when covering the interior part of the domain is defined. An integrated mathematical model of the coverage problem is provided in the form of a nonlinear programming problem. A new strategy for solving the problem is proposed. To demonstrate the efficiency of the developed algorithm an example of solving the problem for optimizing the length of the network connecting centers of the circles is presented.