Covering an Arbitrary Shaped Domain by Identical Circles

DOI

10.2991/csit-19.2019.44How to use a DOI?

Keywords

circular coverage, arbitrary shaped domain, identical circles, tracing, mathematical model, nonlinear optimization.

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.

Copyright

© 2019, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Alexandr Pankratov
AU  - Tatyana Romanova
AU  - Oleksiy Antoshkin
AU  - Yuliia Pankratova
AU  - Sergiy Shekhovtsov
AU  - Vadim Kartak
PY  - 2019/12
DA  - 2019/12
TI  - Covering an Arbitrary Shaped Domain by Identical Circles
BT  - Proceedings of the 21st International Workshop on Computer Science and Information Technologies (CSIT 2019)
PB  - Atlantis Press
SP  - 253
EP  - 257
SN  - 2589-4900
UR  - https://doi.org/10.2991/csit-19.2019.44
DO  - 10.2991/csit-19.2019.44
ID  - Pankratov2019/12
ER  -