Optimizing the Quality of Electric Lighting with the Use of Minkowski’s Geometric Difference

Mashrabjon Mamatov, Jalolxon Nuritdinov

2022

Abstract

In the paper, using the geometric difference of Minkowski, which are often used in the theory of differential games, the geometric data of the set of a certain lighting instrument are obtained. Found a way to build the set that needs to be installed in the lighting set to provide the lighting level corresponding to the requirement. In this work, conditions are obtained for the sufficiency and necessity of given triangles on the Euclidean plane, i.e. it is shown that if the place of illumination is a triangle of sufficiently large size and the illuminated place of the lighting set is also a triangle, then the place of installation of the set will have a triangular shape. Methods for finding the Minkowski difference of some groups of triangles by vectors corresponding to their sides are also shown and proved. At the end of the article is a theorem on the Minkowski difference of triangles. The theorem on the difference of Minkowski triangles is proved. The results obtained can be applied in the implementation of the installation of lighting devices for residential buildings, offices and enterprises.

Paper Citation

in Harvard Style

Mamatov M. and Nuritdinov J. (2022). Optimizing the Quality of Electric Lighting with the Use of Minkowski’s Geometric Difference. In Proceedings of the 3rd International Symposium on Automation, Information and Computing - Volume 1: ISAIC; ISBN 978-989-758-622-4, SciTePress, pages 751-756. DOI: 10.5220/0012046100003612

in Bibtex Style

@conference{isaic22,
author={Mashrabjon Mamatov and Jalolxon Nuritdinov},
title={Optimizing the Quality of Electric Lighting with the Use of Minkowski’s Geometric Difference},
booktitle={Proceedings of the 3rd International Symposium on Automation, Information and Computing - Volume 1: ISAIC},
year={2022},
pages={751-756},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0012046100003612},
isbn={978-989-758-622-4},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Symposium on Automation, Information and Computing - Volume 1: ISAIC
TI - Optimizing the Quality of Electric Lighting with the Use of Minkowski’s Geometric Difference
SN - 978-989-758-622-4
AU - Mamatov M.
AU - Nuritdinov J.
PY - 2022
SP - 751
EP - 756
DO - 10.5220/0012046100003612
PB - SciTePress