MODEL OF THE FULL COVERAGE OF A PARTICULAR AREA TAKING INTO ACCOUNT OF SPECIAL TYPE RESTRICTIONS

Abstract

The relevance of the article lies in the lack of models and methods of maximum and complete coverage of specified areas, taking into account the limitations of a special kind.

The main problem of coverage problems is to find the minimum and optimal solutions with certain constraints, which will be determined by the models and methods of coverage.

In order to solve the problem of covering a given area in two-dimensional space, there are different methods of coverage, namely covering a given area with circles of the same radius, circles of variable radius, rectangles, polygons, and objects with variable metric characteristics.

The purpose of the article is to formulate the problem statement and develop a model of complete coverage of a given area (non-convex polygon with a set of sub-areas of coverage), taking into account the limitations of a special type.

In this work, a mathematical model of complete coverage of a given area by non-convex polygons with variable metric characteristics was developed, taking into account the following limitations: minimum area of mutual intersection of coverage objects; the minimum area of intersection of objects of coverage and addition of the set area to two-dimensional space; the parameters of placement of coverage objects should belong to the points in the specified sub-areas, taking into account the priority sub-areas; belonging of priority areas to the objects of the coverage area; belonging of priority points of subregions to objects of coverage; restrictions of a special kind that affect the metric characteristics of the objects of coverage.

The obtained model allows to develop a substantiated method of geometric modeling of full coverage and to carry out computer modeling of coverage of a given area, taking into account the limitations of a special type.

Further research will focus on solving other problems arising from the general formulation, and on the development of methods of geometric optimization.

Keywords: full coverage, special type restriction, general model, given area, subregions.