Kravtsiv S. Geometric modeling of objects coverage taking into account restrictions of a special type

The object of the study is the process of covering given areas by convex polygons, taking into account the limitations of the special type. The purpose of the dissertation is to develop a method of geometric modeling of the coverage of given areas, taking into account the limitations of the special type and its practical implementation to solve the class of problems of coverage. The tasks were solved on the basis of the provisions of applied geometry, system approach, elements of topology, methods of mathematical and geometric modeling, geometric design, elements of functional analysis, methods of analytical, multidimensional, computational geometry, methods of optimization, and methods of discretization. This paper formalizes the restrictions of a special kind in the problems of covering given regions by convex polygons. The method and methods of covering the given area are considered taking into account the limitations of the special kind, the basis of which are the methods of combinatorial optimization. Algorithmic software has been developed and computer simulations of the coverage of given areas have been carried out, taking into account the limitations of the special type on the examples of practical tasks in the field of civil protection. The general model of coverage of a given area with the restrictions of a special kind is improved and its peculiarities are investigated. The Blyznyukivsʹkyy district of Kharkiv region was covered by the areas of departure of operational and rescue units. The results of the dissertation research were implemented in the practical activity of the Main Department of the State Service of Ukraine for Emergencies in the Kharkiv region and in the educational process of the National University of Civil Protection of Ukraine.