Sosurka O. A mathematical model and solution method for the covering problem of a compact polyhedral set with a family of a right parallelepipeds

The object of research is the process of covering a three-dimensional polyhedral set by a finite set of right parallelepipeds. The aim of the dissertation is mathematical and computer modelling of the coverage, developing of a method for solving the covering problem of compact polyhedral set by a finite set of right parallelepipeds. The method of general topology, geometry, mathematical analysis, mathematical programming, computational geometry are used. The results are a continuation of a series of research problems of geometric design, coupled with the development of methods for solving problems of packing, cutting and covering. The practical significance of the work lies in the fact that the developed mathematical models can be used to solve the covering problems. Based on the results of the thesis developed software: "3D covering problem" and "3D minimal covering problem". Scientific novelty: developed the method of Г-functions, proposed the mathematical model of three-dimensional covering of compact polyhedral set by the set of right parallelepipeds, proposed method for solving three-dimensional covering problem a finite set of right parallelepipeds of different sizes. The application of the results of the research is planned. Results can be used to solve the problems of air and space observations, in the process of pattern recognition and contours in robotics, in molecular modeling.