CONCEPTS OF THE SPREAD OF GEOMETRIC TECHNOLOGY TO THE MODELING OF PHYSICAL OBJECTS AND PROCESSES

Abstract

The logical basis for presenting information in applied fields is geometric objects. Therefore, in each of the scientific and practical problems, first of all, its geometric content is studied. The formation of a conceptual approach begins with the search for a classical scientific basis for the possibilities of using geometric terminology and technologies of geometric modeling and computer graphics. The search for the interconnection of approaches, methods, technologies developed in various fields of science remains relevant and promising - from classical approaches to the study of phenomena in the natural sciences to experiments and production of product samples in engineering. A general approach to defining the concepts of applying geometric technology for modeling objects and processes of different physical nature is considered. The basis of consideration was the theory of generalized parallel sets. It has been confirmed that the conceptual approaches "radial" and "wave" made it possible to extend the use of geometric methods to a fairly large range of problems in various scientific and practical fields. The chosen strategy has a scientific basis, which is proven by classical physical and mathematical research, which in the historical aspect covers more than one decade. A certain systematization of geometric modeling problems, which have already been solved or still require research and the application of new methods and technologies, and which are solved on the basis of the theory of generalized parallel sets and have their origins in various scientific and practical fields, is proposed. Modeling in these problems is aimed at sets of geometric objects, in particular, for example, point sets, grids, families of lines and surfaces. For the formation of generalized scientific concepts in the field of geometric modeling and the application of geometric technologies related to the study of physical objects and processes, common input data can be mathematical models (concepts, theorems, statements), on the one hand, and phenomenological descriptions of these objects and processes, on the other hand.

Keywords: geometric modeling, theory of generalized parallel sets, physical objects and processes, rays, wave fronts, families of lines and surfaces.