GEOMETRIC THEORY OF POINT SOLID MODELING

The main provisions of the geometric theory of solid-state modeling are considered. The components of the theory, their interrelationships and mutual influences are determined. The concept of geometric solid-state modeling is presented and the analysis of the features of the construction and use of solid-state models is carried out. The main problems and difficulties of solid-state modeling are highlighted. To eliminate the identified problems and shortcomings, it is proposed to use the apparatus of point calculus. The purpose of the work is to evaluate the possibilities of point calculus in the addition, modernization and development of existing approaches and methods of solid-state modeling. The properties and features of point calculus are highlighted. The proposed solid-state modeling geometric theory does not possess these properties, but it can be supplemented and modernized. The possibility and prospects of the point calculus and solid-state modeling geometric theory mutual integration are investigated. Based on these studies, conclusions are drawn about the point-based solid-state models possible advantages. The assessment of the point calculus possibility and place integration into the solid-state modeling geometric theory is given. The analysis of point calculus existing scientific and applied tools for use in the solid-state modeling geometric theory and its applications framework is carried out. In order to test the proposed approaches of combining point calculus and the solid-state modeling geometric theory concept proposed in this work, the task of point solid-state model theoretical substantiation, construction and research was considered. A new type of the solid-state model representation in the ordered points set form is defined. A new analytical geometric model description is presented. It contains data about its shape, the simulated object position in space and its internal properties. This makes it possible to complement all shaping operations on solids and brings the analytical description of the solid model to a new level. It also complements and modernizes the graphical solid representation and has broad prospects for implementation into existing computer-aided design systems.