ON THE ISSUE OF PRACTICAL APPLICATION OF CURVES WITH NATURAL PARAMETERISATION

Abstract

Nowadays, computer information technologies are quite widespread in various spheres of people's lives. At the same time, the creation of complex technical objects is usually carried out in the environment of CAD/CAM/CAE/PLM (Computer-Aided Design/Computer-Aided Manufacturing/Computer-Aided Engineering/Product Lifecycle Management) systems. The above facts determine the importance of further development of these tools and improvement of appropriate methods of their practical use, in particular regarding automated shaping. The basis of corresponding geometric modelling is parametric curves, which are used in the design of many industrial products. This applies, for example, to airplanes, ships, cars, household appliances, etc., as well as unique buildings and structures. The latter case refers to cultural, educational, sports, medical, engineering and other facilities. The current historical stage of our state's existence is quite difficult due to military operations on its territory. The infrastructure of cities and villages is being destroyed, people are dying and being maimed. In these critical conditions, a significant number of our citizens, most of whom are Christians, are turning to the Almighty for help. Therefore, the problem of preserving existing, restoring damaged and destroyed sacred buildings, and constructing new ones after the end of the war is becoming urgent. Based on the above circumstances, the approach proposed in this publication to the practical application of curved lines with natural parameterization is illustrated by the formation of domes of Orthodox temples. The information presented in the article is based to a certain extent on preliminary proper scientific research carried out by the authors. The main results can be considered the developed methodology for obtaining the necessary mathematical computational procedures for approximation with the required accuracy of the natural parameterisation of the processed curves. This allows for more advanced automated design of technical objects, which is confirmed by the analysed relevant specific examples. Prospects for further scientific research on the topic under consideration were also identified.