Tabakova I. Geometrical modeling of geodetic lines on smooth surfaces taking into account their additional properties

The object of research is the process of forming images of geodesic lines on smooth surfaces defined by equations with differentiated functions. The aim of the study is development and application of a comprehensive model of calculating geodesic lines on smooth surfaces subject to calculating of approximate length of geodesic line on the surface between given points and the "steepness" of inclination of geodesic line to a horizontal plane at the investigated surface point. During the research, methods of the applied, differential, analytical and computational geometry as well as programming methods were used. During the study, methods of constructing a geodesic line, which begins at a given point in a given direction, were developed for various ways of describing a smooth surface, which allows to determine its length and "steepness" of inclination to a horizontal plane at the current surface point. As a result, algorithms for determining a motion path of robot among obstacles by means of geodesic lines built on specially selected intermediate surfaces were proposed. Also algorithms for determining a path of winding of tire cords by means of applying of geodesic principles were proposed. Study results were applied on the ROSAVA factory (Bila Tserkov, Ukraine) for development of mathematical means for geodesic winding of tire cords as well as for teaching of Engineering and Computer Graphics at Kharkiv National University of Radio Electronics.