Botvinovska S. Discrete modeling of the highway contours and crossings based on governing factors of underlying curves' natural equations

The modeling methods of flat and 3-dimentional curves are the object of research for the dissertational work, research was conducted and concentrated on geometrical properties and features discovered in the process of curves' modeling based on their natural equations. Theoretical, methodological and algorithmic theory and procedures of the process described above were improved and the program module was developed to perform modeling of lines of exit pockets at crossing points on different highway levels. The program module of curves' modeling with the help of their natural equations utilizes objective-hierarchical model supervised by the main software engine coordinating work of all elements of the module. This is an automated design system that incurs all basic functions during the construction of modeling object. As a result of the system's work the 3-dimentional curve is constructed based on the set of initial conditions, complying with assigned curvature and torsion moments applied to the end points. The modeling of curves basing on assigned curvature and torsion is essentially nonlinear problem that is not solvable by using solely empirical approach. Various classification schemes of lines of exit pockets are developed accounting for necessary number of banding points. The developed program module consists of following object-oriented components: objects of a subject domain - curve, service objects - services, intuitive and self-explanatory GUI (graphic-user interface) and convenient system of input and output for both, graphic and the text data.