Lagodina L. Weighted vector-parametric polycoordinate representations in the geometric modeling of objects and processes

The dissertation for obtaining the degree of the candidate of sciences (Engineering), specialty 05.01.01 - Engineering geometry and computer graphics. - Kyiv National University of Construction and Architecture. - Kyiv, 2016. The dissertation is devoted to the development of new ways of modeling smooth curved contours of objects and processes on the basis of the weighted vector-parametric polycoordinate representations. The paper suggests the study of the properties of smooth curves' polycoordinate representations using one coordinate which are the basis of the vector-parametric polycoordinate representations of curves and surfaces. The weight coefficients are proposed, their properties are investigated, the use of which enables improvement of the adequacy of the form- making. The paper suggests the study of the properties of smooth curves' polycoordinate representations using one coordinate which are the basis of the vector-parametric polycoordinate representations of curves and surfaces. The weighted ratios are proposed, their properties are investigated, the use of which enables improvement of the adequacy of the form-making. On the basis of the weighted vector-parametric polycoordinate representations the methods of approximation and interpolation of smooth curves, methods of modeling of smooth curves in polar, cylindrical and spherical coordinate systems, modeling of kinematic smooth surfaces are developed. The suggested new ways of polycoordinate method allow to design simply enough thecurved contours of units and machines working in a moving environment, and to predict the processes of spread of environmental pollution on the surface of the earth and water objects.