Chelombitko V. Geometrical modeling of patterns of printing protection of securities by lines with variable curvature

The thesis is devoted to developing a computer model of the description and creation of figured lines along which their curvature varies according to preset the law, and their color changes in proportion to the specified curvature. The main results of work include the following. For the first time a method of designing figured curves by the natural equation depending on the description of their curvature is developed, and their color changes in proportion to curvature. The way of the description of figured curves taking into account a correcting of their geometrical shape by change of the equation of curvature by means of R-functions, and also ways of the simplified creation of figured curves of a triangular and square shaped are proposed. Besides, a way of scaling of the figured curves described by the natural equations, by solving a system of modified differential equations, where the coordinate functions proportionally the scale factor changed, and also offset along coordinate axes and to the rotation of the figured curves described by the natural equations are improved. The results of work implemented in production for designing of protection of printed documents, for aesthetic and artistic decorations book publications and brochures, and also into learning process KNURE.