Grytsyk V. Modelling and synthesis of complex pictures of symmetrical structure.

Object of research: is complex pictures of symmetrical structure. The purpose of the investigation is the development of the method for description and modeling of complex symmetrical ornamental pictures and creation of the editor for ornamental pictures on the basis of this method. Investigation methods are the following: the theory of groups, theory of graphs, theory of algorithms, computer modeling, theory of phormal grammars. Results of researches: method for depicting and modeling of complex ornamental pictures is developed; language for depicting of structural parts of ornamental pictures is developed and its properties are examined; mathematical models of structural parts of ornamental pictures on the basis of recourse approach to the symmetry transformation groups are obtained; mathematical models of pictures transformation for Phjodorov groups on the surface and strip in matrix form are obtained; algorithms of synthesis of Phjodorov groups on the surface and strip on the basis of axial symmetr ies are suggested; analytical expressions for coefficients of ornamental pictures compressing (archivation) on the basis of above-said method are obtained; editor of ornamental pictures is projected, what gives an opportunity for modeling and automatical generating of complex pictures of symmetrical structure and for their effective preservation; editor of ornamental-embroideries is projected, giving the opportunity to reproduce complex pictures on the fabric. The results are introduced in the production and educational spheres. Application field: polygraphy, textile industry, advertising, educational establishments.