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Tolok A. V.

Degree	Doctor of Engineering, Professor, MSTU STANKIN
E-mail	a.tolok@stankin.ru
Location	Moscow
Articles	Graphic image-models in information technologies To understand about what graphic image-models our speech is going, it is necessary to distinguish a graphic model from its picture. To apply graphic image-models in a mathematical modeling, it is enough to talk about the graphic reflection of differential characteristics of the modeled analytical function. To solve multidimensional problems, it is enough to create multidimensional graphic image-models. Read more... Recursive calculations process parallelizing for cube dichotomy fragmentation An approach to data structure description simplifying data processing and increasing application efficiency is presented. Principle of the binary addressing is used for cube dichotomy data structuring. Read more... R-functions as the means in fractal geometry applications The mathematical means of the R-functions theory appeared rather convenient for exposition of fractal geometry objects with the help of the functions (x) = 0, x∈E n, where (x) is the uniform analytical expression. Thus the following constructive tools have been used: R-functions of a {R0} system; a superposition of (x, y) function with the periodic functions, permitting to translate the given function along axes with a step hx and hy, and along a circle of radius R for n times; property of a similarity of the figures circumscribed by the equations (x, y) = 0 and 1 0 K Kx,Ky, where K is the similarity factor. In this work only some, most known objects of fractal geometry are constructed, as for example, a Sierpinski carpet and napkin, Kokh curve, snowflake, cross, etc. Read more... R-functions in computer modeling of 3D car surface design The stage-by-stage modeling of the automobile body by the multiparameter equations with alphabetic parameters for geometrical characteristics and a technique of the surfaces equations of construction with continuous curvature function with the help of R-functions is considered. The work of new high-speed system of the equations of geometrical objects surfaces visualization in 3D is illustrated. Read more... Automating graphic techniques for solving some mathematical problems This paper deals with computer graphics tools application to graphic techniques of mathematical problems solving. Examples of algebraic linear equations and mathematical programming solutions are given. Read more... Graphic techniques of computer-aided solving of few mathematical problems This paper is devoted to the application of computer graphics tools in order to devise graphic techniques of solving of mathematical problems. Examples of solving combined algebraic linear equations and mathematical programming problems are given. Read more... Method of a functional voxelization of polygonal objects on the basis of mathematical apparatus of R-functions One of the pressing problems arising at experts in the field of voxel modeling is development of algorithms of a voxelization of the polygonal models, synthesized in modern CAD systems. Similar tasks arise in process of development of systems of layer-by-layer synthesis where the formed image represents layer-by-layer obtaining raster images. In the late nineties the beginning receives the direction of the functional voxel modeling (FVM) allowing to consider a voxel image as some characteristic of functional space (M-image). The paper considers the principles of construction functional voxel geometrical objects on the closed contour on the basis of the R-functional description. The analysis of the graphic images received by different ways of the description of the closed contour is provided. Problems of obtaining monotony of the received functional space are considered. The provided analysis confirms that the advanced piecewise-analytical method of obtaining the description of a contour of object most conforms to requirements of smoothness and monotony. These requirements and the received analytical description of a functional surface allow to expand considerably application of such models in functional voxel modeling at automation of a wide class of problems for CAD and automation technologies. Read more...