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Authors

SHejko T. I.

Degree
Doctor of Engineering, Professor, Head of Applied Mathematics and Numerical Methods Department, Institute for Mechanical Engineering Problems of National Academy of Sciences of Ukraine
Location
Kharkov
Articles

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.

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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.

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