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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.

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.