R-functions in Development of Analytical Identification of Geometrical Objects

Abstract

In this paper for mathematical and computer modeling of fractal geometry objects, machine parts and building structure the R-functions theory is applied. The mathematical tools of the R-functions theory are very convenient for the fractal geometry objects description. The equations of the Levi fractal, Pythagoras's tree, Koch's curve, cross and snowflake, Menger's sponge (also known as the Menger universal curve), Sierpinski's carpet, etc. have been constructed. The techniques using both the equations of three-dimensional primitives, and information about the equations of boundaries of sections of reset object have been developed. The equations of the automobile body surface, the bearing sleeve, the stepped shaft having two cogged pulleys, the rotary valve, the revolver drum, the screw having the shaped head, cut and lock surface, the cutter lift, the oil filter arm, etc. were constructed. The equations of the hexahedral cartridge having 91 fuel elements have been constructed using only two R-operations.