N-n-digit interrelations between the sets within the R 2 plane generated by quasi-rotation of R 3 space

Abstract

The background of description of the method for geometric objects rotation around the curved axes in the form of curves of the second order is being considered. The above-described method got the name of “quasi-rotation”. The algorithm of geometric construction of the two-two-digit interrelation on the basis of the circular axis of symmetry is provided. The described interrelation is analogous to the mirror symmetry regarding a straight linear axis. The method is suitable for construction of some well-known algebraic curves. The analogies between rotation and quasi-rotation are determined and described. The formula of the same plane preimage-to-image interrelation, generated by the quasi-rotation around the curved axis of the second-order curve is provided. The presented formula allows to derive the equations that effectively describe images of the given sets. The method for geometric construction of the images of geometrical objects lying within the plane of the second-order curve at their quasi-rotation for a given angle regarding the curve is described. The obtained results describe geometrical basics for the quasi-rotation. They serve as the basis for shape-forming of algebraic surfaces of high orders, and can be utilized as the theoretical basis for the computer-aided automated geometric projection.