Generation of the surfaces via quasi-rotation of higher order

Abstract

In this study we report a change in the geometry of space during its quasi-rotation relative to an ellipse. Symmetric interrelation, generated by the quasi-rotation around the elliptic axis is considered. The possibility of an arbitrary point quasi-rotation in the R 3 space around the elliptic axis is confirmed and discussed. Further, we analyze the properties of quasi-rotation surfaces. In the considered examples, a circle within the quasi-rotation axis’s plane is adopted as a generatrix. The algorithm used to build 3D graphs is based on a mathematical description of the method of rotation of a point around a second-order axis curve. A symmetry interrelation with respect to the elliptic axis is considered. The generated images are analyzed to determine the structure of their self-intersection and self-touching. Flat intersections of the surfaces under study are generated. Geometric methods were used to determine the order of the surfaces. It was established that in the considered example that quasi-rotation of the circle that belongs to the quasi-rotational elliptic axis’ plane, a surface of the twentieth order is formed.