Ausheva N. Geometric modeling of real-space objects based on isotropic characteristics

The paper presents solution of scientific and applied problem concentrated in development and formalization of fundamentals of real-space objects modeling based on isotropic characteristics. The modeling of real-space objects based on isotropic characteristics is substantiated to be the novel distinctive way of curves and surfaces generation using provided differential properties. The comprehensive approach covering construction of the basic isotropic primitives: line, curve, grid on a plane, surface in 3D space, is introduced. A number of novel methods and techniques of curves and surfaces generation basing on isotropic characteristics is developed, in this list: flat isotropic Bezier curves, isotropic rational curves, cardinal splines, Pythagorean-hodograph curves, curves in poly-coordinate representation, spatial isotropic curves, geometrical fractal curves, flat isotropic grids, minimal surfaces, surfaces originating from flat orthogonal and isometric grids. Usage of quaternion calculus for representation of isotropic curves and surfaces is suggested. Particular attention is paid to the new technique of 3D geometric model creation of a multi-ply yarn in knitwear industry. The suggested technique utilizes quaternions. Further improvement is made to the method of minimal surfaces formation by virtue of isotropic curves.