Tkachenko O. Matematical modelling of surfaces the difficult geometrical form with use interlineation and interflatation functions.

Object of research - the process of constructing equations of lines and flat surfaces in compliance with the given technological conditions. The subject of research - mathematical modeling of planar lines and surfaces in compliance with the set of properties and using the theory of spline interlination and spline interflatation. Purpose - to build and study mathematical models of flat lines and surfaces of three-dimensional bodies of complex shape through the use of operators interlination and interflatation functions. Methods: Methods of mathematical descriptions of lines and surfaces, methods of functional analysis, approximation theory of functions of several adjustments using splines, interlination and interflatation functions, methods of application for the description of lines and surfaces by means of MathCad, MatLab and the programming language Fortran. A method for constructing polynomial splines basis of degree of defect 1 at irregular grid nodes in the form of explicit formulas present in each interval between nodes, the method of description of complex curves in implicit form by interlination functions method for describing complex surfaces in implicit form by interflatation functions that ensures required surface properties, including izogeometrical, parametric methods describing surfaces using spline functions interlination. Based on the results you can develop software packages to automate the design of complex technical surfaces with predetermined properties. The results were partly used to develop mathematical models and software packages for building three-dimensional mathematical model of a closed surface pen blades.