Pasichnyk V. Mathematical modelling of a three-dimensional body surface using the interlineation of functions

The process of 3D body surface mathematical modeling is the object of the research. Creating the mathematical 3D body surface model using the interlineation and spline-interpolation functions with optimal selection of quantity and the mathematical model parameter values. During performance the research the interlineation and spline-interpolation functions of one and two variables methods are used; function approximations using Fourier's sums; general theory the approximation of the functions which adjusted by experimental data, many variables function theory fundamental assertion about founding for their optimal value. To realize computational modeling computer is used. In the work for 3D bodies which surface can be unambiguously described in cylinder coordinate system for the first time general method for constructing mathematical body surface using the interlineation functions are formulated and investigated. Constructed mathematical models allow greatly reduce the quantity of parameters which are necessary for surface restoration with given accuracy compared with mathematical models which use splines without optimal junction. In case when traces of approximating function which describes the 3D body surface are not given on interlination lines there is suggestion in work to change these traces by Fourier's sums which are built using experimental data. Theoretical results are applied to the mannequin surface mathematical model optimization in sewing industry. The results of testing show that we can build the mathematical model with an needed accuracy and less number of parameters than in the classic surface presentation by splines. The results of dissertation work were used during national budget science-research subject 04-02-DB "New high-performance methods for solving plain and spatial computer tomography objectives, based upon the use of the interlineation and spline-interpolation functions". Mathematical modeling methods used in national enterprise "Zaporizke machine-building constructor office "Progress" O. Ivchenko". Practical importance of received results is that developed mathematical model, methods, algorithms and program means totality can be used in geophysics, in light production in clothes SAPR, in machine-building etc.