ABSTRACTS OF ARTICLES OF THE JOURNAL "INFORMATION TECHNOLOGIES".
No. 1. Vol. 25. 2019

DOI: 10.17587/it.25.46-51

E. V. Konopatskiy, Assistant Professor, e-mail: e.v.konopatskiy@mail.ru
Donbas National Academy of Civil Engineering and Architecture, Makeevka

Approximation of Geometric Objects Using Arcs of Curves Passing through to Advance Given Points

The paper proposes a method for approximating geometric objects of multidimensional affine space using arcs of algebraic curves passing through to advance given points. As an example, we used a geometric model of the distribution by strength characteristics over the entire volume of a concrete column. The estimation methods of accuracy the approximation of geometrical models were also investigated. Methods of mathematical statistics were used for this purpose. As a result, a very good convergence between the geometric model and the initial experimental data was achieved (the average relative approximation error was E_reall = 2,16 % at the determination coefficient R² = 0,94). The advantages of using the arcs curves passing through the predetermined points for the approximation the geometric objects of multidimensional space include the fact that part of the initial points is involved in the process of approximation as nodal. This contributes to the achievement of high approximation accuracy. On the other hand, the disadvantages of the proposed method include the lack of a technique for selecting nodal approximation points from the array of initial data. This is a prospect for further research.
Keywords: approximation, geometric object, geometric modeling, the arc of the curve, passing through to advance given points, multidimensional interpolation, factors of influence, the response function, point equation, approximation accuracy, the coefficient of determination

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