Development of generalized technique for formation of characteristic functions and Balyuba-Naidysh coordinates in the composition method of geometrical modeling

• Main Authors: Yevhen Adoniev, Andrii Naidysh, Viktor Vereschaga
• Format: Article
• Language: English
• Published: PC Technology Center 2018-04-01
• Series: Tehnologìčnij Audit ta Rezervi Virobnictva
• Subjects: Balyuba-Naidysh point calculation; formation of characteristic functions; parametric connection; multifactor modeling
• Online Access: http://journals.uran.ua/tarp/article/view/141383

The object of the study is the technique for the formation of characteristic functions and Balyuba-Naidysh coordinates (BN-coordinates) in the composite method of geometric modeling. The existing methods of modeling economic, technological and any other processes on real objects are rather complicated, with significant limitations on the number of incoming factors. One of the most problematic places is the complexity and narrow scope of each of the existing modeling methods, restrains their distribution and practical implementation on real business entities. Hence the need to develop a universal method for modeling multifactor systems. The closest to this is the composite method of geometric modeling (CMGM), the universality of which is ensured, first of all, thanks to the use of the intrinsic technique of generating characteristic functions and BN-coordinates. The use of the Balyuba curves (B-curves) constructed in BN-coordinates in KMGM gives significant advantages to CMGM. One-, two-, three-parameter B-curve can be considered in the n-dimensional Euclidean space En. As a result, CMGM can be used to solve problems in n-dimensional space, and the result of the solution can be decomposed into n one-dimensional projections, on which it is easy to analyze the solution. This can be used, in particular, in information systems to support management decisions. A feature of the B-curves is that the BN-coordinates p(t); q(t); r(t) are its parametric model, which is a constant. Applying a variety of variants of changing points, it is possible to obtain a lot of variants of B-curves, which is important for carrying out computer experiments in order to increase the adequacy of the constructed geometric model. The principle of the formation of characteristic functions is the operation of multiplying parameters and artificially assigned coefficients. As a result of the definition the product at the node points becomes zero or one, and in the intervals between nodal points it changes from zero to one. The number of factors of the characteristic function is equal to the number of nodal points that the characteristic function interpolates. The BN-coordinates of one B-curve form a system of interrelated fractional-rational functions. Thus, a generalizing technique for the algebraic formation of characteristic functions has been developed, and a transition from characteristic functions to BN-coordinates for the interpolation of three points has been determined. The technique used here can also be used for geometric interpolation of four or more points. The possibility of increasing the number of initial points of a geometric figure for BN-interpolation, extends the capabilities of models of multifactor processes and systems.