Improvement of the method of functional representation of the shape of a three-dimensional object

Authors

DOI:

https://doi.org/10.15587/2706-5448.2026.361358

Keywords:

3D modeling, functional representation, Transformer, Fourier transform, calibration of the action orbit of the similarity group, quality assessment of the functional representation

Abstract

The object of research is the process of creating a three-dimensional computer model of an aerodynamic product.

The research is devoted to solving the problem of combining a Transformer class model and a method of representing figures through a Fourier series. Such a combination is possible provided that a universal method of representing multidimensional data of different types is used. The results of the combination can improve the solution of the problem of creating a 3D model that meets the specified environmental requirements with sufficiently high accuracy. However, the issues of applying a universal method of representing multidimensional data remain largely unexplored.

A universal method of representing mathematical descriptions of a 3D object and the physical environment that affects the characteristics of this object has been improved. A new method of calibrating the action orbit of the similarity group of figures by displacement has been developed. A method of applying the Fourier transform for figures that form multiple-valued functions after the second phase of the transformation has been improved. A quantitative quality assessment of the functional representation of a figure based on the Hausdorff distance has been developed. A method for eliminating the existing shortcomings of this distance has also been developed.

An experimental verification of the obtained research results has been carried out. It has been established that the use of the proposed improvements ensures the invariance of the functional representation with respect to spatial characteristics of 99.9%. The largest root mean square deviation is 0.000008 absolute units of the Hausdorff distance.

The obtained results provide a universal method for representing any three-dimensional objects. Unlike most existing methods, the improved method allows to operate on 3D models as points in the Hilbert functional space. This possibility allows to significantly simplify the use of modern machine learning models of the Transformer class for solving scientific and applied problems of mathematical physics.

Author Biographies

Yevhenii Ruksov, Dnipro University of Technology

PhD Student

Department of Software and Computer Systems

Borys Moroz, Dnipro University of Technology

Doctor of Technical Sciences

Department of Software and Computer Systems

Maksym Ievlanov, Kharkiv National University of Radio Electronics

Doctor of Technical Science

Department of Information Control Systems

Dmytro Moroz, Dnipro University of Technology

Doctor of Philosophy (PhD)

Department of Software and Computer Systems

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Improvement of the method of functional representation of the shape of a three-dimensional object

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Published

2026-05-29

How to Cite

Ruksov, Y., Moroz, B., Ievlanov, M., & Moroz, D. (2026). Improvement of the method of functional representation of the shape of a three-dimensional object. Technology Audit and Production Reserves, 3(2(89), 21–30. https://doi.org/10.15587/2706-5448.2026.361358

Issue

Vol. 3 No. 2(89) (2026): Information and control systems

Section

Information Technologies

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Copyright (c) 2026 Yevhenii Ruksov, Borys Moroz, Maksym Ievlanov, Dmytro Moroz

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