APPLICATION FEATURES RADIAL BASIS FUNCTIONS FOR IMPROVING THE PERFORMANCE AND QUALITY OF THREE-DIMENSIONAL OBJECTS VISUALIZATION 

Yuri N. Kosnikov, Doctor of technical sciences, professor, professor of sub-department of information and computing systems, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: kosnikov@gmail.com 

004.925 

10.21685/2227-8486-2021-1-7 

Background. The article is a continuation of the publication devoted to the radial basis functions use in geometric modeling of three-dimensional visualization objects. The topic relevance is determined by the increasingly widespread RBF used, including for the purpose of interpolation reconstruction of various natures non-analytical surfaces. RBFs bring a positive effect in solving not only purely geometric visualization problems, but also in improving its quality. This article discusses techniques for improving the interpolation performance without losing the visualization quality.
Materials and methods. Methods of segmental surfaces interpolation with smooth segments joining are considered. They are based on the selection of segments with the same reference points number or lying in the same coordinate range. For smooth segments joining, the method of transferring reference points is applied. The possibility of RBF-interpolation for calculating the directions of normal vectors drawn through the surface reference points is shown. The application of the finite difference method for calculating the values of blending functions, in particular, the proposed orthogonal basis functions, in real time is justified.
Results. Evaluation of the performance and accuracy of segmental interpolation with smooth segments joining by the reference points transfer method the effectiveness of this technique shows. RBF-interpolation of normal vectors allows you to get the correct normals to the object surface, which are necessary for modeling its illumination. The finite difference method makes it possible to calculate the value of RBF and orthogonal basis functions in 3–4 summation operations.
Conclusions. Segmental interpolation provides the quality of the reconstructed surface that is sufficient for engineering applications for visualization purposes. For smooth segments joining, the method of transferring reference points is recommended. The calculation of the normals directions is possible by the same methods and algorithms as the calculation of the blending functions values. The finite difference method allows you to significantly speed up the interpolation processes of visualization, providing the construction of the threedimensional objects surfaces in real time. 

radial basis function, blending function of orthogonal basis, segmental interpolation, reference points transfer method, illumination modeling, finite difference method 

Kosnikov Yu.N. Application features radial basis functions for improving the performance and quality of three-dimensional objects visualization. Modeli, sistemy, seti v ekonomike, tekhnike, prirode i obshchestve = Models, systems, networks in economics, technology, nature and society . 2021;1:78–91. (In Russ.). doi:10.21685/2227-8486- 2021-1-7