RADIAL BASIS FUNCTIONS USE IN GEOMETRIC MODELING OF THREE-DIMENSIONAL OBJECTS OF VISUALIZATION 

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

004.925.83 

10.21685/2227-8486-2020-4-6 

Subject and goals. The use of radial basis functions (RBF) in the field of visualization has a peculiarity that should be taken into account. This article is of a review and staging nature, which determines its relevance, since materials devoted to the systematic study of RBF in visualization tasks appear infrequently. RBFs bring a positive effect both in solving purely geometric visualization problems and in improving its quality. This article deals with the problems of geometric modeling of non-analytical surfaces defined by a set of reference points. The purpose of the article is to show methods for creating geometric shapes that meet the requirements of ergonomics and allow the use of effective grid visualization algorithms. The possibilities of RBF for improving the quality and performance of visualization will be discussed in the next article.
Methods. There are two approaches to regularizing the placement of reference points. The first is to move to new reference points that belong to the reconstructed surface and are arranged in an orderly manner. The second approach uses an auxiliary coordinate system, in which the original reference points are placed at the nodes of the coordinate grid.
Results and conclusions. The use of an explicit form of representation of interpolation expressions for both open and closed surfaces of visualization objects is justified. Local interpolation based on RBF for regularization of reference points is described. The possibilities of the radial and orthogonal basis functions for surface interpolation are evaluated. Varieties of orthogonal basis functions that allow their calculation in increments are proposed. The features of geometric modeling in visualization tasks include: setting the surface of visualization objects with dispersed reference points, usability of modeling results, and the ability to perform modeling operations in real time. Based on the analysis of these features, the criteria for choosing modeling tools are formulated. Recommendations on the choice of these tools are given: explicit or parametric form of interpolant recording, local (segment) interpolation with segment joining, use of RBF with compact support, application of orthogonal basis functions. 

geometric modeling, visualization, three-dimensional object, radial basis function, blending function of orthogonal basis