Radial basis function and multi-level 2D vector field approximation

We propose a new approach for meshless multi-level radial basis function (ML-RBF) approximation which offers data-sensitive compression and progressive details visualization. It leads to an analytical description of compressed vector fields, too. The proposed approach approximates the vector field at multiple levels of detail. The low-level approximation removes minor flow patterns while the global character of the flow remains unchanged. And conversely, the higher level approximation contains all small details of the vector field. The ML-RBF has been tested with a numerical forecast data set and 3D tornado data set to prove its ability to handle data with complex topology. Comparison with the Fourier vector field approximation has been made and significant advantages, i.e. high compression ratio, accuracy, extensibility to a higher dimension etc., of the proposed ML-RBF were proved. (C) 2020 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.