ARBF: adaptive radial basis function interpolation algorithm for irregularly scattered point sets

Abstract

Radial basis functions (RBFs) are isotropic, simple in form, dimensionally independent and mesh-free and are suitable for interpolation and fitting of scattered data. In a scattered point set, the calculation accuracy of multiquadric (MQ) RBF interpolation is strongly related to the selection of the shape factor. There is still no uniform method for determining the shape factor. Many scholars focus on determining the single optimal shape factor and seldom consider the change in the shape factor with the spatial point density in scattered point sets. In this paper, an adaptive radial basis function (ARBF) interpolation algorithm is proposed. The shape factors of MQ functions are determined adaptively by the local point densities of the points to be interpolated. To evaluate the computational performance of the ARBF interpolation algorithm, twelve groups of benchmark tests are conducted in this paper. We found that (1) the numerical error of ARBF interpolation is approximately 10% less than that of commonly used RBF interpolation with the shape factor recommended by Hardy. (2) The computational efficiency of ARBF interpolation is 1–2.5% lower than that of commonly used RBF interpolation with the shape factor recommended by Hardy.