Comparison study of Gauss, MQ and TPS for interpolation application

Abstract

There are mainly two parts in this paper. In the first part, we briefly introduce the basic theory of the radial basis function (RBF) and its application in scattered data interpolation, and investigate the difference among three kernel functions: multi-quadric, Gauss and thin plate spline, in detail. According to the multiple examples, we make a lot of experiments, and develop a system in the C++ programme language and the OpenGL open graphics library to make simulation experiments. Finally, we analyse and summarise the different characteristics of the each kernel function in the process of interpolation. In addition, on the basis of the well-known interpolation theory and the analysis of the experimental data, we list several examples for interpolation comparisons. In the second part, the distance of the current marked points down to its most neighbouring marked points is used as shape parameter. Combining with other shape parameter for analysis and comparisons, the results represent the different influences of RBF shape parameter on the curve and surface construction. Our experiment results obtained in this article have theoretical guide values in graphic interpolation modelling.