Department of Applied Mathematics

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Interpolating countour lines with radial basis functions
(Stellenbosch : Stellenbosch University, 2022-04) Schall, Philip; Weideman, Andre; Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences (Applied Mathematics)
ENGLISH SUMMARY : With the growing demand for digital elevation models (DEMs) in science and visualisation, there exists a need to generate these models cheaply and efficiently. While current methods such as remote sensing are often prohibitively expensive, interpolating contour data offer an economical way of generating DEMs. In this thesis, we investigate the feasibility of using radial basis function (RBF) based interpolation methods to interpolate DEMs from contour data. We present the basic theory of RBF interpolation, and introduce a number of RBF based techniques which are able to deal with the complexities of contour data. These complexities are mainly related to the extremely large data set sizes, and the irregular or scattered nature of the data. Furthermore, we compare RBF based interpolation methods to other established interpolation methods, and investigate the accuracy and quality of the resulting DEMs. We find that, particularly in our application, RBF based interpolation methods offer a robust, easily implementable and effective solution.