Interpolation and approximation methods for large geometric datasets: DCSE/TR-2016-05

A surface reconstruction of large scattered datasets using interpolation or approximation methods is often a task in many engineering problems. Several techniques have been developed for the surface reconstruction, but they mostly require the conversion of a scattered dataset to an ordered dataset, i.e. a semi-regular mesh is obtained by using some tessellation techniques, which is computationally expensive. Therefore, we focus to the Radial Basis Function (RBF) methods which are appropriate for large scattered datasets in d−dimensional space. The RBF methods are non-separable as it is based on the distance between two points, and lead to a solution of a linear system of equations. Using RBF methods; the implicit or explicit analytical representation of the surface can be obtained. It is one of the advantages over the classical triangulation methods. The following report contains the state of the art in the given computer graphics area; it aims to the description of important data structures for storage of the large scattered datasets and several existing RBF methods. Then, the report shows the common problems of these methods. Finally, the report focuses on the presumptive future work