Application of Polynomial Interpolation for Iterative Complementation of the Missing Nodes in a Regular Network of Squares Used for the Construction of a Digital Terrain Model

Abstract

Due to the continuous increase in the volume of spatially located information, the current requirements imposed on the Spatial Information System (SIS) concern increasing data mining capabilities. Modern measurement systems, based on devices which enable the automatic recording of observation results on a mass scale (LiDAR—Light Detection and Ranging, MBES—Multi Beam Echo Sounder, etc.), allow for a very large volume of information on the surface to be measured and acquired in a relatively short time. One of the methods to reduce the volume of data enabling the generation of a model surface is to convert unevenly distributed measurement points into a regular network of squares (GRID). However, the generation of a complete grid is not always possible. In the measurement spectrum, there may be areas where measurement points have not been recorded. Measurement points can also be eliminated by either filtering the erroneously recorded data or eliminating the measured vegetation or the utilities in the area. To address these problems, the current article proposes a method for complementing the missing internal nodes in a regular network of squares using polynomial interpolation algorithms. Moreover, the paper demonstrates the possibilities of using the presented method for adding additional points between the already existing nodes of the network of squares. The application of the methodology presented in this article enables the effective elimination of (or a reduction in) the gaps in the GRID structure, which, in turn, allows such a network of squares to be used to generate a more accurate Digital Terrain Model.