Adjusting the Regular Network of Squares Resolution to the Digital Terrain Model Surface Shape

Abstract

A regular network of squares is formed by points uniformly distributed (mostly in the square corners) over the surface that is represented by the network. Each point (node) of the network has specified coordinates (X and Y) with a fixed constant distance between them. The third coordinate in a node (H) is determined by the application of interpolation based on the points distributed (usually dispersed as a point cloud e.g., from LiDAR) over the surface of the area surrounding the node. The regular network of squares formed in this manner allows the representation of a digital terrain model (DTM) to be performed in spatial information systems (SIP, GIS). The main problem that arises during the construction of such a network is the proper determination of its resolution (the base distance between the coordinates X and Y) depending on the topography. This article presents a method of the regular network of squares resolution determination depending on the morphological shape of the terrain surface. Following the application of the procedures being described, a differently shaped terrain is assigned various network densities. This enables the minimisation of inaccuracies of the surface model being formed. Consequently, a regular network of squares is formed with different base square sizes, which is adjusted with its resolution to the morphology of the surface it describes. Such operations allow the terrain model accuracy to be maintained over the entire area while reducing the number of points stored in the DTM database to the minimum.

Design and Experimental Study on an Innovative UAV-LiDAR Topographic Mapping System for Precision Land Levelling

“…TIN is a vector-based interpolation model that forms a network of triangles of irregular size and shape. TIN's triangular linear interpolation process begins with determining the triangular to which the interpolation point belongs, then calculating the parameters of a, b, and c for the plane equations of each triangular using the 3D coordinates of three vertices, expressed as Equation (9). The elevation data of every interpolation point within the triangular could be acquired according to Equation (10).…”

“…Generally, two major precision farmland levelling techniques can be enumerated: laser farmland levelling and GNSS (Global Navigation Satellite System) farmland levelling [6]. An accurate topographic map is essential to precision farmland levelling; this map type refers to a 2D (two-dimensional) graphic representation of a terrestrial land surface feature Drones 2022, 6, 403 2 of 18 using contour lines, hypsometric tints, and relief shading [7][8][9]. As for the laser leveler, the preset height of the laser transmitter directly determines the cutting depth of each point, i.e., cut-fill ratios.…”

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

“…This is most often determined by the availability and density of measurement points, the morphology of the surface being measured, the type of interpolation algorithm used, or the accuracy of the final compilation [46,47]. The entire process of node determination, which is also referred to as gridding, can be defined as the interpolation of the Hw value at the nodes of a regular grid (with the coordinates of Xw, Yw) based on the function value at measurement points (with the coordinates x, y, h) [48][49][50]. When creating a surface model using the GRID structure, the aim should be to obtain as complete a grid of nodes as possible over the study area.…”