Application of Spline Interpolating Functions in the Paradigm of the Universal Standard Exchange of Digital Hydrographic Data

Abstract

The necessity of duplication of satellite navigation by a correlation-extreme navigation system with the actual comparability of indicators of the positioning accuracy of alternative systems is substantiated. When studying the issue of replication of the mapping standard as a basic principle of perspective navigation, the expediency of using the spline approach as an effective additional arsenal of capabilities to the list of reserved interpolating functions of the S-100 universal standard has been revealed. The phenomenon of the application of spline function methods in the framework of the implementation of the concept of modeling the navigation isosurface in order to accurately synthesize the topography of the seabed relief is considered. The theoretical substantiation of using the concept of a spline gradient in the processing of navigation information within the framework of the hypothesis of the gradient fan postulate applicability is carried out. The magnitude and spatial distribution of computational interpolation errors are interpreted into the definition of uncertainty surface, which is a two-dimensional statistical estimation of the accuracy of modeling bathymetric data by analogy with the concept of navigation isosurface. Deterministic interpolation is implemented on the basis of processing an experimental database of measurement data with further transformation into a gridded grid massif. The focus on the use of gridded data in the compilation of digital bathymetric models makes it possible to provide a detailed restoration of the underwater landscape. The interpolation gridding technology has provided a formalized structured representation of a two-dimensional grid of recorded measurements results for visualization of the navigation isosurface in three-dimensional Euclidean space. The hybrid spline algorithm is adapted to reconstruct a detailed profile of an underwater relief with the required morphological properties by mathematically simulating the plasticity of geospatial topography. Based on the technology of spline functions, the three-dimensional perspective of an isolinear bathymetric model investigated by the National Genoese Institute of the water area in the Tyrrhenian Sea is restored. A precedent for the implementation of spline interpolation together with the possibility of visualizing a volumetric perspective on electronic media for the subsequent practical use of three-dimensional electronic maps in order to increase the safety potential of navigation due to the effectiveness of visual orientation of the navigator in difficult sailing circumstances has been created.