Research of the differential properties of the navigational isosurface

The topic of this paper is a qualitative study of navigational isosurfaces to establish the practicality of polynomial approximation for a class of differentiable functions with minimized “smoothness.” When solving problems of restoring the scalar field of navigation parameters, it is certainly important to form an initial correct judgment about the isogeometric proximity between the approximate and approximating functions, provided specific information is given about the differential properties of the synthesized navigation isosurface. It is assumed that the structure of the graphical model of the object under study and the characteristics of function approximation theory should be consistent with each other when forming a unified information approach. As a concrete illustrative example, a study of the differential properties of a formalized representation of an astronavigational isosurface — with geometric interpretation in the form of computer screenshots obtained as a result of the work of a compiled software module — has been performed. An assumption is made regarding the realistic possibility of choosing the optimal approximate navigation function based on visualization of the “smoothness” of a navigation function of any dimension in accordance with Schoenberg’s hypothesis about the relationship between minimum curvature and maximum smoothness of an algebraic line. The search for a solution to the problem of graphical transformation of break points of an abstract isoline, formalized in strict mathematical terms as a special case of a navigational isosurface, is determined. The developed methodology is proposed for effective verification of the reliability of big geospatial data. The prospective importance of proper mathematical processing of marine spatial data from geographic information systems is emphasized as a priority in providing consumers with reliable information for practical purposes. The relevance of the need to conduct a qualitative study of navigational isosurfaces to successfully approximate them from the unified standpoint of spline function theory coincides with the prediction of the emergence of complex hypothetical isolines, which are expected to be studied during the evolution of technical means of navigation.