The existing level of numerical methods of geodetic and cartometric operations does not correspond to the current level of development of computer geographic information technologies, and standard tools of instrumental geographic information systems use approximate numerical methods. The approximation of these methods is to use, as a rule, a Taylor series with a limited number of terms without considering the Earth's curvature. This does not ensure their effective use in geoinformation analysis and modelling. The study's relevance is substantiated by the need to improve these methods by moving from approximate to rigorous numerical methods and using the reference ellipsoid surface. Previous studies have shown that standard methods of instrumental geographic information systems are not strict, but approximate, since mathematical models use a limited number of terms in the Taylor series. The research aims to apply rigorous mathematical methods to improve the accuracy of analytical and numerical methods of geodetic and cartometric operations in geographic information systems. The advantage of the proposed analytical and numerical methods of cartometric, geodetic, and morphometric operations on the reference ellipsoid is that they significantly increase the accuracy of calculating the metric characteristics of geospatial objects due to the proposed numerical methods.
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