Refined algorithm for calculating area distortion adjustments of geospatial objects in geodetic projections

<ns0:p>Area, as one of the fundamental geometric parameters of land parcels, is a key factor in land management, land cadaster, land taxation, and related fields. The geodetic area should ideally be determined on the surface of the reference ellipsoid; however, in engineering practice, it is usually calculated from the coordinates of turning points in the Gauss-Krüger projection. The influence of projection is approximately accounted for by introducing a correction to the computed area value derived from rectangular coordinates. At the same time, the geodetic area may differ significantly from its approximate value.There are no exact (closed-form) formulas to calculate the areas of arbitrary parcels on the ellipsoid surface based on the geodetic coordinates of turning points. Therefore, the most accurate values of geodetic areas of geospatial objects are obtained by numerical methods, including those used in geographic information systems.A simpler method of determining “undistorted” land parcel areas relies on equal-area geodetic projections.This study employs the Sanson, Gauss-Krüger and Cassini projections.For the Gauss-Krüger and Cassini projections, algorithms are provided for calculating corrections based on the ordinate of the parcel’s centroid and the ordinates of all turning points. The accuracy of the proposed algorithms has been analyzed using mathematical modeling.</ns0:p>