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

Authors

DOI:

https://doi.org/10.31548/zemleustriy2025.02.0%25p

Keywords:

geodetic area, geodetic projections, area distortion, correction to calculated area

Abstract

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.

Key words: geodetic area, geodetic projections, area distortion, correction to calculated area.

Author Biographies

  • S. Radov, Cherkasy State Technological University 
    Candidate of Technical Sciences, Associate Professor
  • S. Rotte, Cherkasy State Technological University 
    Candidate of Technical Sciences, Associate Professor
  • A. Volontyr, Cherkasy State Technological University 
    senior teacher
  • V. Lytvyn, Cherkasy State Technological University 
    assistant
  • P. Stanko, Cherkasy State Technological University 
    assistant

References

1. Hudz, I. M. (2021). Osnovy matematychnoyi kartohrafiyi [Fundamentals of Mathematical Cartography]. Lviv: Lviv Polytechnic Publishing House, 504.

2. Ministry of Agrarian Policy and Food of Ukraine. (2016, December 2). Procedure for the use of the State Geodetic Reference Coordinate System USK-2000 in land management works, 509. Availabte at: https://zakon.rada.gov.ua/laws/show/z1646-16#Text.

3. Kin, D., & Karpinskyi, Y. (2020). Peculiarities of the method of calculation feature’s geodetic area on the reference ellipsoid in GIS. International Conference of Young Professionals «GeoTerrace-2020». DOI: https://doi.org/10.3997/2214-4609.20205757.

4. Kin, D. (2024). Shchodo pidvyshchennya tochnosti analitychnykh ta chyselʹnykh metodiv heodezychnykh ta kartometrychnykh operatsiy [To improve the accuracy of analytical and numerical methods of geodetic and cartometric operations]. Current achievements of geodetic science and industry. Issue І (47), 149-160. DOI: https://doi.org/10.33841/1819-1339-1-47-149-160.

5. Radov, S., Rotte, S., Soboliev, M., Lytvyn, V. & Volontyr, A. (2025). Vysokotochnyy alhorytm peretvorennya koordynat dlya rivnopromizhnoyi poperechnoyi tsylindrychnoyi proektsiyi [High-precision coordinate transformation algorithm for equidistant transverse cylindrical projection]. Interdepartmental scientific and technical collection "Geodesy, cartography and aerial photography", 101, 26-33. DOI: https://doi.org/10.23939/istcgcap2025.101.026.

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Published

2025-06-30

Issue

No. 2 (2025): Land management, cadastre and land monitoring

Section

Topographic and Geodetic and Сartographic Support in Land Management

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