Evaluation of Topography-to-Projection Distortions in the State Coordinate System of North Macedonia

Year 2026, Volume: 10 Issue: 1, 213 - 221, 16.12.2025

Bashkim Idrizi

https://doi.org/10.31127/tuje.1795368

Abstract

Accurate geodetic reference systems are fundamental for surveying, cartography, engineering, and spatial data management. In North Macedonia, the process of reducing measured lengths from the Earth’s surface to a two-dimensional map projection involves three successive transformations: from the topographic surface to the geoid, from the geoid to the reference ellipsoid, and from the ellipsoid to the adopted map projection. Each step introduces measurable length differences which, if not properly considered, may lead to distortions in geospatial datasets and reduced reliability of the national coordinate system.
This study presents a comprehensive analysis of length differences for the entire territory of North Macedonia. A test grid of 25,635 points at 1 km spatial resolution was developed, enabling detailed assessment across the national area. Calculations were performed using mathematical models of geodesy and cartography, implemented in QGIS and spreadsheet environments.
The analysis focused on three representative map projections: UTM zone 34N, the official Macedonian Gauss–Krüger projection (central meridian 21°, scale factor 0.9999), and a modified Gauss–Krüger projection with displaced central meridian and adjusted scale factor. Results indicate substantial differences in mean linear deformations: −46.01 cm/km for UTM 34N, −16.01 cm/km for the state projection, and −17.17 cm/km for the modified Gauss–Krüger projection. Local variations ranged from negative values exceeding −80 cm/km to positive differences of nearly +20 cm/km, with spatially uneven distribution across the territory.
Comparative insights with neighboring Balkan countries demonstrate that Macedonia’s mountainous relief amplifies elevation-related distortions, whereas lowland countries record lower values. The findings underline the necessity of incorporating elevation effects when defining or reforming state coordinate systems. The study contributes directly to ongoing discussions on modernization of North Macedonia’s geodetic framework, particularly in relation to the prospective adoption of ETRS89 with GRS80.

Keywords

North Macedonia , Coordinate Reference System , Map Projections , Distortions , Length differences

Ethical Statement

Author does not have any conflict of interest with journal editorial board.

Supporting Institution

South-East European Research Institute on Geo Sciences - Skopje

Project Number

10.17605/OSF.IO/MPUHG

Thanks

This article is based on results from the National Scientific Project “State Plane Coordinate Reference System of the Republic of North Macedonia” (DOI: 10.17605/OSF.IO/MPUHG), publicly accessible at www.scrsproject.mk. The author gratefully acknowledges the South East European Research Institute on Geosciences and all project partners for their valuable collaboration and for granting permission to use project data in this publication. The article will also be referenced on the project’s official website following its publication.

References

• Idrizi, B. and Ribarovski, R. (2010). Historical overview, quality and current condition of the geodetic networks in Macedonia. FIG Working Week Proceedings, April 11-16, 2010, Sydney, Australia. https://www.fig.net/resources/proceedings/fig_proceedings/fig2010/papers/ts01h/ts01h_idrizi_ribarovski_4242.pdf
• Grafarend E., Krumm F., (2014): Map projections, Cartographic Information Systems; Springer. DOI 10.1007/978-3-642-36494-5.
• Idrizi, B. (2015). Developing Raster Datasets for Length Differences between Topography, Geoid, Ellipsoid and Map Projection for Macedonian Territory. FIG WW 2015 Proceedings. https://www.fig.net/resources/proceedings/fig_proceedings/fig2015/papers/ts04d/TS04D_idrizi_7798.pdf
• Dennis, M. L. (2016). Ground truth: Low distortion map projections for engineering, surveying, and GIS. In B. L. Livingston, C. Cate III, A. Pridmore, J. W. Heidrick, & J. Geisbush (Eds.), Proceedings of Pipelines 2016: Out of sight, out of mind, not out of risk (pp. 857–869). ASCE. https://ascelibrary.org/doi/10.1061/9780784479957.079
• Dennis, M. (2023). The future is here: Introducing the State Plane Coordinate System of 2022. FIG proceedings 2023. https://fig.net/resources/proceedings/fig_proceedings/fig2023/papers/cinema03/CINEMA03_dennis_12044.pdf
• Rollins, C. M., & Meyer, T. H. (2019). Four methods for low-distortion projections. Journal of Surveying Engineering, 145(4). https://doi.org/10.1061/(ASCE)SU.1943-5428.0000295
• Vonderohe, A. P., & Dennis, M. L. (2022). Minimizing root-mean-square linear distortion in common conformal map projections. Journal of Surveying Engineering, 148(1). https://doi.org/10.1061/(ASCE)SU.1943-5428.0000381
• Baselga Moreno, S. (2021). Two conformal projections for constant-height surface to plane mapping. Journal of Surveying Engineering, 147(2). https://doi.org/10.1061/(ASCE)SU.1943-5428.0000345
• Baselga Moreno, S. (2020). Optimising 2-parameter Lambert conformal conic projections for ground-to-grid distortions. Survey Review, 53(380), 415–421. https://doi.org/10.1080/00396265.2020.1797339
• Idrizi B. (2006): Developing of globally homogeneous geographic data set through Global mapping project; Kartografija i geoinformacije; Zagreb. ISSN 1333-896X. https://hrcak.srce.hr/clanak/9676
• Idrizi, B. (2013). Developing model for utilization Global Earth Gravimetrical Models in Macedonian territory. Proceedings - FIG Working Week, Abuja, Nigeria. ISBN: 978-87-92853-05-3, ISSN 2307-4086
• Iliffe J., Lott R. (2008): Datums and map projections; Whittles publishing; Scotland. ISBN: 978-1904445-47-0
• Official Gazette No. 55. Year 2013. Law for real estate cadaster. Agency for real estate cadaster. Skopje. North Macedonia. https://www.katastar.gov.mk/wp-content/uploads/Regulativa/zakoni/zakoni/Zakon%20za%20KN%202013.pdf
• Official Gazette No. 151. Year 2013. Regulation for basic geodetic works. Agency for real estate cadaster. Skopje. North Macedonia. https://www.katastar.gov.mk/wp-content/uploads/Regulativa/Pravilnici/osnovni%20geodetski%20raboti.pdf
• Official Gazette No. 159. Year 2013. Regulation for compilation of topographic maps, ortho photo maps/plans and cartographic products. Skopje. North Macedonia. https://www.katastar.gov.mk/wp-content/uploads/Regulativa/Pravilnici/topografski%20karti15913.pdf
• Ribarovski, R., Markoski, B., Srbinoski, S., & Jovanov, J. (1998). Избор на најсоодветна картографска проекција за претставување на територијата на Република Македонија [Choice of the best map projection for projecting the territory of the Republic of Macedonia]. Scientific project, University “St. Cyril and Methodius,” Faculty of Civil Engineering, Department of Geodesy. Skopje.
• Idrizi, B. Pashova, L. Kabashi, I. Mulic, M. Krdzalic, D. Tutic, D. Vucetic, N. Kevic, K. Nikolic, G. Djurovic, R. (2018). Study on length differences from topography to map projection within the state coordinate systems for some countries on the Balkan Peninsula. FIG Working Week 2018. Istanbul. Turkey. https://fig.net/resources/proceedings/fig_proceedings/fig2018/papers/ts08e/TS08E_idrizi_pashova_et_al_9602.pdf
• Snyder, J. P. (1987). Map projections--A working manual (Vol. 1395). US Government Printing Office. https://pubs.usgs.gov/pp/1395/report.pdf
• Snyder, J. P. (1997). Flattening the earth: two thousand years of map projections. University of Chicago Press. https://press.uchicago.edu/ucp/books/book/chicago/F/bo3632853.html
• Bugayevskiy, L. M., & Snyder, J. (1995). Map projections: A reference manual. CRC Press. https://www.taylorfrancis.com/books/mono/10.1201/b16431/map-projections-bugayevskiy-john-snyder
• International Standardization Organization, 2019. Geographic information — Referencing by coordinates. ISO 19111:2019 https://www.iso.org/standard/74039.html (accessed July 2025)
• Bruyninx, C. et al. (2015). Implementation of the ETRS89 in Europe: Current Status and Challenges. In: van Dam, T. (eds) REFAG 2014. International Association of Geodesy Symposia, vol 146. Springer, Cham. https://doi.org/10.1007/1345_2015_130
• Staudinger, M. (1999). Spatial reference systems: the OGC’s efforts and concepts of measurement-based GIS. Spatial reference systems for Europe proceedings, http://www.crs-geo.eu/pub03ProceedingsWS1999.pdf
• Şasi, A., & Yakar, M. (2017). Photogrammetric modelling of Sakahane masjid using an unmanned aerial vehicle. Turkish Journal of Engineering, 1(2), 82-87. https://doi.org/10.31127/tuje.316675
• Yakar, M., Yilmaz, H. M., & Yurt, K. (2010). The effect of grid resolution in defining terrain surface. Experimental Techniques, 34(6), 23-29.
• Karataş, L., Alptekin, A., Karabacak, A., & Yakar, M. (2022). Detection and documentation of stone material deterioration in historical masonry buildings using UAV photogrammetry: A case study of Mersin Sarisih Inn. Mersin Photogrammetry Journal, 4(2), 53-61
• Karataş, L., Alptekin, A., Karabacak, A., & Yakar, M. (2022). Detection and documentation of stone material deterioration in historical masonry buildings using UAV photogrammetry: A case study of Mersin Sarisih Inn. Mersin Photogrammetry Journal, 4(2), 53-61.
• Çimen, Ö., & Günaydın, H. İ. (2024). Assessment of engineering geology and grouting applications in Yalnızardıç Dam Site (Antalya, Türkiye). Turkish Journal of Engineering, 8(1), 20-30. https://doi.org/10.31127/tuje.1221774
• Kesikoğlu, M. H., Çiçekli, S. Y., & Kaynak, T. (2020). The identification of seasonal coastline changes from Landsat 8 satellite data using artificial neural networks and k-nearest neighbor. Turkish Journal of Engineering, 4(1), 47-56. https://doi.org/10.31127/tuje.599359
• Institute, G. (2025). National Scientific Project: State Plane Coordinate Reference System - Republic of North Macedonia. https://doi.org/10.17605/OSF.IO/MPUHG