Double stereographic projection as an alternative to UTM for large scale maps

Abbasi, Madjid; Dousti, Reza; Afsharnia, Hamed

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Volume 15, Issue 1 (9-2025)

JGST 2025, 15(1): 1-25

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Double stereographic projection as an alternative to UTM for large scale maps

Madjid Abbasi ^*

, Reza Dousti

, Hamed Afsharnia

Abstract: (150 Views)

The UTM projection is practically the standard map projection used in Iran. For medium and small-scale maps, there is not much problem in using UTM, but in large-scale maps where the high accuracy quantities are extracted, the inherent distortions caused by projecting the geometric features from the Earth’s surface to the plane are inevitable. It is easy to show that with this projection system, one kilometer distance on the Earth’s surface may differ up to tens of centimeters with its corresponding length on the map. On the other hand, the coordinate system changes from one UTM zone to another, which may confuse map users as well as some surveyors in transition areas. Although this problem is not specific to UTM, the problem can be reduced by choosing planar projections. Most of the map users prefer to avoid the coordinate system change and the distortions due to the map projection. As a result, most surveyors in Iran use a kind of local coordinate system with the contradictory name of "local UTM". Assuming a spherical earth with smooth topographical features up to a radius of less than 30km, this localization procedure is an "azimuthal" planar projection. In this case, the distances in the radial direction relative to a central point are undistorted. In rough topography, however, this projection system is neither conformal nor equidistant. In this research, the problems caused by this localization approach are discussed in detail, and the use of a double stereographic projection is proposed as a solution. The advantage of this projection is that it is conformal and equidistant up to about 30 km from a central point. The scale factor is practically equal to unity; thus, it does not apply significant distortion to the projected geometric features. After the theoretical analysis, some numerical examples of the behavior of height, grid and combined scale factors, as well as the discussed map projections are presented.

Article number: 1

Keywords: large-scale maps, UTM projection, Equidistant Azimuthal projection, Double Stereographic projection

Full-Text [PDF 3186 kb] (117 Downloads)

Type of Study: Research | Subject: Geo&Hydro
Received: 2024/07/21

References

1. Annoni A., C. Luzet, E. Gubler and J. Ihde (2003) Map Projections for Europe. European Commission Joint Research Center, Printed in Italy

2. Anvaari M.A. (1999) Choosing a Proper Map Projection for Khorasan Province. Proc. of Geomatics Conference, NCC, pp. 71-80 (in Persian)

3. Bomford G. (1980) Geodesy. Clarendon Press, Oxford. Fourth Edition, pp. 82-85

4. Habib M. (2013) Proposal for Developing the Syrian Stereographic Projection. Survey Review, Volume 40, Issue 307, pp. 92-101 [DOI:10.1179/003962608X253547]

5. Hradilek H. and A. C. Hamilton (1973) Systematic Analysis of Distortions in Map Projections. Technical report No. 34, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Canada

6. Iranian Planning and Budget Organization (2005) Surveying Uniform Instructions, Fourth Volume: Cartography. Office of Technical Affairs, Development of Criteria and Reduction of Earthquake Risk, P. 3 (in Persian)

7. Krakiwsky E.J. (1973) Conformal Map Projections in Geodesy. Technical report No. 37, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Canada

8. Marshak S. and Mitra G. (1988). Basic methods of structural geology. Englewood Cliffs, N.J: Prentice Hall. Chicago, USA

9. Ramouz S., Y. Afrasteh, M. Reguzzoni, A. Safari, A. Saadat (2019). IRG2018: A regional geoid model in Iran using Least Squares Collocation. Studia Geophysica et Geodaetica, 63(2), pp. 191-214 [DOI:10.1007/s11200-018-0116-4]

10. Salehi M., J. Asgari and A. Amiri-Simkooei (2016) Precise Coordinate Transformation Between Local System and UTM by Height Interpolation of LiDAR Points (Case Study: City of Isfahan). Scientific-Research Quarterly of Geographical Data (SEPEHR), Vol 25, No. 97, pp. 67-79 (in Persian)

11. Sarpoolaki M., B. Shami and M. Seddighi (2005) Coordinate System and Map Projection used in NCC Maps. NCC Publications, 964-69232-35-X, pp. 5-6 (in Persian)

12. Snyder J.P. (1987) Map Projections-A Working Manual. U.S. Geological Survey Professional paper 1395, Unites States Printing Office, Washington [DOI:10.3133/pp1395]

13. Thomson D.B., M.P. Mephan and R.R. Steeves (1977) The Stereographic Double Projection. Technical report No. 46, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Canada

14. Tong X., D. Liang, G. Xu and S. Zhang (2011) Positional accuracy improvement: a comparative study in Shanghai, China. International Journal of Geographical Information Science, 25:7, 1147-1171, DOI: 10.1080/13658816.2010.515948 [DOI:10.1080/13658816.2010.515948]

15. Tutić D. and L. Miljenko (2008) Stereographic Map Projection of Croatia. 13th International Conference on Geometry and Graphics (ICGG 2008): Proc. Weiss, Gunter. https://www.bib.irb.hr/366767

16. USGS report No. 70047422 (1993) Map Projections. DOI: 10.3133/70047422 [DOI:10.3133/70047422]

17. Vaníček, P., E. Krakiwsky (1986) Geodesy the Concepts, second ed., North-Holland Publishing Company. p. 352

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Abbasi M, Dousti R, Afsharnia H. Double stereographic projection as an alternative to UTM for large scale maps. JGST 2025; 15 (1) : 1
URL: http://jgst.issgeac.ir/article-1-1198-en.html

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Volume 15, Issue 1 (9-2025)

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