The phenomenon of topological inconsistencies of frames of map sheets during the creation of the main state topographic map

1
Kyiv National University of Construction and Architecture
2
Research Institute of Geodesy and Cartography

The aim of this work – research of topological inconsistencies during adjustment and junction of adjacent map sheets of digital topographic maps of scale 1:50000 with the use of rigorous analytical geodetic methods on the reference ellipsoid in the geoinformation environment. The research analyzes the phenomenon of topological inconsistencies of frames of adjacent digital topographic maps of 1:50000 scale within the zones of Gauss-Krueger projections and the feasibility of transition to rigorous analytical geodetic methods in the geoinformation environment during the creation of the topographic database “The Main state topographic map” by determining the differences between the vertices of the frames of digital topographic maps at a scale of 1: 50000 at the boundaries of the projection zones. This phenomenon was discovered during work at the state enterprise “Research Institute of Geodesy and Cartography”. The dependences are shown and analyzed, which show the changes in the distances between the vertices of the frames of adjacent map sheets of scale 1: 50000 in longitude and latitude. These values range from 1 mm to 8 mm, which leads to topological inconsistencies in the form of gaps and overlaps of adjacent map sheets. These gaps and overlaps complicate the process of adjustment of map sheets and make it impossible to automate the process of the junction of features into the topographic database. The scientific novelty of the research is to justify the use of rigorous analytical geodetic methods and tools instead of analog cartometric and standard methods of instrumental GIS; the use of a reference ellipsoid, not just cartographic projections, a spheroid or a sphere. The practical significance of research is the use of rigorous analytical geodetic methods that significantly minimize the values of gaps and overlaps, as the establishment of tolerances for these values does not automate the process of correct adjustment and junction of map sheets. The performed research can be used to create the topographic database “The Basic topographic map scale 1: 10000”, during the creation and updating of geospatial data in the geoinformation environment and the implementation of geodetic methods to determine the cartometric characteristics of features using GIS. Given the results of research, we can conclude that the present stage of application of geographic information systems in topographic and geodetic activities requires increasing the level of data topology and accuracy of all cartometric methods, which leads to the transition to extremely rigorous analytical geodetic methods directly on the reference ellipsoid.

  1. Baranovskyi, V., Karpinskyi, Yu., & Lyashchenko, A. (2009a). Topographic, geodetic and cartographic support of the state land cadastre. Determination of areas of territories. K.: Research Institute of Geodesy and Cartography, 92. (in Ukrainian).
  2. Baranovskyi, V., Karpinskyi, Yu., Lyashchenko, A. Kucher O., (2009b). Topographic, geodetic and cartographic support of the state land cadastre. Coordinate systems and cartographic projections. K.: Research Institute of Geodesy and Cartography, 96. (in Ukrainian).
  3. Baselga, S., & Olsen, M. J. (2021). Approximations, Errors, and Misconceptions in the Use of Map Projections. Mathematical Problems in Engineering, 2021. https://doi.org/10.1155/2021/1094602
  4. Berk, S., & Ferlan, M. (2018). Accurate area determination in the cadaster: Case study of Slovenia. cartography and geographic information science45(1), 1-17. https://doi.org/10.1080/15230406.2016.1217789
  5. Cazabal-Valencia, L., Caballero-Morales, S. O., & Martínez-Flores, J. L. (2016). Logistic model for the facility location problem on ellipsoids. International Journal of Engineering Business Management8, https://doi.org/10.1177/1847979016668979.
  6. Chamberlain, R. G., & Duquette, W. H. (2007). Some algorithms for polygons on a sphere. Pasadena, CA: Jet Propulsion Laboratory. http://hdl.handle.net/2014/40409
  7. Dong, J., Ji, H., Tang, L., Peng, R., & Zhang, Z. (2021). Accuracy analysis and verification of the method for calculation of geodetic problem on earth ellipsoid surface. In E3S Web of Conferences (Vol. 245, p. 02033). EDP Sciences. https://doi.org/10.1051/e3sconf/202124502033
  8. Fisikopoulos, V. (2019). Geodesic Algorithms: An Experimental Study. International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 42(4/W14), 45-47. https://pdfs.semanticscholar.org/0fd3/7bed6be199ee1766ae46a6ec2ed409d030...https://doi.org/10.5194/isprs-archives-XLII-4-W14-45-2019
  9. Galo, M., Monico, J. F. G., & Oliveira, L. C. (2003). Cálculo de áreas de polígonos sobre o elipsóide usando projeções equivalentes. Curitiba: Universidade Federal do Paraná, 465-479. http://dx.doi.org/10.13140/2.1.3233.0240
  10. Gojković, Z., Radojičić, M., & Vulović, N. (2017). Aplication for coordinate transfomation between Gaus-Kruger projection-Bessel ellipsoid and UTM projection-WGS84 ellipsoid. Podzemni radovi, (30), 29-45. https://doi.org/10.5937/podrad1730029Z
  11. Guidance on the determination of design hydrological characteristics. L., Gidrometeoizdat, 1973. 112 с. (in Russian). https://www.twirpx.com/file/1390547/
  12. Huang, H. (2017). Estimating area of vector polygons on spherical and ellipsoidal earth models with application in estimating regional carbon flows. Student thesis series INES. http://lup.lub.lu.se/luur/download?func=downloadFile&recordOId=8921924&fileOId=8922096.
  13. Idrizi Bashkim (2020) Necessity for geometric corrections of distances in web and mobile maps. Proceedings Vol. 1, 8th International Conference on Cartography and GIS, Nessebar, Bulgaria. 462-470.
  14. Karney, C. (2013). Algorithms for geodesics. Journal of Geodesy, 87, 43–55. https://doi.org/10.1007/s00190-012-0578-z.
  15. Karney, C. F. (2011). Transverse Mercator with an accuracy of a few nanometers. Journal of Geodesy, 85(8), 475-485. https://doi.org/10.1007/s00190-011-0445-3.
  16. Karpinskyi Yu. (2015). System-technical aspects of formation of topological land cadastral coverage. Bulletin of Geodesy and Cartography. Kyiv, No 5-6 (98-99), P. 62-68. (in Ukrainian). http://nbuv.gov.ua/UJRN/vgtk_2015_5-6_13
  17. Karpinskyi, Yu., & Kin, D. (2018). Research cartometric operations in the environment of GIS. Urban planning and spatial planning, 68, 706-711. (in Ukrainian). http://repositary.knuba.edu.ua//handle/987654321/7068
  18. Karpinskyi Yu., & Kin D. (2020). Research of the transition from cartometric to analytical operations. XXV Jubilee International Scientific and Technical Conference «Geoforum – 2020», Lviv, Ukraine. https://doi.org/10.13140/RG.2.2.34353.40806.
  19. 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» (Vol. 2020, No. 1, pp. 1-5). European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.20205757
  20. Kin, D., & Karpinskyi, Y. (2021). Ontology of geodetic, cartometric and morphometric methods in the geoinformation environment. In Geoinformatics (Vol. 2021, No. 1, pp. 1-6). European Association of Geoscientists & Engineers. https://doi.org/10.3997/2214-4609.20215521101
  21. Lazorenko-Hevel, N., & Kin, D. (2019). The edge matching method of digital topographic maps in the scale of 1:50000 for creation the main state topographic map. Engineering geodesy, 67, 56–66. (in Ukrainian). https://doi.org/10.32347/0130-6014.2019.67.56-66
  22. Lazorenko-Hevel N., Karpinskyi Yu. & Kin D. Some peculiarities of creation (updating) of digital topographic maps for the seamless topographic database of the Main State Topographic Map in Ukraine. (2021). Geoingegneria Ambientale e Mineraria, Anno LVIII, n. 1, p 19-24. https://doi.org/10.31490/9788024845050-8
  23. Maling, D. H. (1989). Measurements from maps: principles and methods of cartometry. Oxford: Pergamon presshttps://doi.org/10.1016/B978-0-08-030290-4.50010-4
  24. Martínez-Llario, J. C., Baselga, S., & Coll, E. (2021). Accurate algorithms for spatial operations on the spheroid in a spatial database management system. Applied Sciences, 11(11), 5129.https://doi.org/10.3390/app11115129.
  25. Marx, C. (2021). Performance of a solution of the direct geodetic problem by Taylor series of Cartesian coordinates. Journal of Geodetic Science, 11(1), 122-130. https://doi.org/10.1515/jogs-2020-0127
  26. Morgaś, W., & Kopacz, Z. (2016). Analytical dependence relations of converting geodetic coordinates into UTM coordinates recommended in hydrographic work. Zeszyty Naukowe Akademii Marynarki Wojennej57(2 (205)), 61-73. https://doi.org/10.5604/0860889X.1219971
  27. Morgaś, W., & Kopacz, Z. (2017). Conversion of geodetic coordinates into flat (2-dimensinal) coordinates PL-UTM for the purposes of navigation. Zeszyty Naukowe Akademii Marynarki Wojennej58. https://doi.org/10.5604/0860889X.1237622
  28. Nishiyama, Y. (2012). Measuring Areas: From Polygons to Land Maps. International Journal of Pure and Applied Mathematics, 81(1), 91-99. http://www.ijpam.eu/
  29. Panou, G., Delikaraoglou, D., & Korakitis, R. (2013). Solving the geodesics on the ellipsoid as a boundary value problem. Journal of Geodetic Science3(1), 40-47. https://doi.org/10.2478/jogs-2013-0007
  30. Panou, G., & Korakitis, R. (2021). Analytical and numerical methods of converting Cartesian to ellipsoidal coordinates. Journal of Geodetic Science, 11(1), 111-121 https://doi.org/10.1515/jogs-2020-0126
  31. Pędzich, P., Balcerzak, J., & Panasiuk, J. (2009). New approach to the Gauss-Kruger projection of an ellipsoid onta a sphere (No. R3/RS). Department of Cartography, p. 11. https://repo.pw.edu.pl/info/report/WUT31f242c159a84e35aa3642ca455cff39/#...
  32. Pędzich, P. & Kuźma, M. (2012). Application of methods for area calculation of geodesic polygons on Polish administrative units. Geodesy and Cartography, vol. 61, nr 2, pp. 105 – 115. https://doi.org/10.2478/v10277-012-0025-6
  33. Rapp, R. H. (1993). Geometric geodesy part 2. The Ohio State University.
  34. Rechtzamer, G. R. (1974). Fundamentals of cartography (textbook). L., 217. (in Russian). https://www.twirpx.com/file/1390547/
  35. Setiawan, A., & Sediyono, E. (2020). Area calculation based on GADM geographic information system database. Telkomnika, 18(3), 1416-1421. http://doi.org/10.12928/telkomnika.v18i3.14901
  36. Sjöberg, L. E., & Shirazian, M. (2012). Solving the direct and inverse geodetic problems on the ellipsoid by numerical integration. Journal of Surveying Engineering138(1), 9-16. https://www.diva-portal.org/smash/record.jsf?pid=diva2%3A515798&dswid=-9...https://doi.org/10.1061/(ASCE)SU.1943-5428.0000061
  37. Turiño, C. E. (2008). Gauss Krüger projection for areas of wide longitudinal extent. International Journal of Geographical Information Science22(6), 703-719. https://doi.org/10.1080/13658810701602286
  38. Vermeer, M., & Rasila, A. (2019). Map of the World: An Introduction to Mathematical Geodesy. CRC Press. https://doi.org/10.1201/9780429265990
  39. Voser, S. A. (1999). Cartometric Aspects of Hybrid Analysis within GIS. Semantic Modelling for the Acquisition of Topographic Information from Images and Maps, 61. http://mapref.org/savpub/LinkedDocuments/voser-smati99.pdf
  40. Yildirim, F. & Kadi, F. (2021). Determining the area corrections affecting the map areas in GIS applications. Reports on Geodesy and Geoinformatics, 112(1) 9-17. https://doi.org/10.2478/rgg-2021-0003.