UDC: 
DOI: 
10.22389/0016-7126-2019-946-4-39-54
1 Lapaine М.
Year: 
№: 
946
Pages: 
39-54

University of Zagreb

1, 
Abstract:
Map projections are commonly approached as mapping onto developable surfaces; cylindrical projections onto the lateral surface of a cylinder, conic projections onto the lateral surface of a cone, and azimuthal projections onto a plane. If an intermediate developable surface intersects the Earth’s sphere or ellipsoid, the projection is referred to as a secant projection. The intersection of a developable surface and the Earth’s sphere or ellipsoid, e.g. secant parallel is considered a standard parallel. In this paper the definitions of secant and standard parallel in azimuthal projections are given. The first conclusion is that the secant and standard parallels are two distinct notions. The second one is that a standard parallel, if such a parallel exists in an azimuthal projection, is a secant parallel, while the converse statement is not true in general. Furthermore, it is shown that there are azimuthal projections with only one secant parallel that is not standard, with only one standard parallel which is also secant one, with two different secant parallels, and with one standard and one secant parallel.
My thanks to Professor Vladimir S. Tikunov and Professor Maksim V. Nyrtsov for helping in preparing this publication for Russia. Special thanks to anonymous REVIEWERS for advice at making the final version of the work.
References: 
1.   Vahrameeva L.A., Bugaevskij L.M., Kazakova Z.L. Matematicheskaya kartografiya: Ucheb. dlya vuzov. M.: Nedra, 1986, 286 p.
2.   Kavrajskij V. V. Izbrannye trudy. – V 2 t. – T. 2. Vyp. 1. Matematicheskaya kartografiya. Obshchaya teoriya kartograficheskih proektsij. Moskva: izd. Upravleniya nachal'nika Gidrograficheskoj sluzhby VMF, 1958, 680 p.
3.   Lebedeva O. A. Kartograficheskie proektsij. Novosibirsk: Novosibirskij uchebno-metodicheskij tsentr po GIS i DZ, 2000, 35 p.
4.   Serapinas B.B. Matematicheskaya kartografiya: Ucheb. posobie dlya vuzov. M.: Izd. centr «Akademiya», 2005, 336 p.
5.   Albrecht J. (2017) Projection concepts used in the 4th GTECH 361 lecture: Tangents and secants. URL: www.geo.hunter.cuny.edu/~jochen/GTECH361/lectures/lecture04/concepts/Map%20coordinate%20systems/Tangents%20and%20secants.htm (accessed: 03.12.2017).
6.   Behrmann W. (1910) Die beste bekannte flächentreue Projektion der ganzen Erde: Petermanns geographische Mitteilungen. Volume 56–2, no. 3, pp. 141–144.
7.   (2017) ESRI. Projections-types. ArcGIS for Desktop, ArcMap. URL: desktop.arcgis.com/en/arcmap/10.3/guide-books/map-projections/projection-types.htm (accessed: 03.12.2017).
8.   (2017) Geokov. Tangent vs. secant cylindrical projection, Tangent vs. secant conical projection, Tangent vs. secant planar projection. URL: geokov.com/education/map-projection.aspx
9.   Kessler F. (2017) Educating a General Readership on Map Projections in Twentieth Century Thematic World Atlases: A Survey, Proceedings of the 28th ICC, Washington DC, 2–7.7.2017. URL: www.eventscribe.com/2017/ICC/agenda.asp?h=Full Schedule (accessed: 03.11.2017).
10.   Lapaine M. (2017) Standard Parallel and Secant Parallel in Azimuthal Projections. Standardna paralela i presječna paralela u azimutnim projekcijama, Kartografija i geoinfromacije. Volume 16, no. 28, pp. 73–88.
11.   Lapaine M. (2017) Map Projection Definition. Definicija kartografske projekcije. Kartografija i geoinformacije, Volume 16, no. 28, pp. 136–137.
12.   (2007) National Programme on Technology Enhanced Learning. Department of Secondary and Higher Education. Ministry of Human Resource Development. Government of India New Delhi. URL: nptel.ac.in/courses/105102015/42 (accessed: 03.12.2017).
13.   Richardus P., Adler R. K. (1972) Map Projections for geodesists, cartographers and geographers, North-Holland Publishing Company, Amsterdam, London.
14.   Slocum T. A., McMaster R. B., Kessler F. C., Howard H. H. (2009) Thematic Cartography and Geovisualization. Third Edition. Pearson. Prentice Hall, Upper Saddle River.
15.   Snyder J. P., Voxland M. P. (1989) Album of Map Projection, U. S. Geological Survey, Professional Paper.
16.   (2000) Map Projections. U. S. Department of the Interior, U. S. Geological Survey, 509 National Center, Reston, VA 20192, USA. URL: rnlnx635.er.usgs.gov/ mac/isb/pubs/MapProjections/projections.html (accessed: 29.10.2017).
17.   Van Sickle J. (2017) Map projection, GEOG 862: GPS and GNSS for Geospatial Professionals, PennState College of Earth and Mineral Sciences, Department of Geography. URL: www.e-education.psu.edu/geog862/node/1808 (accessed: 03.12.2017).
18.   Wayback Machine (2014) Map Projections: From Spherical Earth to Flat Map. URL: nationalatlas.gov/articles/mapping/a_projections.html (accessed: 03.11.2017).
19.   Wikimedia Commons (2016) File: Cylindrical Projection secant. svg. (2016, August 6). URL: commons.wikimedia.org/w/index.php?title=File:Cylindrical_Projection_ secant.svg&oldid=203275591 (accessed: 15.11.2017).
Citation:
Lapaine М., 
(2019) Secant Parallels in Azimuthal Projections. Geodesy and cartography = Geodezia i Kartografia, 80(4), pp. 39-54. (In Russian). DOI: 10.22389/0016-7126-2019-946-4-39-54
Publication History
Received: 26.06.2018
Accepted: 04.03.2019
Published: 20.05.2019

Content

2019 April DOI:
10.22389/0016-7126-2019-946-4

QR-code page

QR-код страницы