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From Cartography of the Universe to Molecular Cartography – the Use of Map Projections

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From Cartography of the Universe to Molecular Cartography – the Use of Map Projections Polish Cartographical Review Vol. 47, 2015, no. 4, pp. 191–201 DOI: 10.1515/pcr-2015-0014 PAWEŁ PĘDZICH Department of Cartography Faculty of Geodesy and Cartography, Warsaw University of Technology [email protected] From cartography of the Universe to molecular cartography – the use of map projections Abstract. Map projections are very important in the compilation of various types of maps and spatial databases. Geographical information systems provide their users with the significant opportunities in the choice of map projections, coordinate systems, their definitions and transitions between them. The role of map projection can be considered depending on an objective, for which a map has to be used, user of this map and a form of its publication. The Internet, mobile devices and GIS caused that the map projections are used for two main purposes: data visualization and performing of calculations and analyses. The role of map projections is still important, despite the changes occurring in cartography. The rules for the applications of map projections developed over the centuries are still valid. However, the new rules resulting from the new functions of map projections are also created. The aim of this article, that is the author’s overview of map projections, is to illustrate the broad spectrum of applications for the map projections. Keywords: map projections, rules for the selection of map projections, mathematical cartography 1. Introduction by the persons without sufficient knowledge and education in this field. The history of map projections has been counting for more than two thousand years. 2. Small scale map projections The first map projections have appeared in the in geographical atlases antiquity yet, in connection with the compila- tion of the celestial maps. As the years passed, In the case of small scale maps published in along with the development of different areas geographical atlases, the map projections are of life, the new types of maps, as well as the selected mainly – but not only – depending on new map projections, had been being created. an area shown on a map. For the maps of entire During the period of two thousand years hun- globe the map projections compiled by Aitoff, dreds of projections have been elaborated and Hammer, Mollweide are most often used (B. Ogo- used in many different ways. rzelska 2010). J.P. Snyder (1987) also refers Numerous books and articles have been to the map projections by Eckert IV and VI, written about the selective methods of maps, McBryde, Boggs, Robinson, as well as the depending on the objectives, for which a map sinusoidal map projections and cylindrical ones does a good service. Known in Poland and by Mercator and Miller. To present the maps repeatedly cited in the literature, a compilation of hemispheres the transverse azimuthal pro- done by F. Uhorczak (1962) presents the use jections by Lambert, Postel, Nicolosi or stereo- of map projections to develop the small scale graphic and orthographic ones are used. On the maps. There are a lot of publications on this maps of the polar regions normal azimuthal pro- subject, e.g. the work written by J.P. Snyder jections are used, while for the mapping of the (1987). Although, this subject is worth bringing continents conical map projections by Albers, to the readers, especially at the time, when Lambert, Delisle, Ptolemais are most commonly a great deal of maps are compiled increasingly used, as well as pseudoconic one by Bonne, 192 Paweł Pędzich azimuthal by Lambert, and stereographic projec- tion in an oblique position (B. Ogorzelska 2010). 3. Map projections used in navigation In the case of navigational maps, traditionally dominated map projections are: the Postel projection, gnomonic projection and Mercator projection. The Postel projection is used in the marine and terrestrial radio communication, as Fig. 1. Loximuthal projection (J.P. Snyder 1987) well as for the compilation of tele-communica- tional maps, due to the keeping of the lengths of lines, which go from the centre point of a map. In the gnomonic projection all the orthodro- mes become the straight lines, therefore it is used for planning of long cruises. Because of a large map projection distortion, the large areas of globe should not be represented on the maps of this projection. The Mercator projec- tion due to its conformal properties and linear Fig. 2. Two-point azimuthal equidistant projection loxodromic map projection is also used in the (https://ktwop.files.wordpress.com/2012/09/ navigation. The projection of loxodromes to unusual-map-projections-tobler-1999.pdf) the straight lines is a convenient property of the projections used in the navigation. One should be aware, that, unfortunately, the length loxodromic distortions within the Mercator pro- had been being used as the default, i.e. they jection are very considerable. had been being reverted automatically to a pre- An interesting example of the projections pre- selected option, for the initial period, but it was serving the loxodromic lengths and azimuths not a hard rule. In practice, due to the lack of in- are the so called loximuthal projections (fig. 1). ternational standards concerning the use of map These are pseudoconic projections – neither projections in ECDIS, the commercial systems conformal nor equal-area ones. The loxodromes, provide us with the various choices of map routed from a central point, preserve the lengths projections (A. Pallikaris 2014). and azimuths in these projections. Another interesting projection, which could 4. Projections of topographic be used in the navigation, is the azimuthal and general topographic maps two-point projection (fig. 2). It is neither equal- -area nor equiangular projection, it has two The map projection UTM (Universal Trans- points, from which all the directions are preserved. verse Mercator) is a standard for the compila- It can be used to determine the position of a ship tion of topographic maps all over the word. This at sea, e.g., if the exact positions of those two projection is a modification of the previously radio transmitters and the directions from the developed Gauss-Krüger projection, with the ship to the transmitters are known. Other two- fixed scale of 0.9996 on the axial meridians in -point equidistant projection retains the lengths the six-degreed projection zones. UTM projec- of lines connecting the two selected points on tion has been used for the development of the sphere with any other point of this sphere. topographic maps in Poland. Different scale This projection can be used to determine the values on the axial meridians depending on distance to the ship, if its location between the the system of coordinates have been applied. beginning and end of the trip is known. The Lambert projection, which is a conical A number of different map projections has equiangular projection, is used at today’s been used in ECDIS (Electronic Chart Display general topographic maps at the scales of Information System). The plate carrée projec- 1:500,000 and 1:1,000,000. This projection is the tion, as well as the Mercator projection, usually basis for the systems of coordinates PL-LCC From cartography of the Universe to molecular cartography – the use of map projections 193 in Poland. It is also used by many other countries the shape of the Earth, ellipsoidal reference to develop the navigation aeronautical charts. systems, systems of geographical coordinates, On the other hand, the azimuthal stereogra- map projections, measurement units etc., has phic projection is used as a standard for the compiled by this organization (http://www.gis- compilation of topographic maps of the polar -support.pl/co-to-jest-epsg/). areas. It has been used in the armies of NATO as the basis for the construction of GRID’s Regi- 6. Map projections in web mapping stration UPS (Universal Polar Stereographic). The online maps can be compiled in various 5. Map projections used in the spatial projections, depending on the purpose and des- analysis and GIS tination, but the projection called WebMercator, which is a modification of the Mercator projec- The map projections have a dual role in the tion and is the standard in the online mapping geographic informational systems. They are used applications, such as Google Maps, Bing Maps, to compile the maps presenting the results of MapQuest, deserves our special attention. spatial analysis and to perform the calcula- This map projection is used in the spherical tions and analysis. form, even while projecting the ellipsoid, which Seeing that the contemporary GIS software means, that it is not strict a conformal and the allows for the relatively easy transformation of loxodromes do not reproduce themselves map projections, so, any user, more or less exactly into the straight lines. Due to the simple consciously, can compile his or her own map in mathematical formulas, it offers the possibility a map projection freely chosen by him/herself. of high-speed computing. Since the poles are According to M. Maher (2010), it is a user, projected at the infinity, a map of the whole who decides about a choice of map projection world in the WebMercator projection is limited for a project, which is performing by him/her. to a strip between the parallels of the latitudes The author gives the general principles and ±85.051129°. This map projection is an inappro- criteria for the selection of map projections priate one for the compilation of a map, which from GIS, depending on a scale of a map, as depicts the whole globe or the areas sized as well as a size and location of the geographical the continents or large countries. regions. In order to avoid these disadvantages, B. Jenny While compiling the maps, presenting the (2012) proposed to use the so-called adapting results of spatial analysis in relation to the certain map projections.
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