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A map projection is the systematic transformation of the curved surface of the earth to the plane of the map. The earth is roughly spherical in shape, and three dimensional. Maps, however, are flat and only two dimensional. There is a variety of ways in which the 3D earth can be translated onto the 2D map, but the process of doing so (map projection) needs to be consistent and thorough if the map is to be credible and ‘accurate’.
The various systems of map projection employed can be expressed as mathematical formulae. Every point on the earth’s surface has a unique location given by its geographical coordinates (latitude and longitude). A systematic map projection takes those geographical coordinates and translates them into Cartesian coordinates (x,y) on the map by means of a mathematical formula. Before the advent of rapid computing power, projecting a map required a great deal of time to calculate, but computer programs are now readily available which allow even very complex map projections to be carried out rapidly.
In converting the 3D earth to Cartesian coordinates, the fixed relationship between all points on the globe cannot be kept and distortions have to be introduced. A map projection may distort angles, areas or distances; any map projection cannot keep more than one of angle, area or distance correct. So for example, it is not possible to have a map which keeps both areas and distances correct.
Map projections fall into one of a number of groups, but there are four main groups of projections: equal area or equivalent (which keep areas correct), equal distance (or equidistant, which keep distances correct), equal angle (also called conformal which keep angles correct), and hybrid (where angles, distances nor areas are correct, but they have other properties such as keeping shapes familiar which make them useful). There are other projections that do not fall into these categories, but they are really only the realm of the specialist.
Within each of those four groups, there are three main methods of taking the 3D globe and transferring it onto the 2D map. The best way to imagine it is to see the earth as an illuminated globe covered with the web of lines of latitude and longitude (the graticule), and with a powerful light bulb in the middle of it. Firstly, imagine a large rectangular sheet of paper wrapped around it so that the paper touches the Equator all the way round. With the light bulb switched on, the graticule projected onto the paper would look like a regular rectangular grid with the lines of the graticule meeting at right angles. This type of projection is called cylindrical or rectangular. The most familiar example is the Mercator projection.
Now make a cone out of the paper and rest it on the globe so that the paper is centred on the North Pole and touches the globe almost on the Equator or on any parallel north of it. The graticule now projected comes out with meridians as straight lines, as if radiating from a point, and parallels as arcs of a circle. This type of projection is called conical. Finally, take the paper and rest it so that it is touching only the North Pole. The pattern now projected has parallels as concentric circles, and meridians radiating from a single point. This type of projection is called azimuthal or planar.
Map projections are given names that show which group they fall into, for example a cylindrical equidistant projection — the name tells you which group it falls into (cylindrical) and its particular property (it is equidistant). A conformal conical projection has correct angles, and is based on a cone. Some map projections have common names by which they are known: for example a conformal cylindrical projection is called a Mercator projection; and a cylindrical equidistant projection is called a Plate Carrée projection. Hybrid projections are usually named after their inventors: for example the Robinson, the Mollweide and the HammerAitoff are all named after the cartographers or mathematicians who devised them.
Which map projection will best suit my needs?
The answer depends partly on the purpose of the map and partly on the proportion of the earth’s surface you need to show. The smaller the scale of the map (i.e. the more of the earth it shows), the more important it becomes to choose the right projection. In particular, if you map a distribution (e.g. income, disease, bird populations, human populations) then it is important to use an equal area projection, or one that is not strictly equal area but distorts the area of world a little whilst keeping the shapes recognisable.
Maps of the world in a single sheet:
Many people expect to see the world shown as a rectangle, because it seems familiar and looks ‘right’ like that. Rectangular projections (also called cylindrical projections) neatly fit onto printed pages. But most rectangular projections are not really the best way of showing the world because they make the round world look as if it has straight edges and sharp corners. The following projections are suitable for mapping the entire world on a single sheet, retaining the familiar shapes of continents:
 Boggs eumorphic
 Mollweide
 HammerAitoff
 Eckert IV
 Robinson
If a rectangular projection is the only option then a cylindrical equal area projection can be used, but this distorts shapes. The bestknown such projection is the Peters projection (more correctly the GallPeters projection) which has been adopted by a number of charities. Although it is an equalarea projection, it distorts the shape of much of the world and gives a false impression of the shape of continents compared to the real globe. A Mercator projection, although very familiar, should never be used for a distribution map because it exaggerates the areas of landmasses towards the poles to an unreasonable extent. For example, on a Mercator map, Alaska and Brazil look similar in area, but in reality Brazil is about five times the area of Alaska.
You might also consider showing the world in hemispheres (or four hemispheres based on 0°, 90°E, 180° and 90°W) using an orthographic projection. This looks like a view of a globe, and although not strictly equal area, is a good way of showing the world, with continents looking almost as they do on a globe.
Maps of Continental areas:
 Europe: Bonne, Lambert azimuthal, Albers.
 Asia and North America: Lambert azimuthal, Bonne
 South America and Africa: Lambert azimuthal, Bonne, Mollweide
Maps of large countries in midlatitudes:
 USA, Russia, CES, China: Lambert Azimuthal, Lambert Conformal Conical, Bonne
Polar Regions:
 Stereographic, Lambert Azimuthal
Hemispheres:
 Orthographic. As mentioned above, the orthographic projection looks like a ‘globe shot’. You cannot show a total hemisphere (180˚°), but you can show almost a hemisphere.
British Isles
Because the British Isles are not large when compared to the whole globe, the distortions of shape, area and distance introduced by most commonly available projections are too small to be of great concern, if the map is to be on an A4 or A3 sheet of paper. However, if you are to create a larger map, then Bonne projection is probably a good choice.
Where can I see what map projections look like?
PDF file views (printable, or downloadable into FreeHand, Illustrator and CorelDraw) of a wide range of map projections, including all those mentioned above, can be found at:
Map projection software *
A basic, Windowsbased mapprojection program called MicroCAM is available in the public domain (for noncommercial purposes) for download from:
Center for Spatially Integrated Social Science (CSISS)
Note that Microcam was written for Windows XP and the author of the program is no longer supporting it. Another free program to replace it is called Map Window
Some Java based and free map projection programs are:
http://www.giss.nasa.gov/tools/gprojector/ and http://www.flexprojector.com/
Alternatively there is also this useful Map Projection web site
Also, the USGS has two online bibliographies that are useful for GIS and Cartographic (Map Projection) research.
There are other commercially available map projection software programs available for purchase, but these are usually aimed at the professional cartographer in need of creating maps frequently.
author:
Giles Darkes
January 2008
*updated courtesy of Paul Anderson October 2011




