So, we've established that having a GPS position with geographic coordinates in degrees isn't sufficient; you also need a map representing the earth at a consistent scale, say in (kilo)metres. How to get from one to the other? This is called 'projection', which can basically be defined as a method of reducing the three-dimensional earth to a two-dimensional representation. There are a large number of ways of doing this, none of which is perfect. To illustrate this, try peeling an orange and then squashing the peel flat in such a way that it accurately represents its form before being peeled - impossible, eh! Just as the distortions are less obvious the smaller the piece of orange peel you take, so the distortions of projections are less obvious the more you zoom in.
I'm no expert on projections, so I'll just mention the main types I use on this site, which are all in Europe.
In much geographical software, this is the default representation of geographical coordinates, simply converting degrees into x/y coordinates, in other words, pretending the earth is a flat rectangle. This is an equidistant projection, also known as geographical projection. It has the obvious advantage of being geometrically simple, but is in no way an accurate representation of the earth. 'Plate carrée', by the way, means 'square plane'; the overall plane is of course not square, as the earth has 360° of longitude but only 180° of latitude, but each 1°x1° segment is square. Here's the world as represented by Plate Carrée:
Clearly, the further you move from the equator you more this distorts the shape of the earth.
Mercator's was first produced in 1569 specifically for navigation at sea, for which it is still used. Although it's no longer used much in atlases, it is used by the commercial online mapping systems, such as Google. Here's the world according to Google:
Like Plate Carrée, this is fine on the equator but becomes ever more useless as you approach the poles. Note though how the distortions differ from Plate Carrée. Because Mercator's makes Greenland, for example, look the same size as Africa, it's not suitable for distribution maps, so it's unfortunate that Google Maps have become so widely used for that. Its advantage for Google et al is that it's geometrically simple and scales simply; the distortions also diminish as you zoom in.
Because of the problems with a simple Mercator, a variation that is widely used by national cartographers, who only have to concern themselves with their own local area, is the Transverse Mercator. This turns Mercator on its side, so the 'equator' becomes a latitude meridian. This means the distortions are minimised around that meridian. The Ordnance Survey in Britain uses a transverse Mercator projection, with the planar coordinates being the National Grid.
A development of transverse Mercator is the Universal Transverse Mercator (UTM) which divides the earth into 60 transverse Mercator zones (so 6° each) and is widely used in Europe. Normally, it is based on the WGS84 ellipsoid, but versions based on ETRS89 and ED50 are also used in Europe.
Because UTM zones and other national TM projections are only based on a small segment of the earth's surface, they have an origin instead of using 0°0°; for example, that of the OS in Britain uses 49°N 2°W as its origin.
The European Petroleum Survey Group defines a Geodetic Parameter Data Set which lists most projections and coordinate systems. Each projection has a code which is widely used in software to identify and convert from one to another. EPSG:4326 is WGS84 geographic coordinates; EPSG:4230 is ED50 (EPSG:230nn are UTM subsets of this); EPSG:4258 is ETRS89 (EPSG:258nn are UTM subsets of this). The OSGB projection is EPSG:27700. EPSG:3857 is a relatively new code to describe the form of Mercator used by Google et al which treats the earth as a sphere not an ellipsoid (spatialreference.org has this as 3785). Mercator itself is EPSG:3395, though more used is 41001, which is not an EPSG code but one from OSGEO.
(Note that software generally uses 4326 as shorthand for the Plate Carrée projection. Strictly speaking, this is incorrect. 4326 is the representation of the geographic coordinate system based on the WGS84 datum/ellipsoid, which is by definition not projected. There ought to be a separate code for Plate Carrée, but isn't. See this blog post for further discussion of this issue.)
- Wikipedia is a good place to start to get more information on projections, with pages on the main ones and plenty of references to other sources
- see also the projections page at wiki.GIS.com
- and also the ITC's map projections page
- spatialreference.org is a good place to explore projection definitions, and see the EPSG Registry itself
- see Winwaed Software's demos for an excellent summary of equal-area projections which, as you can see, are much better for atlas-type general maps than Mercator's, as they represent the curved nature of the earth much better