Coordinate conversion

This article explains Latitude Longitude and UTM, also providing a tool to convert between them. There are many coordinate systems to represent the point location on Earth or another planet.

Convert between UTM and WGS84 Latitude Longitude

Latitude and longitude

Latitude and longitude are the two angles, measured from the centre of the globe
Latitude and longitude are the two angles, measured from the centre of the globe
Latitude and longitude system uses angular units to represent the location. In the past latitude and longitude were usually given in degrees, minutes and seconds but it is also possible to use decimal parts of degree instead of minutes and seconds (this representation is easier to work with when writing the software). The most obvious benefit of this system is that two numbers clearly define the location anywhere on the planet, following relatively simple rules. This system is well compatible with the simple tools used by the past mariners and explorers (latitude can be found from the sun inclination and longitude from the sunrise or sunset time using marine chronometer). The latitude spans from -90 to 90 degrees, with zero at equator and positive values towards the North. The longitude spans from -180 to 180 degrees, with zero at Royal Observatory, Greenwich, in England and positive values towards the east. Alternatively, the suffix letters South, North, East and West can be used.

The biggest shortcoming of the latitude-longitude system is that the length of the single degree on the surface, when expressed in meters, is location-dependent. Especially the length of the longitude degree varies greatly with latitude, starting from over 111 kilometers at equator, decreasing till somewhere about 60 over Europe and South America and approaching zero near the poles. This makes calculation of the distance between the two points a complex task. Also, numeric values of the latitude and longitude usually tell little to the human being. Representation near the poles is not accurate and algorithms may internally switch into some alternative representation that assumes poles at some different location.

It is also difficult to project an image on the top of the map using latitude and longitude coordinate system, as it is not sufficient to stretch it linearly so that top left and bottom right corners are in the correct location. For the image stretches this simple way the internal points still will not be in place where they should be. The line that is straight on the planet surface and is also straight in the image must appear as curve in the map.

Universal Transverse Mercator

Projecting the globe into cylinder. Red line (that touches the cylinder) is projected precisely when blue line is projected with distortions. Blue line could also be projected well after turning the cylinder around the globe (or the globe inside the cylinder) - this would be the different UTM zone
Projecting the globe into cylinder. Red line (that touches the cylinder) is projected precisely when blue line is projected with distortions. Blue line could also be projected well after turning the cylinder around the globe (or the globe inside the cylinder) - this would be the different UTM zone
. UTM (Universal Transverse Mercator) was proposed as an attempt to eliminate this problem. Its two main coordinates (easting and northing) are directly expressed in meters, allowing trivial calculation of distances and in general much easier human interpretation. However as the Earth is not flat, representation in meters can only work well in some restricted area. To solve this problem, the Earth is divided into 60 zones that are small enough to have the meter representation possible. Hence in UTM the location is represented by the three values: the easting, the northing and the zone.

The zone is a number followed by the first setter of the hemisphere (South or North) that is required to define the location uniquely (some software uses negative and positive numbers instead). Alternatively, the latitude band may be specified instead, providing redundant information. Each zone is segmented into 20 latitude bands that have letters assigned.

Neither easting nor northing ever takes negative values in they own zone. However northing might be rounded to zero in northern hemisphere closer than one meter from equator, if integer values are used (convert a point with zero latitude into UTM).

Inside the single zone, UTM uses transverse Mercator projection to map between the round surface of the planet and flat surface of the map. It projects points into imaginary cylinder wrapped around the globe. The cylinder is then unfolded, obtaining the flat map. This projection is accurate where cylinder touches the globe and increasingly inaccurate where there is some gap between them. Various UTM zones are just various positions of the cylinder, each touching different points of the globe.

Work with UTM becomes more difficult when the line between the two points of interest crosses the zone boundary. If only one boundary is crossed, the data set can be "locked" to one zone only, using it also to represent the location of another point. In some zones are officially expanded to cover geographic units of interest completely. If the points are more distant, UTM largely looses its benefits and it may be easier to work with latitude and longitude instead.

Literature