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Key Concepts in Coordinate Systems and Mapping

The art and science of map making is constantly changing. The associated ideas, best practices, and terminology can occasionally be confusing (for example, geoid, ellipsoid, datum, coordinate system, projection, etc.). What does it really take to turn real-world locations into coordinates and then into maps?

The high level goal – starting with locations and ending up with coordinates you can plot on a map or visa-versa – is addressed with a coordinate system (also called a coordinate reference system). A coordinate system along with coordinates is enough to uniquely identify a spot on earth. For example, Safe Software is near (510359E, 5442815N) in the UTM10N/WGS84 coordinate system. This concept alone contains a lot of information.

## First Concept: Modeling the Earth

If you start with the assumption that the world is flat and try to make maps over a large area, it doesn’t work. The curvature of the earth gets in the way and prevents the measured angles and lengths from adding up. The typical strategy is to approximate the earth as an ellipsoid (flattened sphere) that fits your data well (whether it is a country, continent, or the whole world). In the example above, the WGS84 ellipsoid is 6,378,137m “wide” and 6,356,752.3142m “tall”. A more accurate strategy is to use the geoid, which is a smooth surface over the earth that roughly corresponds to the idea of “sea level”.

## Second Concept: Tying the Model to the Earth

The next challenge is to associate coordinates (typically latitude, longitude, and height above the chosen ellipsoid) with real locations. There are lots of ways to do that (for example, by consulting a GPS receiver or looking for nearby survey monuments). A datum extends a model of the earth with whatever else is needed to do this. Again going back to the example, the WGS84 datum is defined by the locations of US Department of Defense GPS stations located around the world, and is typically what GPS devices report by default.

## Third Concept: Flattening it Out

The last (optional) concept is to flatten the map out. Again, there are many choices (called projections) that allow you to map, for example, between lat/long in degrees and northings/eastings in meters. Flattening the map adds distortion, but you can choose projections that preserve important properties to a greater or lesser extent, including area, distance, direction, shape, and scale. Our example uses the UTM10N projection, part of the family of “Universal Transverse Mercator” projections.