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Map projection is the process of transforming angular (spherical / elliptical) coordinates into planar coordinates. All map projections introduce distortion (e.g., to areas, angles, distances) in the resulting planar coordinates. Understanding what, where, and how much distortion is introduced is an important consideration for spatial computations and visual interpretation of spatial patterns, as well as for general aesthetics of any map.
- What is a map projection?
- Construction of projections
- Distortion in map projections
- Selecting a projection
- Working with projections in an online world
A map projection is the mathematical transformation from angular coordinates (e.g., degrees of latitude and longitude) into planar coordinates. In other words, a map projection simply defines the relationship between every point on the Earth’s curved surface and the equivalent location in two-dimensional, Euclidean (planar) coordinates. For example, consider a simple map projection such as the Plate Carrée (Figure 1):
x = R * (λ – λ0)
y = R * φ
where λ is the longitude, λ0 is the central meridian, φ is the latitude, and R is the radius of the reference globe.
Figure 2. Developable surfaces for forming planar (left), conic (middle), and cylindrical (right) projections. For each developable surface a point or line of tangency is shown in grey. For the planar developable surface it is at the north pole, for conic it is at 45°N, and for cylindrical it is at the equator.
Some common types of projection are:
Figure 6. Three equal area map projections: Goode's homolosine (left), Craster equal area (center), and Lambert equal area (right).
When designing maps for distribution online, there are often limited options for selecting the projection for a given map. If the data is ‘mashed up’ onto an existing tiled basemap, the projection is likely to be the Web Mercator projection, a variant on the Mercator projection. The Web Mercator is a nearly conformal projection, and thus, has been suggested as inappropriate for many small-scale thematic mapping purposes (see Battersby et al. 2014 for discussion). The use of Web Mercator for web mapping applications presents serious limitations for both spatial analysis and visual analysis. However, in current web mapping environments, projection choice is often limited.
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Battersby, S. E., Finn, M. P. Usery, E. L., Yamamoto, K. H. (2014). Implications of Web Mercator and its use in online mapping. Cartographica. 49(2): 85-101. doi: 10.3138/carto.49.2.2313.
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Finn, M.P., Usery, E. L., Woodard, L., and Yamamoto, K. H. (2017). The Logic of Selecting an Appropriate Map Projection in a Decision Support System (DSS). Chapter 10, doi: 10.1007/978-3-319-51835-0_10 in Choosing a Map Projection, Lapaine, M. and Usery, E. L., editors. Lecture Notes in Geoinformation and Cartography. Springer.
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Monmonier, M. (2004). Rhumb Lines and Map Wars: A Social History of the Mercator Projection. Chicago, Illinois: University of Chicago Press.
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- Describe the geometric properties of the globe that may be distorted in the map projection process
- Describe at least one technique for visualizing distortion (e.g., Tissot’s indicatrices, or continuous distortion surfaces) and use it to visualize distortion
- Identify and describe the distortion pattern in a specific map projection using a common visualization method (e.g., Tissot’s indicatrices) or distortion surface.
- Compare multiple map projections to explain the difference in distortion patterns, and how the maps would be suited for different analysis or visualization purposes
- Design a thematic map that uses a map projection appropriate to the theme and map purpose.
- What is a developable surface? Is this how map projections are actually calculated? Describe the difference between the concept of developable surfaces and the mathematical transformations used for map projection.
- Describe the differences between an equal area, conformal, and compromise projection. Provide an example of a mapping problem that would be best suited for each type of projection.
- Why should a cartographer or GIS analyst be concerned about the map projection of the dataset when performing spatial analysis? When preparing a map for visual communication of spatial patterns?
- When selecting a projection based on property (equal area, conformal, etc.), what aesthetic considerations guide the final selection of a map projection with the desired property?
- What are the projection-related trade-offs that a web map designer must face when working with tiled map services?
- Why is it impossible to preserve both area and angular measurements in a planar map projection?
- Flex Projector (http://www.flexprojector.com/): a freeware, cross-platform application for creating custom world map projections
- Geocart 3 (https://www.mapthematics.com/Index.php): software for exploring map projections and distortion patterns
- USGS Map Projections (https://egsc.usgs.gov/isb//pubs/MapProjections/projections.html): USGS web site presenting key properties, characteristics, and preferred uses of many historically important projections and of those frequently used by mapmakers today.
- Adaptive Composite Map Projections (http://cartography.oregonstate.edu/demos/AdaptiveCompositeMapProjections/): Adaptive Composite Map Projections from the Cartography and Geovisualization Group at Oregon State University