Azimuthal Equidistant Projections

Figure 1. An azimuthal equidistant map centered on the North Pole.

The azimuthal equidistant projection has been around for centuries, mostly for a single, specialized use: This projection excels at making maps of the polar regions. When developed using the proper aspect, azimuthal equidistant maps can accurately show distances and directions from the pole to all other points on the map. This quality has made them immensely popular among polar travelers and explores for at least the last 300 years.

Recently, the use of azimuthal equidistant projections has increased somewhat, as people in advertising and promotion have realized that by changing the aspect of the projection, you can generate maps that show accurate distances and direction from any single point on the Earth's surface. Thus, so long as you have some "central point" to which users of the map can relate, the azimuthal equidistant projection can be used very effectively to create maps that accurately show distances and directions to this central point. Thus, in addition to making maps of the poles, nowadays the azimuthal equidistant projection is used fairly commonly to make maps centered on tourist destinations. These maps are frequently used to entice visitors to come to these destinations by showing them how accessible the site is and how many other attractions are located nearby.

• Form: Azimuthal equidistant projections are planner. Indeed, azimuthal is another term (besides "planner") used to describe the planner form.

• Case: Azimuthal equidistant projections are tangent. The point of tangency is the "central point" from which distances and directions are accurately shown.

• Aspect: Azimuthal projections can use any possible aspect; normal, transverse, or oblique.

• Variation Within Azimuthal Equidistant Projections: Azimuthal equidistant projections differ only in their aspect. Any point, anywhere on the Earth, can be used as the point of tangency.

• Distortions
  • Shearing: Azimuthal equidistant projections do distort shapes. This distortion is present everywhere on the map, but becomes more pronounced as you move farther from the point of tangency.
  • Tearing: Azimuthal equidistant maps tend to be circular in shape, and typically are used to show no more than half the Earth (i.e., one hemisphere) in any one map. Tearing occurs along the map's circular edge. While it is possible to create interrupted maps using azimuthal equidistant projections, I don't think I've ever seen one in actual use.
  • Compression: Azimuthal equidistant maps are not equivalent; they do suffer from compression. Compression is present all over the map, but becomes more pronounced as you move farther from the point of tangency.
  • Equivalence: Azimuthal equidistant maps are not equivalent; they do suffer from compression. Compression is present all over the map, but becomes more pronounced as you move farther from the point of tangency.
  • Conformality: Azimuthal equidistant maps are not conformal, shape distortion is present throughout the map. As with most other forms of distortion, the amount of shape distortion present in an azimuthal equidistant map increases as you get farther from the map's point of tangency.
  • Equidistance: An azimuthal equidistant map accurately shows distances from its point of tangency to all other points on the map. Distances between other pairs of points (i.e., a distance between two points, neither of which is the map's point of tangency) are not accurate.
  • Azimuthality: An azimuthal equidistant map accurately shows directions from its point of tangency to all other points on the map. Directions between other pairs of points (i.e., a direction between two points, neither of which is the map's point of tangency) are not accurate. Note that under a few very unusual conditions involving highly flattened spheroids and transverse or oblique aspects, it is possible to produce an azimuthal equidistant map where even the directions from the map's point of tangency are not shown with any great level of accuracy. However, these situations really are quite unusual.
  
  
• Uses: While it is possible to use the azimuthal equidistant projection to create maps covering the entire globe, it is very uncommon to show anything larger than a single hemisphere on such a map. Indeed, many cartographers recommend that you limit azimuthal equidistant maps to a region within 30 degrees of latitude and/or longitude of the point of tangency. Beyond this 30-degree range, the amount of shape distortion in the map increases rapidly.