Projection families based on the shape of the projection surface.

Planar(aka Azimuthal)

Any method that projects locations from an earth model onto a flat plane. Often used to focus attention on one point.

CylindricalAny method that projects locations from an earthmodel onto a cylinder. Often used to focus attention along the equator (normal aspect), a meridian (transverse aspect), or a diagonal line (oblique aspect). Tangent and secant cases available.

ConicAny method that projects locations from an earthmodel onto a cone. Often used to focus attention on a mid-latitude parallel (tangent case) or a pair of mid-latitude parallels (secant case).

OtherA catch-all column for all other projection shapes.

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Equal Area(aka Equivalent)

Any method that projects locations from an earth model and preserves

geodesic areas in the outputted data, map, or view.

The Albers Equal-area Conic projection, or Albers projection for short, uses the secant case of this conic method to preserve geodesic areas in the output. Although scale and shape are not preserved, such distortions are minimal between the two standard parallels. Commonly used with mapping zones that have long east-west extents and short north-south extents. Named after Heinrich C. Albers.

Equidistant(aka Equal distance)

Any method that projects locations from an earth model and preserves

geodesic distances from a point in the outputted data, map or view.

The Lambert Azimuthal Equidistant projection uses the tangent case of this planar method to preserve all geodesic distances from one chosen point to all other points on earth. Geodesic areas and shapes are not preserved; inflation increases with distance from the point of interest. Named after Johann H. Lambert.

ConformalAny method that projects locations from an earth model and preserves

geodesic shapes (local angles) in the outputted data, map, or view.

The Transverse Mercator projection uses the secant case of this rotated cylindrical method to preserve geodesic shapes in the gore of interest. Although scale and area are not preserved, such distortions are minimal between the two standard circles (if SF is less than 1.0 along the central meridian). Used commonly with the UTM and State Plane Coordinate Systems that have mapping zones with long north-south extents and short east-west extents. Carl Gauss and Johann Kruger adapted Mercator’s method for making navigational charts for this purpose.

The Lambert Conformal Conic projection uses the secant case of this conic method to preserve geodesic shapes in the band of interest. Although scale and area are not preserved, such distortions are minimal between the two standard parallels. Commonly used with aeronautical charts and zones in the State Plane Coordinate System that have mapping zones with long east-west extents and short north-south extents. Named after Johann H. Lambert.

CompromiseA catch-all row for all other

projection methods that do not consistently preserve any geodesic

property in the outputted data.

The Web Mercator Projection is, very unfortunately, the de-facto standard for making web maps (e.g., Apple Maps, Google Maps, ArcGIS Online). This method relies on the WGS84 authalic sphere to provide mobile device users with fast performance (spherical math is much faster to compute than ellipsoidal math), but the distortions are conspicuous and they increase substantially with distance from the equator. Accordingly, the US DOD and NGIA have both declared this projection method unacceptable for any official use.

The Vertical Near-side Perspective projection preserves no geodesic property whatsoever in the output, but it does produce a nifty perspective view of the globe as if viewing it from a satellite or airplane. Commonly used to build cool-looking locator maps that show where a place or region is located on a round earth.

Table 1: Two sets of projection families (Kimerling et al. 2012: p39) with the six methods you are most likely to encounter on the job.

: The most common coordinate projection surfaces, by case (tangent vs. secant).

: The three most commonly used coordinate projection surfaces (planes, cylinders, and cones) and

their tangent and secant cases. This figure was adapted from Figure 3.10 in Kimerling et al. (2009:45). Locations on an ellipsoid, which are specified using three-dimensional geographic coordinates (λ,ɸ,r), can be projected onto a new surface (cone, cylinder, or plane) and assigned planar coordinates (E,N).

Our national State Plane Coordinate System (SPCS) (Bolstad, 2016:124-128, 684) is composed of 121 small mapping zones that are composed of counties and nested within state boundaries. Geographic locations in each zone are projected using a mathematical method designed for the zone, then assigned new planar coordinates that are specific to the zone. A SPCS zone with a major east-west axis uses a custom version of the secant case of Lambert’s Conformal Conic projection method ( and see Bolstad, 2016:123). A SPCS zone with a major north-south axis uses a custom version of the secant case of Mercator’s Transverse Cylindrical projection method (not shown in Bolstad, 2016, but shown here at ). Each zone in the national SPCS has a unique name (e.g., PA-South, MS-East, TX-Central), coordinate origin, and distortion pattern.

The global Universal Transverse Mercator (UTM) system (Bolstad, 2016:128-131, 684) is composed of 120 large mapping zones that are distributed globally; each zone is 6-degrees wide and spans from the equator to near a pole. Geographic locations in each zone are projected onto a cylindrical surface and assigned new planar coordinates that are specific to the zone. Because all UTM zones have major north-south axes, each uses a custom version of the secant case of Mercator’s Transverse Cylindrical projection method (not shown in Bolstad, 2016, but shown here at ). Each mapping zone in the global UTM System has a unique name (UTM Zone 16N, UTM Zone 33S), coordinate origin, and distortion pattern.