Equirectangular projection/Maps and Distortion

Equirectangular Projection for Maps

The following image shows an equirectangular projection of the world. The standard parallel is the equator (plate carrée projection)

Equirectangular projection of the world; the standard parallel is the equator (plate carrée projection).

Distortion

Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator. The deformation of a circle into an ellipse is visible on different location the world map.

Deformation of a Circle - Distortion Indicator

The deformation of the circle is an indicator for the distortion of the image.

Equirectangular projection with Tissot's indicatrix of deformation and with the standard parallels lying on the equator

Areas of Interest

In the image above the distortion in the planar projection is

• minimal close to the equator and
• maximal at the south pole and north pole.

Rotating circle over the equator (e.g. intersecting with North and South Pole) can be used to have projections with minimal distortion in the area of interest.

North Pole and South Pole

The strongest distortion can be found at the north pole and south pole in the following true-colour satellite image of the earth. In the equirectangular projection the top horizontal line of pixels represent the single pixel for the north pole on the sphere model of the earth. Similar to that the south pole as one pixel is stretched out bottom line of pixels in the equirectangular projection.

Learning Activities

• Explain why a projection of a sphere to a two dimensional plane can preserve some parameters can be kept and some parameters are transformed and create a distortion.
• What are the benefits and constraints of an equirectangular projection (e.g. in the context of navigation of vehicles?

See also

• Collaborative Mapping