Hammer retroazimuthal projection

(c) GFDL, CC BY-SA 3.0
The full Hammer retroazimuthal projection, centered on the north pole.
The full Hammer retroazimuthal projection centered on Mecca, with Tissot's indicatrix of deformation. Back hemisphere has been rotated 180° to avoid overlap.

The Hammer retroazimuthal projection is a modified azimuthal proposed by Ernst Hermann Heinrich Hammer in 1910. As a retroazimuthal projection, azimuths (directions) are correct from any point to the designated center point.[1] Additionally, all distances from the center of the map are proportional to what they are on the globe. In whole-world presentation, the back and front hemispheres overlap, making the projection a non-injective function. The back hemisphere can be rotated 180° to avoid overlap, but in this case, any azimuths measured from the back hemisphere must be corrected.

Given a radius R for the projecting globe, the projection is defined as:

where

and

The latitude and longitude of the point to be plotted are φ and λ respectively, and the center point to which all azimuths are to be correct is given as φ1 and λ0.

See also

  • Craig retroazimuthal projection
  • List of map projections

References

  1. ^ Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. Chicago: University of Chicago Press. pp. 228–229. ISBN 0-226-76747-7. Retrieved 2011-11-14.

External links

Media files used on this page

Hammer Retroazimuthal with Tissot's Indicatrices of Distortion.svg
Author/Creator: Justin Kunimune, Licence: CC BY-SA 4.0
The world on a Hammer Retroazimuthal projection, with 10° graticule and Tissot's indicatrices overlaid. The center is at 21.4°N, 39.8°E. Each red circle is 1,000 km in diameter. Coastline data from www.naturalearthdata.com. Colors inspired by Eric Gaba. Projection generated with my own code, at github.com/jkunimune15/Map-Projections.
Hammer retroazimuthal projection combined1.jpg
(c) GFDL, CC BY-SA 3.0
Combined front and rear Hammer retroazimuthal projection