# Hammer retroazimuthal projection

The frontside hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 0°E.
The backside hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 0°E.

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] In whole-world presentation, the back and front hemispheres overlap, making the projection a surjective function. Given a radius R for the projecting globe, the projection is defined as:

$x = R K \cos \phi_1 \sin (\lambda-\lambda_0)$
$y = -R K [\sin \phi_1 \cos \phi - \cos \phi_1 \sin \phi \cos (\lambda-\lambda_0)]$

where

$K = z/\sin z$

and

$\cos z = \sin \phi_1 \sin \phi + \cos \phi_1 \cos \phi \cos (\lambda - \lambda_0)$

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.

## 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.