# Hammer retroazimuthal projection

The front hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.
The back hemisphere of the Hammer retroazimuthal projection. 15° graticule; center point at 45°N, 90°W.

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 non-injective 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.