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

{\displaystyle {\begin{aligned}x&=RK\cos \varphi _{1}\sin(\lambda -\lambda _{0})\\y&=-RK{\big (}\sin \varphi _{1}\cos \varphi -\cos \varphi _{1}\sin \varphi \cos(\lambda -\lambda _{0}){\big )}\end{aligned}}}

where

${\displaystyle K={\frac {z}{\sin z}}}$

and

${\displaystyle \cos z=\sin \varphi _{1}\sin \varphi +\cos \varphi _{1}\cos \varphi \cos(\lambda -\lambda _{0})}$

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.