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. 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:

$x = R K \cos \varphi_1 \sin (\lambda-\lambda_0)$

$y = -R K [\sin \varphi_1 \cos \varphi - \cos \varphi_1 \sin \varphi \cos (\lambda-\lambda_0)]$

where

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

and

$\cos z = \sin \varphi_1 \sin \varphi + \cos \varphi_1 \cos \varphi \cos (\lambda - \lambda_0)$

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.

See also

• List of map projections

External links

• Description of Hammer Retroazimuthal front hemisphere.
• Description of Hammer Retroazimuthal back hemisphere.