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:

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

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

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

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

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