Hammer-Aitoff Equal-Area Projection

The Hammer-Aitoff equal-area projection, also called the Hammer projection, is a map projection that is a modification of the Lambert azimuthal equal-area projection. It consists of halving the vertical coordinates of the equatorial aspect of one hemisphere and doubling the values of the meridians from the center (Snyder 1987, p. 182). Like the Lambert azimuthal equal-area projection, it is equal area, but it is no longer azimuthal.

For a unit sphere with central meridian , let be the longitude and the latitude, measured in radians. Applying the modification above to the equatorial Lambert azimuthal equal-area projection formulas (Snyder 1987, p. 185) gives the projected Cartesian coordinates and as

			(1)
			(2)

For the inverse projection, define the intermediate variable

(3)

Then the longitude and latitude are given by

			(4)
			(5)

In the longitude formula, the inverse tangent takes the signs of both and into account to select the correct quadrant.