Formulae
Equatorial coordinate
X = ( 2 √2 cos(δ) sin(α/2) ) ⁄ √( 1 + cos(δ) cos(α/2) )
Y = ( √2 sin(δ) ) ⁄ √( 1 + cos(δ) cos(α/2) )
where (α, δ) = (Right Ascension, Declination)
Horizontal coordinate
X = ( 2 √2 cos(alt) sin(az/2) ) ⁄ √( 1 + cos(alt) cos(az/2) )
Y = ( √2 sin(alt) ) ⁄ √( 1 + cos(alt) cos(az/2) )
where (az, alt) = (Azimuth, Altitude)
Wikipedia
Hammer Projection
Planetarium - Version 1.3.1