Projections

Plate Carrée (Equirectangular, φ1 = 0°)

x = λ 2 π y = φ 2 π

Equirectangular, φ1 = 15°

x = λ 2 π y = φ 2 π ( 3 + 1 )

Equirectangular, φ1 = 30°

x = λ 2 π y = φ π 3

Plate Carrée (Equirectangular, φ1 = 45°)

x = λ 2 π y = φ 2 2 π

Equirectangular, φ1 = 60°

x = λ 2 π y = φ π

Mercator

x = λ 2 π y = ln ( tan ( π 4 + φ 2 ) ) 2 π

Gall Stereographic

x = λ 2 π y = tan ( φ 2 ) ( 2 + 1 ) 2 π

Miller

x = λ 2 π y = 5 ln ( tan ( π 4 + 2 φ 5 ) ) 8 π

Lambert (Cylindrical Equal Area, φ1 = 0°)

x = λ 2 π y = sin ( φ ) 2 π

Behrmann (Cylindrical Equal Area, φ1 = 30°

x = λ 2 π y = 2 sin ( φ ) 3 π

Hobo-Dyer (Cylindrical Equal Area, φ1 = 37°30'

x = λ 2 π y = sin ( φ ) ( cos ( 5 π 24 ) ) 2 2 π

Gall-Peters (Cylindrical Equal Area, φ1 = 45°)

x = λ 2 π y = sin ( φ ) π

Balthasart (Cylindrical Equal Area, φ1 = 50°)

x = λ 2 π y = sin ( φ ) ( cos ( 5 π 18 ) ) 2 2 π

Sinusoidal

x = λ cos ( φ ) 2 π y = φ 2 π

Kavrayskiy VII

x = λ 1 3 ( φ π ) 2 2 π y = φ 3 3 π

Wagner VI

x = λ 1 3 ( φ π ) 2 2 π y = φ 2 π

Aitoff

α = arccos ( cos ( φ ) cos ( λ 2 ) ) x = cos ( φ ) sin ( λ 2 ) sinc ( α ) π y = sin ( φ ) sinc ( α ) 2 π

Hammer

x = cos ( φ ) sin ( λ 2 ) 2 1 + cos ( φ ) cos ( λ 2 ) y = sin ( φ ) 4 1 + cos ( φ ) cos ( λ 2 )

Winkel I

x = λ ( cos ( φ ) π + 2 ) 2 π ( π + 2 ) y = φ π + 2

Winkel Tripel

α = arccos ( cos ( φ ) cos ( λ 2 ) ) x = sinc ( α ) λ + cos ( φ ) sin ( λ 2 ) π sinc ( α ) π ( π + 2 ) y = sin ( φ ) + φ sinc ( α ) 2 sinc ( α ) ( π + 2 )

Van der Grinten

θ = arcsin ( | 2 φ π | ) A = | π λ λ π | 2 G = cos ( θ ) sin ( θ ) + cos ( θ ) 1 P = G ( 2 sin ( θ ) 1 ) Q = A 2 + G x = { λ 2 π , φ = 0 0 , λ = 0 φ = ± π 2 sign ( λ ) | A ( G P 2 ) + A 2 ( G P 2 ) 2 ( P 2 + A 2 ) ( G 2 P 2 ) | 2 ( P 2 + A 2 ) , otherwise y = { 0 , φ = 0 sign ( φ ) tan ( θ 2 ) 2 , λ = 0 φ = ± π 2 sign ( φ ) | P Q A ( A 2 + 1 ) ( P 2 + A 2 ) Q 2 | 2 ( P 2 + A 2 ) , otherwise

Eckert V

x = λ ( 1 + cos ( φ ) ) 4 π y = φ 2 π

Azimuthal Equidistant (Polar)

x = sin ( λ ) ( .25 φ 2 π ) y = - cos ( λ ) ( .25 φ 2 π )

Definitions and Notes