Conversion of coordinates

Spherical coordinates

• x = r sin(θ) cos(φ)
  y = r sin(θ) sin(φ)
  z = r cos(θ)
• r = √x² + y² + z²
  tan φ = y / x
  cos θ = z / r
• 0 ≤ φ < 2π
  0 ≤ θ < π

Hammer-Aitoff projection

• x = √8 cos(φ) sin(λ/2) / √1 + cos(φ) cos(λ/2)
• y = √2 sin(φ) / √1 + cos(φ) cos(λ/2)

Here, λ = −180°...+180° is the longitude and φ = −90°...+90° the latitude in the original coordinate system. The resulting coordinates x and y are in the range of ±√8 and ±√2, respectively.