# Craig retroazimuthal projection

Craig retroazimuthal projection centered on Mecca.

The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a cylindrical projection preserving the direction from any place to one other, predetermined place while avoiding some of the bizarre distortion of the Hammer retroazimuthal projection. It is sometimes known as the Mecca projection because Craig, who had worked in Egypt as a cartographer, created it to help Muslims find their qibla. The projection is defined by:

$x = \lambda\,$
$y = \frac\lambda{\sin(\lambda)}(\sin(\phi)\cos(\lambda) - \tan(\phi_0) \cos(\phi))\,$

given latitude $\phi$, longitude relative to the fixed location $\lambda$, and latitude of the fixed location $\phi_0$.

The above equation has a discontinuity at $\lambda = 0$; to resolve this, at 0° longitude, take $\lambda/\sin(\lambda) = 1$, the ratio's continuous completion.[1]