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A Craig retroazimuthal centered on Mecca (×). The "pinch" and (not visible here) "twist" at each edge is endemic in some form to all retroazimuthals and prevents any one of them having global coverage.

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 another, 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'd 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 φ, longitude relative to the fixed location λ, and latitude of the fixed location φ0. For λ = 0 take λ / sin(λ) = 1, its continuous completion.[1]


  1. ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 227-228, ISBN 0-226-76747-7.

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