Craig retroazimuthal projection

The Craig retroazimuthal map projection was created by James Ireland Craig in 1909. It is a modified cylindrical projection. As a retroazimuthal projection, it preserves directions from everywhere to one ___location of interest that is configured during construction of the projection. The projection 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. In such maps, Mecca is the configurable ___location of interest.^[1]

Craig retroazimuthal projection centered on Mecca

Given latitude φ to plot, latitude φ₀ of the fixed ___location of interest, longitude λ to plot, and the longitude λ₀ of the fixed ___location of interest, the projection is defined by:

${\displaystyle {\begin{aligned}x&=\lambda -\lambda _{0}\\y&={\frac {\lambda -\lambda _{0}}{\sin \left(\lambda -\lambda _{0}\right)}}{\Big (}\sin \varphi \cos \left(\lambda -\lambda _{0}\right)-\tan \varphi _{0}\cos \varphi {\Big )}\end{aligned}}}$

But when λ − λ₀ = 0, y above is undefined, so instead use the ratio's continuous completion:^[2]

${\displaystyle y=\sin \varphi \cos \left(\lambda -\lambda _{0}\right)-\tan \varphi _{0}\cos \varphi =\sin \varphi -\tan \varphi _{0}\cos \varphi }$

See also

• List of map projections
• Hammer retroazimuthal projection

References

1. Lev M Bugayevskiy; John Parr Snyder (1995). Map Projections: A Reference Manual. Bristol: Taylor and Francis. p. 133. ISBN 978-0-7484-0303-5.
2. John Parr Snyder (1993). Flattening the Earth: Two Thousand Years of Map Projections. pp. 227–228. ISBN 0-226-76747-7.

Further reading

• Tobler, Waldo (2002). "Qibla, and Related, Map Projections". Cartography and Geographic Information Science. 29 (1): 17–23. doi:10.1559/152304002782064574. ISSN 1523-0406.

External links

• An interactive Java Applet to study the metric deformations of the Craig Projection.
• Biography of James Ireland Craig (1868-1952).