Editing Craig retroazimuthal projection

{{Short description|Retroazimuthal compromise map projection}}
[[File:Craig projection SW.jpg|thumb|300px|Craig retroazimuthal projection centered on [[Mecca]]]]

The '''Craig retroazimuthal''' [[map projection]] was created by [[James Ireland Craig]] in 1909. It is a modified [[Map projection#Cylindrical|cylindrical projection]]. As a [[Map projection#Retroazimuthal|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.<ref>
{{Cite book
| page=133
| url = https://books.google.com/books?id=vTLAqGTAc8cC 
| title = Map Projections: A Reference Manual 
| year = 1995
| publisher = Taylor and Francis 
| author1 = Lev M Bugayevskiy 
| author2 = John Parr Snyder 
| location = Bristol 
| isbn = 978-0-7484-0303-5}}</ref>

Given latitude ''φ'' to plot, latitude ''φ''{{sub|0}} of the fixed location of interest, longitude ''λ'' to plot, and the longitude ''λ''{{sub|0}} of the fixed location of interest, the projection is defined by:

:<math>\begin{align} 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{align}</math>

But when ''λ''&nbsp;−&nbsp;''λ''{{sub|0}} = 0, ''y'' above is undefined, so instead use the ratio's [[continuous function|continuous]] completion:<ref>
{{Cite book
| title = Flattening the Earth: Two Thousand Years of Map Projections
| author = John Parr Snyder
| year = 1993
| pages = 227–228
| isbn = 0-226-76747-7
}}</ref>

:<math>y = \sin \varphi \cos \left(\lambda - \lambda_0\right) - \tan \varphi_0 \cos \varphi = \sin \varphi - \tan \varphi_0 \cos \varphi</math>

==See also==

*[[List of map projections]]
*[[Hammer retroazimuthal projection]]

==References==
{{Reflist}}

==Further reading==
*{{cite journal|last1=Tobler|first1=Waldo|title=Qibla, and Related, Map Projections|journal=Cartography and Geographic Information Science|volume=29|issue=1|year=2002|pages=17–23|issn=1523-0406|doi=10.1559/152304002782064574}}

==External links==
*[https://web.archive.org/web/20070927225423/http://www.uff.br/mapprojections/Craig_en.html An interactive Java Applet to study the metric deformations of the Craig Projection].
*[http://www-history.mcs.st-and.ac.uk/Biographies/Craig_James.html Biography of James Ireland Craig (1868-1952)].

{{Map projections}}

[[Category:Map projections]]
[[Category:Salah]]