TheBonne projection is a pseudoconical equal-areamap projection, sometimes called adépôt de la guerre,[1]: 104 modified Flamsteed,[1]: 104 or aSylvanus projection.[1]: 92 Although named afterRigobert Bonne (1727–1795), the projection was in use prior to his birth, by Sylvanus in 1511,Honter in 1561,De l'Isle before 1700 andCoronelli in 1696. Both Sylvanus and Honter's usages were approximate, however, and it is not clear they intended to be the same projection.[1]: 60
The Bonne projection maintains accurate shapes of areas along thecentral meridian and thestandard parallel, but progressively distorts away from those regions. Thus, it best maps "t"-shaped regions. It has been used extensively for maps of Europe and Asia.[1]: 61
The projection is defined as:
where
andφ is the latitude,λ is the longitude,λ0 is the longitude of the central meridian, andφ1 is the standard parallel of the projection.[2]
Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On thecentral meridian and the standard latitude shapes are not distorted.
The inverse projection is given by:
where
taking the sign ofφ1.
Special cases of the Bonne projection include thesinusoidal projection, whenφ1 is zero (i.e. theEquator), and theWerner projection, whenφ1 is 90° (i.e. theNorth orSouth Pole). The Bonne projection can be seen as an intermediate projection in the unwinding of aWerner projection into aSinusoidal projection; an alternative intermediate would be aBottomley projection.[3]
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