Bonne projection

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A Bonne projection of the Earth. Standard parallel is

π / 4

A Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre or a Sylvanus projection. Although named after Rigobert Bonne (1727-1795), the projection was in use prior to his birth, in 1511 by Sylvano, Honter in 1561, De l'Isle before 1700 and Coronelli in 1696^[1].

The projection is:

$x = \rho \sin E\,$

$y = \cot \phi_1 - \rho \cos E\,$

where

$\rho = \cot \phi_1 + \phi_1 - \phi\,$

$E = \frac {\lambda \cos \phi} {\rho}$

and $\phi\,$ is the latitude, $\lambda\,$ is the longitude from the central meridian, and $\phi_1\,$ is the standard parallel of the projection^[2].

Special cases of the Bonne projection include the sinusoidal projection, when $\phi_1\,$ is zero, and the Werner projection, when $\phi_1\,$ is $\pi / 2\,$ .

Parallels of latitude are concentric circular arcs, and the scale is true along these arcs. On the central meridian and the standard latitude shapes are not distorted.

[edit] References

^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp.60-62, ISBN 0-226-76747-7
^ Map Projections - A Working Manual, USGS Professional Paper 1395, John P. Snyder, 1987, pp.138-140