300px|thumb|Bonne projection of the world, standard parallel at 45°N.

300px|thumb|Bonne projection with [[Tissot's indicatrix of deformation.]]

300px|thumb|World map by Bernard Sylvanus, 1511

The Bonne projection is a pseudoconical equal-area map projection, sometimes called a dépôt de la guerre, modified Flamsteed,

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.

The inverse projection is given by:

:<math>\begin{align}\varphi &= \cot \varphi_1 + \varphi_1 - \rho \\

\lambda &= \lambda_0 + \frac{\rho} {\cos \varphi} \arctan \left(\frac {x}{ \cot \varphi_1 - y} \right) \end{align}</math>

where

:<math> \rho = \pm \sqrt{ x^2 + \left( \cot \varphi_1 - y\right)^2 }</math>

taking the sign of φ<sub>1</sub>.

Special cases of the Bonne projection include the sinusoidal projection, when φ<sub>1</sub> is zero (i.e. the Equator), and the Werner projection, when φ<sub>1</sub> is 90° (i.e. the North or South Pole). The Bonne projection can be seen as an intermediate projection in the unwinding of a Werner projection into a Sinusoidal projection; an alternative intermediate would be a Bottomley projection.

See also

  • List of map projections

References

  • Table of examples and properties of all common projections, from radicalcartography.net
  • An interactive Java Applet to study the metric deformations of the Bonne Projection
  • Bonne Projection (wolfram.com)