Winkel Tripel projection

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A Winkel Tripel projection of the Earth

The Winkel tripel projection is a modified azimuthal map projection, one of three projections proposed by Oswald Winkel in 1921. The projection is the arithmetic mean of the equirectangular projection and the Aitoff projection^[1]:

$(\lambda, \phi) \mapsto \left(\frac{\lambda \cos \phi_1 + 2 B \cos \phi \sin {\frac{\lambda}{2}}}{2} , \frac{\phi + B \sin \phi}{2}\right)$

where $\lambda\,$ is the longitude from the central meridian of the projection, $\phi\,$ is the latitude, and $\phi_1\,$ is the standard parallel for the equi-rectangular projection, and

$B = \frac{\alpha}{\sin \alpha}\,$

where

$\alpha = \arccos (\cos \phi \cos {\frac{\lambda}{2}})\,$

noting that when $\alpha = 0\,$ then B is explicitly defined to be 1. In his proposal, Winkel set :

$\phi_1 = \arccos {\frac{2}{\pi}}\,$ .

In 1998, the Winkel Tripel projection replaced the Robinson projection as the standard projection for world maps made by the National Geographic Society.