Miller cylindrical projection

A Miller projection of the Earth.

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of  ⁴⁄₅, projected according to Mercator, and then the result is multiplied by  ⁵⁄₄ to retain scale along the equator.^[1] Hence:

${\displaystyle {\begin{aligned}x&=\lambda \\y&={\frac {5}{4}}\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {2\varphi }{5}}\right)\right]={\frac {5}{4}}\sinh ^{-1}\left(\tan {\frac {4\varphi }{5}}\right)\end{aligned}}}$

or inversely,

${\displaystyle {\begin{aligned}\lambda &=x\\\varphi &={\frac {5}{2}}\tan ^{-1}e^{\frac {4y}{5}}-{\frac {5\pi }{8}}={\frac {5}{4}}\tan ^{-1}\left(\sinh {\frac {4y}{5}}\right)\end{aligned}}}$

where λ is the longitude from the central meridian of the projection, and φ is the latitude.^[2] Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "EPSG:54003 - World Miller Cylindrical"

See also

• List of map projections

References

1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, ISBN 0-226-76747-7.
2. "Miller Cylindrical Projection". Wolfram MathWorld. Retrieved 25 March 2015.

External links

• Table of examples and properties of all common projections, from radicalcartography.net
• An interactive Java Applet to study the metric deformations of the Miller Projection.
• Math formulae information
• Spatial information
• Historical information