Miller cylindrical projection

File:Miller projection SW.jpg

A Miller projection of the Earth.

File:Miller with Tissot's Indicatrices of Distortion.svg

Miller projection with 1,000 km indicatrices of distortion.

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. Hence:

$$\begin{array}{rl}x& =\lambda \\ y& =\frac{5}{4}\ln [\tan (\frac{\pi }{4}+\frac{2\phi }{5})]=\frac{5}{4}{\sinh }^{}(\tan \frac{4\phi }{5})\end{array}$$

or inversely,

$$\begin{array}{rl}\lambda & =x\\ \phi & =\frac{5}{2}{\tan }^{-1}{e}^{\frac{4y}{5}}-\frac{5\pi }{8}=\frac{5}{4}{\tan }^{-1}(\sinh \frac{4y}{5})\end{array}$$

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

In GIS applications, this projection is known as: "ESRI:54003" and "+proj=mill".

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.

In GIS applications, this projection is known as: "ESRI:54080" and "+proj=comill".

See also

• List of map projections

External links

• Math formulae information
• Historical information
• Miller projection in proj4