# Miller Cylindrical¶

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of $$\frac{4}{5}$$, projected according to Mercator, and then the result is multiplied by $$\frac{5}{4}$$ to retain scale along the equator.

 Classification Neither conformal nor equal area cylindrical Available forms Forward and inverse spherical Defined area Global, but best used near the equator Implemented by Gerald I. Evenden Options +lat_0 Latitude of origin (Default to 0)

## Usage¶

The Miller Cylindrical projection is used for world maps and in several atlases, including the National Atlas of the United States (USGS, 1970, p. 330-331) [Snyder1987].

Example using Central meridian 90°W:

\$ echo -100 35 | proj +proj=mill +lon_0=90w
-1113194.91      4061217.24


## Mathematical definition¶

The formulas describing the Miller projection are all taken from Snyder’s manuals [Snyder1987].

### Forward projection¶

$x = \lambda$
$y = 1.25 * \ln \left[ \tan \left(\frac{\pi}{4} + 0.4 * \phi \right) \right]$

### Inverse projection¶

$\lambda = x$
$\phi = 2.5 * ( \arctan \left[ e^{0.8 * y} \right] - \frac{\pi}{4} )$