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)
Miller Cylindrical

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

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

Further reading

  1. Wikipedia