Miller Cylindrical

The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942.

Classification: Neither conformal nor equal area cylindrical

Available forms: Forward and inverse spherical

Defined area: Global, but best used near the equator

Alias: mill

Domain: 2D

Input type: Geodetic coordinates

Output type: Projected coordinates

Projection String

+proj=mill
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Required Parameters

• None

Optional Parameters

• +lon_0: Longitude of projection center. Defaults to 0.
• +R: Radius of the sphere.
• +x_0: False easting. Defaults to 0.
• +y_0: False northing. Defaults to 0.

Usage Example

Using Central meridian 90°W:

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

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

• Wikipedia on Miller Cylindrical
• "New Equal-Area Map Projections for Noncircular Regions", John P. Snyder, The American Cartographer, Vol 15, No. 4, October 1988, pp. 341-355.