Miller cylindrical projection explained

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

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

or inversely,

$\begin \lambda &= x \\ \varphi &= \frac\tan^e^\frac - \frac = \frac\tan^\left(\sinh\frac\right)\end$

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: "ESRI:54003 – World Miller Cylindrical".^[3]

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.^[4]

References

Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, .
Web site: Miller Cylindrical Projection. Wolfram MathWorld. 25 March 2015.
Web site: Projected coordinate systems. ArcGIS Resources: ArcGIS Rest API. ESRI. 16 June 2017.
Introducing the Patterson Cylindrical Projection. 10.14714/CP78.1270. 2015. Patterson. Tom. Šavrič. Bojan. Jenny. Bernhard. Cartographic Perspectives. 78. 77–81. free.

Miller cylindrical projection explained

See also

References

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