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"[3] and "+proj=mill".[4]

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.[5]

In GIS applications, this projection is known as: "ESRI:54080" and "+proj=comill".[6]

See also

References

  1. Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, .
  2. Web site: Miller Cylindrical Projection. Wolfram MathWorld. 25 March 2015.
  3. Web site: Projected coordinate systems. ArcGIS Resources: ArcGIS Rest API. ESRI. 16 June 2017.
  4. https://proj.org/en/9.5/operations/projections/mill.html Open-source software PROJ
  5. Introducing the Patterson Cylindrical Projection. 10.14714/CP78.1270. 2015. Patterson. Tom. Šavrič. Bojan. Jenny. Bernhard. Cartographic Perspectives. 78. 77–81. free.
  6. https://proj.org/en/9.5/operations/projections/comill.html Open-source software PROJ

External links

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