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A Miller projection of the Earth.
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Miller projection with 1,000 km indicatrices of distortion.
The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4&fras1;5, projected according to Mercator, and then the result is multiplied by 5&fras1;4 to retain scale along the equator.[1] Hence:
![{\displaystyle {\begin{aligned}x&=\lambda \\y&={\frac {5}{4}}\ln \left[\tan \left({\frac {\pi }{4}}+{\frac {2\varphi }{5}}\right)\right]={\frac {5}{4}}\sinh ^{-1}\left(\tan {\frac {4\varphi }{5}}\right)\end{aligned}}}](http://img.tfd.com/wiki/math/51/448dd8b80e38c444b174e3399065fc9f9d7ebe3e.svg)
or inversely,
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]
See also
- List of map projections
References
- ^ Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, ISBN 0-226-76747-7.
- ^ "Miller Cylindrical Projection". Wolfram MathWorld. Retrieved 25 March 2015.
- ^ "Projected coordinate systems". ArcGIS Resources: ArcGIS Rest API. ESRI. Retrieved 16 June 2017.
- ^ http://cartographicperspectives.org/index.php/journal/article/view/cp78-patterson-et-al/1362
External links