Miller cylindrical projection

{{Short description|Cylindrical compromise map projection}}

File:Miller projection SW.jpg.]]

File:Miller with Tissot's Indicatrices of Distortion.svg

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.Flattening the Earth: Two Thousand Years of Map Projections, John P. Snyder, 1993, pp. 179, 183, {{ISBN|0-226-76747-7}}. Hence:

or inversely,

where λ is the longitude from the central meridian of the projection, and φ is the latitude.{{cite web|title=Miller Cylindrical Projection|publisher=Wolfram MathWorld|url=http://mathworld.wolfram.com/MillerCylindricalProjection.html|access-date=25 March 2015}} Meridians are thus about 0.733 the length of the equator.

In GIS applications, this projection is known as: "ESRI:54003"{{cite web|title=Projected coordinate systems|url=http://resources.arcgis.com/en/help/arcgis-rest-api/index.html#/Projected_coordinate_systems/02r3000000vt000000/|website=ArcGIS Resources: ArcGIS Rest API|publisher=ESRI|access-date=16 June 2017}} and "+proj=mill".[https://proj.org/en/9.5/operations/projections/mill.html Open-source software PROJ]

Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees.{{Cite journal|url=http://cartographicperspectives.org/index.php/journal/article/view/cp78-patterson-et-al/1362|doi = 10.14714/CP78.1270|title = Introducing the Patterson Cylindrical Projection|year = 2015|last1 = Patterson|first1 = Tom|last2 = Šavrič|first2 = Bojan|last3 = Jenny|first3 = Bernhard|journal = Cartographic Perspectives|issue = 78|pages = 77–81|doi-access = free}}

In GIS applications, this projection is known as: "ESRI:54080" and "+proj=comill".[https://proj.org/en/9.5/operations/projections/comill.html Open-source software PROJ]