The Miller cylindrical projection is a modified Mercator projection, proposed by Osborn Maitland Miller in 1942. The latitude is scaled by a factor of 4⁄5, projected according to Mercator, and then the result is multiplied by 5⁄4 to retain scale along the equator. Hence:
x = λ y = 5 4 ln [ tan ( π 4 + 2 φ 5 ) ] = 5 4 sinh − 1 ( tan 4 φ 5 ) {\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}}}
or inversely,
λ = x φ = 5 2 tan − 1 e 4 y 5 − 5 π 8 = 5 4 tan − 1 ( sinh 4 y 5 ) {\displaystyle {\begin{aligned}\lambda &=x\\\varphi &={\frac {5}{2}}\tan ^{-1}e^{\frac {4y}{5}}-{\frac {5\pi }{8}}={\frac {5}{4}}\tan ^{-1}\left(\sinh {\frac {4y}{5}}\right)\end{aligned}}}
where λ is the longitude from the central meridian of the projection, and φ is the latitude. Meridians are thus about 0.733 the length of the equator. In GIS applications, this projection is known as: "ESRI:54003" and "+proj=mill". Compact Miller projection is similar to Miller but spacing between parallels stops growing after 55 degrees. In GIS applications, this projection is known as: "ESRI:54080" and "+proj=comill".
See also List of map projections
References
External links
Math formulae information Historical information Miller projection in proj4
