Miller cylinder projection

Miller cylinder projection of the earth

The Miller cylinder projection is a modified Mercator projection proposed by Osborn Maitland Miller in 1942 . It is neither conformal nor true to area . The modification has the effect that the distances between the lines of latitude grow less strongly with increasing pole proximity compared to the Mercator projection, whereby the surface distortion is reduced.

construction

The x and y coordinates of a point on the map are determined by the following equation:

${\displaystyle x=\lambda -\lambda _{0},}$

${\displaystyle y={\frac {5}{4}}\ln \left[\tan \left({\frac {1}{4}}\pi +{\frac {2}{5}}\varphi \right)\right]={\frac {5}{4}}\sinh ^{-1}\left[\tan \left({\frac {4}{5}}\varphi \right)\right]}$

wherein and the longitude and latitude of the point and the longitude of the map center denote (angle in radians ). ${\displaystyle \lambda }$ ${\displaystyle \varphi }$ ${\displaystyle \lambda _{0}}$

The latitude is first multiplied by the factor , then the Mercator projection is applied and finally the result is multiplied by the reciprocal value. ${\displaystyle 4/5}$ ${\displaystyle 5/4}$

Web links

Commons : Miller Cylinder Projection  - collection of images, videos, and audio files

Individual evidence

1. ↑ Eric W. Weisstein: Miller Cylindrical Projection. Wolfram MathWorld, accessed May 30, 2013 . 
2. ↑ Carlos Alberto Furuti: Cylindrical Projections. Retrieved May 30, 2013 .