Wagner VI projection

From HandWiki
Wagner VI projection of the world.

Wagner VI is a pseudocylindrical whole Earth map projection. Like the Robinson projection, it is a compromise projection, not having any special attributes other than a pleasing, low distortion appearance. Wagner VI is equivalent to the Kavrayskiy VII horizontally elongated by a factor of ​[math]\displaystyle{ 2 }[/math][math]\displaystyle{ \sqrt{3} }[/math]. This elongation results in proper preservation of shapes near the equator but slightly more distortion overall. The aspect ratio of this projection is 2:1, as formed by the ratio of the equator to the central meridian. This matches the ratio of Earth’s equator to any meridian.

The Wagner VI is defined by:[1]

[math]\displaystyle{ \begin{align} x &= \lambda \sqrt{1 - 3\left(\frac{\varphi}{\pi}\right)^2} \\ y &= \varphi \end{align} }[/math]

where [math]\displaystyle{ \lambda }[/math] is the longitude and [math]\displaystyle{ \varphi }[/math] is the latitude.

See also