Wagner VI projection
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] [2]
[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.
Inverse formula:
[math]\displaystyle{ \begin{align} \psi &= \arcsin\left({\frac{\sqrt{3}}{\pi}}y\right) \\ \lambda &= \frac{x}{\cos{\psi}} \\ \varphi &= y \end{align} }[/math]
See also
References
- ↑ Wagner, Karlheinz (1949). Kartographische Netzentwürfe. Bibliographisches Institut, Leipzig. p. 197.
- ↑ Snyder, John P. (1993). Flattening the Earth: Two Thousand Years of Map Projections. p. 205. ISBN 0-226-76747-7. https://books.google.com/books?id=0UzjTJ4w9yEC&pg=PA205.
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