Miller Cylindrical Projection

$\begin{figure}\begin{center}\BoxedEPSF{maps/micy.epsf scaled 500}\end{center}\end{figure}$

A Map Projection given by the following transformation,

$\displaystyle x$	$\textstyle =$	$\displaystyle \lambda-\lambda_0$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle {\textstyle{5\over 4}}\ln[\tan({\textstyle{1\over 4}}\pi+{\textstyle{2\over 5}}\phi)]$	(2)
	$\textstyle =$	$\displaystyle {\textstyle{5\over 4}} \sinh^{-1}[\tan({\textstyle{4\over 5}}\phi)].$	(3)

Here

and

are the plane coordinates of a projected point, $\lambda$ is the longitude

of a point on the globe, $\lambda_0$ is central longitude used for the projection, and $\phi$ is the latitude

of the point on the globe. The inverse Formulas are

$\displaystyle \phi$	$\textstyle =$	$\displaystyle {\textstyle{5\over 2}} \tan^{-1}(e^{4y/5})-{\textstyle{5\over 8}}\pi={\textstyle{5\over 4}}\tan^{-1}[\sinh({\textstyle{4\over 5}}y)]$	(4)
$\displaystyle \lambda$	$\textstyle =$	$\displaystyle \lambda_0+x.$	(5)

References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 86-89, 1987.