Cassini Projection

$\begin{figure}\begin{center}\BoxedEPSF{maps/cass.epsf scaled 400}\end{center}\end{figure}$

A Map Projection.

$\displaystyle x$	$\textstyle =$	$\displaystyle \sin^{-1}B$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle \tan^{-1}\left[{\tan\phi\over\cos(\lambda-\lambda_0)}\right],$	(2)

where

$\begin{displaymath} B=\cos\phi\sin(\lambda-\lambda_0). \end{displaymath}$

(3)

The inverse Formulas are

$\displaystyle \phi$	$\textstyle =$	$\displaystyle \sin^{-1}(\sin D\cos x)$	(4)
$\displaystyle \lambda$	$\textstyle =$	$\displaystyle \lambda_0+\tan^{-1}\left({\tan x\over\cos D}\right),$	(5)

where

$\begin{displaymath} D=y+\phi_0. \end{displaymath}$

(6)

References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 92-95, 1987.