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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.




© 1996-9 Eric W. Weisstein
1999-05-26