Orthographic Projection

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

A projection from infinity which preserves neither Area nor angle.

$\displaystyle x$	$\textstyle =$	$\displaystyle \cos\phi\sin(\lambda-\lambda_0)$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle \cos\phi_1\sin\phi-\sin\phi_1\cos\phi\cos(\lambda-\lambda_0).$	(2)

The inverse Formulas are

$\displaystyle \phi$	$\textstyle =$	$\displaystyle \sin^{-1}\left({\cos c\sin\phi_1+{y\sin c\cos\phi_1\over\rho}}\right)$	(3)
$\displaystyle \lambda$	$\textstyle =$	$\displaystyle \lambda_0+\tan^{-1}\left({x\sin c\over\rho\cos\phi_1\cos c-y\sin\phi_1\sin c}\right),$	(4)

where

$\displaystyle \rho$	$\textstyle =$	$\displaystyle \sqrt{x^2+y^2}$	(5)
$\displaystyle c$	$\textstyle =$	$\displaystyle \sin^{-1} \rho.$	(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. 145-153, 1987.