Vertical Perspective Projection

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

A Map Projection given by the transformation equations

$\displaystyle x$	$\textstyle =$	$\displaystyle k'\cos\phi\sin(\lambda-\lambda_0)$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle k'[\cos\phi_1\sin\phi-\sin\phi_1\cos\phi\cos(\lambda-\lambda_0)],$	(2)

where

is the distance of the point of perspective in units of Sphere Radii and

$\displaystyle k'$	$\textstyle =$	$\displaystyle {P-1\over P-\cos c}$	(3)
$\displaystyle \cos c$	$\textstyle =$	$\displaystyle \sin\phi_1\sin\phi+\cos\phi_1\cos\phi\cos(\lambda-\lambda_0).$	(4)

References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 173-178, 1987.