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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.




© 1996-9 Eric W. Weisstein
1999-05-26