Azimuthal Equidistant Projection

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

An Azimuthal Projection which is neither equal-Area nor Conformal. Let $\phi_1$ and $\lambda_0$ be the Latitude and Longitude of the center of the projection, then the transformation equations are given by

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

Here,

$\begin{displaymath} k'={c\over\sin c} \end{displaymath}$

(3)

and

$\begin{displaymath} \cos c=\sin\phi_1\sin\phi+\cos\phi_1\cos\phi\cos(\lambda-\lambda_0), \end{displaymath}$

(4)

where

is the angular distance from the center. The inverse Formulas are

$\begin{displaymath} \phi=\sin^{-1}\left({\cos c\sin\phi_1+{y\sin c\cos\phi_1\over c}}\right) \end{displaymath}$

(5)

and

$\begin{displaymath} \lambda=\cases{ \lambda_0+\tan^{-1}\left({x\sin c\over c\co... ...+\tan^{-1}\left({x\over y}\right)& for $\phi_1=-90^\circ$,\cr} \end{displaymath}$

(6)

with the angular distance from the center given by

$\begin{displaymath} c=\sqrt{x^2+y^2}. \end{displaymath}$

(7)

References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 191-202, 1987.