Conic Equidistant Projection

Conic Equidistant Projection

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

A Map Projection with transformation equations

$\displaystyle x$	$\textstyle =$	$\displaystyle \rho\sin\theta$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle \rho_0-\rho\cos\theta,$	(2)

where

$\displaystyle \rho$	$\textstyle =$	$\displaystyle (G-\phi)$	(3)
$\displaystyle \theta$	$\textstyle =$	$\displaystyle n(\lambda-\lambda_0)$	(4)
$\displaystyle \rho_0$	$\textstyle =$	$\displaystyle (G-\theta_0)$	(5)
$\displaystyle G$	$\textstyle =$	$\displaystyle {\cos\phi_1\over n}+\phi_1$	(6)
$\displaystyle n$	$\textstyle =$	$\displaystyle {\cos\phi_1-\cos\phi_2\over\phi_2-\phi_1}.$	(7)

The inverse Formulas are given by

$\displaystyle \phi$	$\textstyle =$	$\displaystyle G-\rho$	(8)
$\displaystyle \lambda$	$\textstyle =$	$\displaystyle \lambda_0+{\theta\over n},$	(9)

where

$\displaystyle \rho$	$\textstyle =$	$\displaystyle \mathop{\rm sgn}\nolimits (n)\sqrt{x^2+(\rho_0-y)^2}$	(10)
$\displaystyle \theta$	$\textstyle =$	$\displaystyle \tan^{-1}\left({x\over\rho_0-y}\right).$	(11)

© 1996-9 Eric W. Weisstein
1999-05-26