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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