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Lambert Conformal Conic Projection

\begin{figure}\begin{center}\BoxedEPSF{maps/laco.epsf scaled 400}\end{center}\end{figure}


$\displaystyle x$ $\textstyle =$ $\displaystyle \rho\sin[n(\lambda-\lambda_0)]$ (1)
$\displaystyle y$ $\textstyle =$ $\displaystyle \rho_0-\rho\cos[n(\lambda-\lambda_0)],$ (2)

where
$\displaystyle \rho$ $\textstyle =$ $\displaystyle F\cot^n({\textstyle{1\over 4}}\pi+{\textstyle{1\over 2}}\phi)$ (3)
$\displaystyle \rho_0$ $\textstyle =$ $\displaystyle F\cot^n({\textstyle{1\over 4}}\pi+{\textstyle{1\over 2}}\phi_0)$ (4)
$\displaystyle F$ $\textstyle =$ $\displaystyle {\cos\phi_1\tan^n({\textstyle{1\over 4}}\pi+{\textstyle{1\over 2}}\phi_1)\over n}$ (5)
$\displaystyle n$ $\textstyle =$ $\displaystyle {\ln(\cos\phi_1\sec\phi_2)\over\ln[\tan({\textstyle{1\over 4}}\pi...
...\over 2}}\phi_2)\cot({\textstyle{1\over 4}}\pi+{\textstyle{1\over 2}}\phi_1)]}.$ (6)

The inverse Formulas are
$\displaystyle \phi$ $\textstyle =$ $\displaystyle 2\tan^{-1}\left[{\left({F\over\rho}\right)^{1/n}}\right]-{\textstyle{1\over 2}}\pi$ (7)
$\displaystyle \lambda$ $\textstyle =$ $\displaystyle \lambda_0+{\theta\over n},$ (8)

where
$\displaystyle \rho$ $\textstyle =$ $\displaystyle \mathop{\rm sgn}\nolimits (n)\sqrt{x^2+(\rho_0-y)^2}$ (9)
$\displaystyle \theta$ $\textstyle =$ $\displaystyle \tan^{-1}\left({x\over\rho_0-y}\right).$ (10)


References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 104-110, 1987.




© 1996-9 Eric W. Weisstein
1999-05-26