Polyconic Projection

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

$\displaystyle x$	$\textstyle =$	$\displaystyle \cot\phi\sin E$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle (\phi-\phi_0)+\cot\phi(1-\cos E),$	(2)

where

$\begin{displaymath} E=(\lambda-\lambda_0)\sin\phi. \end{displaymath}$

(3)

The inverse Formulas are

$\begin{displaymath} \lambda={\sin^{-1}(x\tan\phi)\over\sin\phi}+\lambda_0, \end{displaymath}$

(4)

and $\phi$ is determined from

$\begin{displaymath} \Delta\phi=-{A(\phi\tan\phi+1)-\phi-{\textstyle{1\over 2}}(\phi^2+B)\tan\phi\over {\phi-A\over\tan\phi}-1}, \end{displaymath}$

(5)

where $\phi_0=A$ and

$\displaystyle A$	$\textstyle =$	$\displaystyle \phi_0+y$	(6)
$\displaystyle B$	$\textstyle =$	$\displaystyle x^2+A^2.$	(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. 124-137, 1987.