Bonne Projection

$\begin{figure}\begin{center}\BoxedEPSF{maps/bonn.epsf scaled 600}\end{center}\end{figure}$

A Map Projection which resembles the shape of a heart. Let $\phi_1$ be the standard parallel and $\lambda_0$ the central meridian. Then

$\displaystyle x$	$\textstyle =$	$\displaystyle \rho\sin E$	(1)
$\displaystyle y$	$\textstyle =$	$\displaystyle R\cot\phi_1-\rho\cos R,$	(2)

where

$\displaystyle \rho$	$\textstyle =$	$\displaystyle \cot\phi_1+\phi_1-\phi$	(3)
$\displaystyle E$	$\textstyle =$	$\displaystyle {(\lambda-\lambda_0)\cos\phi\over\rho}.$	(4)

The inverse Formulas are

$\displaystyle \phi$	$\textstyle =$	$\displaystyle \cot\phi_1+\phi_1-\rho$	(5)
$\displaystyle \lambda$	$\textstyle =$	$\displaystyle \lambda_0+{\rho\over\cos\phi} \tan^{-1}\left({x\over\cot\phi_1-y}\right),$	(6)

where

$\begin{displaymath} \rho=\pm\sqrt{x^2+(\cot\phi_1-y)^2}. \end{displaymath}$

(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. 138-140, 1987.