Foucaut Sinusoidal

The y-axis is based upon a weighted mean of the cylindrical equal-area and the sinusoidal projections. Parameter \(n=n\) is the weighting factor where \(0 <= n <= 1\).

\[ \begin{align}\begin{aligned}x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi)\\y &= n \phi + (1 - n) \sin \phi\end{aligned}\end{align} \]

For the inverse, the Newton-Raphson method can be used to determine \(\phi\) from the equation for \(y\) above. As \(n \rightarrow 0\) and \(\phi \rightarrow \pi/2\), convergence is slow but for \(n = 0\), \(\phi = \sin^1y\)