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 \(n = 0\), \(\phi = \sin^1y\)
Parameters¶
Note
All parameters are optional for the Foucaut Sinusoidal projection.
-
+n
=<value>
¶ Weighting factor. Value should be in the interval 0-1.
-
+lon_0
=<value>
¶ Longitude of projection center.
Defaults to 0.0.
-
+R
=<value>
¶ Radius of the sphere given in meters. If used in conjunction with
+ellps
+R
takes precedence.
-
+x_0
=<value>
¶ False easting.
Defaults to 0.0.
-
+y_0
=<value>
¶ False northing.
Defaults to 0.0.