# Foucaut Sinusoidal¶

 Classification Pseudocylindrical Available forms Forward and inverse, spherical projection Defined area Global Alias fouc_s Domain 2D Input type Geodetic coordinates Output type Projected coordinates

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>

Central meridian/longitude of natural origin, longitude of origin or longitude of false origin (naming and meaning depend on the projection method).

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lon_0=1.570796r

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.