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
Foucaut Sinusoidal

proj-string: +proj=fouc_s

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.

See Ellipsoid size parameters for more information.

+x_0=<value>

False easting.

Defaults to 0.0.

+y_0=<value>

False northing.

Defaults to 0.0.