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.

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=1.5708r

See Projection Units for more information.

+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.