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>¶

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=1.570796r

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.