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.. _fouc_s:
********************************************************************************
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 |
+---------------------+----------------------------------------------------------+
.. figure:: ./images/fouc_s.png
:width: 500 px
:align: center
:alt: 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 :math:`n=n` is the weighting factor where
:math:`0 <= n <= 1`.
.. math::
x &= \lambda \cos \phi / (n + (1 - n) \ cos \phi)
y &= n \phi + (1 - n) \sin \phi
For the inverse, the Newton-Raphson method can be used to determine
:math:`\phi` from the equation for :math:`y` above. As :math:`n \rightarrow 0` and
:math:`\phi \rightarrow \pi/2`, convergence is slow but for :math:`n = 0`, :math:`\phi =
\sin^1y`
Parameters
################################################################################
.. note:: All parameters are optional for the Foucaut Sinusoidal projection.
.. option:: +n=<value>
Weighting factor. Value should be in the interval 0-1.
.. include:: ../options/lon_0.rst
.. include:: ../options/R.rst
.. include:: ../options/x_0.rst
.. include:: ../options/y_0.rst
|
