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.. _hatano:
********************************************************************************
Hatano Asymmetrical Equal Area
********************************************************************************
+---------------------+----------------------------------------------------------+
| **Classification** | :term:`Pseudocylindrical Projection` |
+---------------------+----------------------------------------------------------+
| **Available forms** | Forward and inverse, spherical projection |
+---------------------+----------------------------------------------------------+
| **Defined area** | Global |
+---------------------+----------------------------------------------------------+
| **Alias** | hatano |
+---------------------+----------------------------------------------------------+
| **Domain** | 2D |
+---------------------+----------------------------------------------------------+
| **Input type** | Geodetic coordinates |
+---------------------+----------------------------------------------------------+
| **Output type** | Projected coordinates |
+---------------------+----------------------------------------------------------+
.. figure:: ./images/hatano.png
:width: 500 px
:align: center
:alt: Hatano Asymmetrical Equal Area
proj-string: ``+proj=hatano``
Parameters
################################################################################
.. note:: All parameters for the projection are optional.
.. include:: ../options/lon_0.rst
.. include:: ../options/R.rst
.. include:: ../options/x_0.rst
.. include:: ../options/y_0.rst
Mathematical Definition
--------------------------------------------------------------------------------
Forward
................................................................................
.. math::
x &= 0.85\lambda \cos \theta
y &= C_y \sin \theta
P(\theta) &= 2\theta + \sin 2\theta - C_p \sin \phi
P'(\theta) &= 2(1 + \cos 2\theta)
\theta_0 &= 2\phi
==================================== ================== ===================
Condition :math:`C_y` :math:`C_p`
==================================== ================== ===================
For :math:`\phi > 0` 1.75859 2.67595
For :math:`\phi < 0` 1.93052 2.43763
==================================== ================== ===================
For :math:`\phi = 0`, :math:`y \leftarrow 0`, and :math:`x \leftarrow 0.85\lambda`.
Further reading
--------------------------------------------------------------------------------
#. `Compare Map Projections <http://map-projections.net/single-view/hatano>`__
#. `Mathworks <http://www.mathworks.com/help/map/hatano.html>`__
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