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.. _hatano:
********************************************************************************
Hatano Asymmetrical Equal Area
********************************************************************************
+---------------------+----------------------------------------------------------+
| **Classification** | :term:`Pseudocylindrical Projection` |
+---------------------+----------------------------------------------------------+
| **Available forms** | Forward |
+---------------------+----------------------------------------------------------+
| **Defined area** | Global, but best between standard parallels |
+---------------------+----------------------------------------------------------+
| **Implemented by** | Gerald I. Evenden |
+---------------------+----------------------------------------------------------+
| **Options** |
+---------------------+----------------------------------------------------------+
| `+lat_1` | Standard Parallel 1 |
+---------------------+----------------------------------------------------------+
| `+lat_2` | Standard Parallel 2 |
+---------------------+----------------------------------------------------------+
| `+sym` | Symmetric form used instead of asymmetric |
+---------------------+----------------------------------------------------------+
.. image:: ./images/hatano.png
:scale: 50%
:alt: Hatano Asymmetrical Equal Area
Mathematical Definition
--------------------------------------------------------------------------------
Forward
................................................................................
.. math::
\begin{array}
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
\end{array}
==================================== ================== ===================
Condition :math:`C_p` :math:`C_p`
==================================== ================== ===================
if ``+sym`` or :math:`\phi > 0` 1.75859 2.67595
if not ``+sym`` and :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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