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diff --git a/docs/source/usage/operations/projections/hatano.rst b/docs/source/usage/operations/projections/hatano.rst new file mode 100644 index 00000000..5d0c63b7 --- /dev/null +++ b/docs/source/usage/operations/projections/hatano.rst @@ -0,0 +1,70 @@ +.. _hatano: + +******************************************************************************** +Hatano Asymmetrical Equal Area +******************************************************************************** + + + + ++---------------------+----------------------------------------------------------+ +| **Classification** | :term:`Pseudocylindrical Projection` | ++---------------------+----------------------------------------------------------+ +| **Available forms** | Forward and inverse, spherical projection | ++---------------------+----------------------------------------------------------+ +| **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:: + + 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_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>`__ + + + |