Hatano Asymmetrical Equal Area¶
Classification | Pseudocylindrical Projection |
Available forms | Forward and inverse, spherical projection |
Defined area | Global |
Alias | hatano |
Domain | 2D |
Input type | Geodetic coordinates |
Output type | Projected coordinates |
Parameters¶
Note
All parameters for the projection are optional.
-
+lon_0
=<value>
¶ Longitude of projection center.
Defaults to 0.0.
-
+R
=<value>
¶ Radius of the sphere given in meters. If used in conjunction with
+ellps
+R
takes precedence.
-
+x_0
=<value>
¶ False easting.
Defaults to 0.0.
-
+y_0
=<value>
¶ False northing.
Defaults to 0.0.
Mathematical Definition¶
Forward¶
\[ \begin{align}\begin{aligned}x &= 0.85\lambda \cos \theta\\y &= C_y \sin \theta\\P(\theta) &= 2\theta + \sin 2\theta - C_p \sin \phi\\P'(\theta) &= 2(1 + \cos 2\theta)\\\theta_0 &= 2\phi\end{aligned}\end{align} \]
Condition | \(C_y\) | \(C_p\) |
---|---|---|
For \(\phi > 0\) | 1.75859 | 2.67595 |
For \(\phi < 0\) | 1.93052 | 2.43763 |
For \(\phi = 0\), \(y \leftarrow 0\), and \(x \leftarrow 0.85\lambda\).