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+Rtakes 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 \(x \leftarrow 0.85\lambda\).
