Hatano Asymmetrical Equal Area¶
Classification |
|
Available forms |
Forward and inverse, spherical projection |
Defined area |
Global |
Alias |
hatano |
Domain |
2D |
Input type |
Geodetic coordinates |
Output type |
Projected coordinates |
proj-string: +proj=hatano¶
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.See Ellipsoid size parameters for more information.
- +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 \(x \leftarrow 0.85\lambda\).