Hatano Asymmetrical Equal Area¶
| Classification | 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 |
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 | \(C_p\) | \(C_p\) |
|---|---|---|
if +sym or \(\phi > 0\) |
1.75859 | 2.67595 |
if not +sym and \(\phi < 0\) |
1.93052 | 2.43763 |
For \(\phi = 0\), \(y \leftarrow 0\), and \(x \leftarrow 0.85\lambda\).