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
Hatano Asymmetrical Equal Area

Mathematical Definition

Forward

\[ \begin{align}\begin{aligned}\begin{array}\\x &= 0.85\lambda \cos \theta\\y &= C_y \sin \theta\\P(\theta) &= 2\theta + \sin 2\theta - C_p \sin \phi\\P'(\theta) &= 2(1 + \cos 2\theta)\\\theta_0 &= 2\phi\\\end{array}\end{aligned}\end{align} \]
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 \(x \leftarrow 0.85\lambda\).