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

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

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 \(x \leftarrow 0.85\lambda\).