# 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

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 +R takes 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 $$x \leftarrow 0.85\lambda$$.