# 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

## Parameters¶

Note

All parameters for the projection are optional.

+lon_0=<value>

Longitude of projection center.

Defaults to 0.0.

Note

The default convention is to interpret this value as decimal degrees. To specify radians instead, follow the value with the "r" character.

Example: +lon_0=1.570796r

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