# 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>

Central meridian/longitude of natural origin, longitude of origin or longitude of false origin (naming and meaning depend on the projection method).

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

See Projection Units for more information.

+R=<value>

Radius of the sphere, given in meters. If used in conjunction with +ellps, +R takes precedence.

See Ellipsoid size parameters for more information.

+x_0=<value>

False easting, easting at false origin or easting at projection centre (naming and meaning depend on the projection method). Always in meters.

Defaults to 0.0.

+y_0=<value>

False northing, northing at false origin or northing at projection centre (naming and meaning depend on the projection method). Always in meters.

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 $$x \leftarrow 0.85\lambda$$.