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

Hatano Asymmetrical Equal Area

proj-string: +proj=hatano

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=1.5708r

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.

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 \(x \leftarrow 0.85\lambda\).

Further reading

  1. Compare Map Projections

  2. Mathworks