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Hatano Asymmetrical Equal Area

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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

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+Hatano Asymmetrical Equal Area +
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proj-string: +proj=hatano

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Parameters

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Note

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All parameters for the projection are optional.

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++lon_0=<value>
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Longitude of projection center.

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Defaults to 0.0.

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

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See Ellipsoid size parameters for more information.

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++x_0=<value>
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False easting.

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Defaults to 0.0.

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++y_0=<value>
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False northing.

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Defaults to 0.0.

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Mathematical Definition

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Forward

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

\(C_y\)

\(C_p\)

For \(\phi > 0\)

1.75859

2.67595

For \(\phi < 0\)

1.93052

2.43763

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For \(\phi = 0\), \(y \leftarrow 0\), and \(x \leftarrow 0.85\lambda\).

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Further reading

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  1. Compare Map Projections

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  2. Mathworks

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