Sinusoidal (Sanson-Flamsteed)

Classification: Pseudocylindrical

Available forms: Forward and inverse, spherical and ellipsoidal

Defined area: Global

Alias: sinu

Domain: 2D

Input type: Geodetic coordinates

Output type: Projected coordinates

Projection String

+proj=sinu
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Parameters

All parameters are optional.

• +lon_0=<value>: Central meridian.
• +R=<value>: Radius of the sphere or semi-major axis of the ellipsoid.
• +x_0=<value>: False easting.
• +y_0=<value>: False northing.

Mathematical Definition

MacBryde and Thomas developed generalized formulas for several of the pseudocylindricals with sinusoidal meridians. The formulas describing the Sinusoidal projection are:

Forward projection: $$x = C\lambda(m+cos\theta) / ( m + 1)$$ $$y = C\theta$$

Inverse projection: $$\lambda = x \cdot \frac{m + 1}{C \cdot (m + \cos(y / C))}$$ $$\theta = y / C$$

Where: $$C = \sqrt { (m + 1 ) / n }$$

Further Reading

• Wikipedia