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Eckert VI Projection

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EckertVIProjection

The equations are

x=((lambda-lambda_0)(1+costheta))/(sqrt(2+pi))
(1)
y=(2theta)/(sqrt(2+pi)),
(2)

where theta is the solution to

theta+sintheta=(1+1/2pi)sinphi.
(3)

This can be solved iteratively using Newton's method with theta_0=phi to obtain

Deltatheta=-(theta+sintheta-(1+1/2pi)sinphi)/(1+costheta).
(4)

The inverse formulas are

phi=sin^(-1)((theta+sintheta)/(1+1/2pi))
(5)
lambda=lambda_0+(sqrt(2+pi)x)/(1+costheta),
(6)

where

theta=1/2sqrt(2+pi)y.
(7)

See also

Eckert IV Projection

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References

Snyder, J. P. Map Projections--A Working Manual. U. S. Geological Survey Professional Paper 1395. Washington, DC: U. S. Government Printing Office, pp. 253-258, 1987.

Referenced on Wolfram|Alpha

Eckert VI Projection

Cite this as:

Weisstein, Eric W. "Eckert VI Projection." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/EckertVIProjection.html

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