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Eckert IV Projection

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EckertIVProjection

The equations are

x=2/(sqrt(pi(4+pi)))(lambda-lambda_0)(1+costheta)
(1)
y=2sqrt(pi/(4+pi))sintheta,
(2)

where theta is the solution to

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

This can be solved iteratively using Newton's method with theta_0=phi/2 to obtain

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

The inverse formulas are

phi=sin^(-1)((theta+sinthetacostheta+2sintheta)/(2+1/2pi))
(5)
lambda=lambda_0+(sqrt(pi(4+pi))x)/(2(1+costheta)),
(6)

where

theta=sin^(-1)(y/2sqrt((4+pi)/pi)).
(7)

See also

Eckert VI 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 IV Projection

Cite this as:

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

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