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Airy Projection


A map projection. The inverse equations for phi are computed by iteration. Let the angle of the projection plane be theta_b. Define

 a={0   for theta_b=1/2pi; (ln[1/2cos(1/2pi-theta_b)])/(tan[1/2(1/2pi-theta_b)])   otherwise.
(1)

For proper convergence, let x_i=pi/6 and compute the initial point by checking

 x_i=|exp[-(sqrt(x^2+y^2)+atanx_i)tanx_i]|.
(2)

As long as x_i>1, take x_(i+1)=x_i/2 and iterate again. The first value for which x_i<1 is then the starting point. Then compute

 x_i=cos^(-1){exp[-(sqrt(x^2+y^2)+atanx_i)tanx_i]}
(3)

until the change in x_i between evaluations is smaller than the acceptable tolerance. The (inverse) equations are then given by

phi=1/2pi-2x_i
(4)
lambda=tan^(-1)(-x/y).
(5)

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Cite this as:

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

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