Airy Projection -- from Wolfram MathWorld

Airy Projection

A map projection. The inverse equations for are computed by iteration. Let the angle of the projection plane be . 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 and compute the initial point by checking

(2)

As long as , take and iterate again. The first value for which 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 between evaluations is smaller than the acceptable tolerance. The (inverse) equations are then given by

			(4)
			(5)

Airy Projection