[Proj] Standard projection for Mediterranean basin

[OvV_HN]

Very interesting!
But, could you please balance the parentheses in equation 4 (and 3), because 
equation 4 cannot be calculated.

Oscar van Vlijmen



----- Original Message ----- 
From: "strebe" <strebe at aol.com>
To: "Jan Hartmann" <j.l.h.hartmann at uva.nl>; "PROJ.4 and general Projections 
Discussions" <proj at lists.maptools.org>
Sent: Tuesday, February 16, 2010 4:55 AM
Subject: Re: [Proj] Standard projection for Mediterranean basin



Jan & colleagues:

Regarding the question of optimal standard parallels for Albers, I found my 
notes from 8 years ago. To summarize, there is no good rule, so perhaps the 
exact calculation I describe below has more importance than just academic.

Regards,
— daan Strebe

.....

3) sin (phi[2]) = [sin (phi[1]) - 2 sin (phi[N]) + sin (phi[1]) sin^2 
(phi[N])] / [2 sin (phi[N]) * sin (phi[1]) - sin^2 (phi[N]) - 1]

However, we do not yet know the proper phi[1]. With much manipulation, we 
discover the iterative equation:

4) cos^2 (phi[1]) * sqrt (1 + sin^2 (phi[0]) - 2 sin (phi[0]) * sin 
(phi[S])) - cos (phi[S]) (1 + sin^2 (phi[0] - 2 sin (phi[0]) sin (phi[1]) = 
0

We solve for phi[1] with (4) and then use (3) to compute phi[2]. Now have 
the optimal Albers for any circumstance.
......