# [Proj] Standard projection for Mediterranean basin

OvV_HN ovv at hetnet.nl
Tue Feb 16 06:57:03 EST 2010

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

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

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

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

```