[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[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.
......
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