[Proj] CEA from an ellipse and +R_A
David James Brockley
djb at mssl.ucl.ac.uk
Fri Jul 11 05:57:49 EDT 2008
I'm trying to convert geodetic lon/lat into CEA xy using the proj API
+proj=cea +long_0=0 +ellps=WGS84 +R_A
What I expect to happen is
y = a * q / 2
where a is the authalic radius calculated from the semi-major of WGS84.
q/2 seems to be a common approximation to q/q_p which is sin
( authalic latitude)
What actually happens is that proj uses the equation for a sphere
rather than an ellipse.
y = a sin( phi )
I can get proj to do what I expect by initialising with
+proj=cea +long_0=0 +a=6371007 +e=0.0818191
but that seems somewhat back to front.
Can anyone tell me the correct way to configure proj for what I am
trying to do?
I'm fairly sure that my expected function for y is correct, since
I've both copied it from the literature and derived it by hand from
the spherical case by substituting authalic radius for radius and
authalic latitude for latitude - I've also realised that the /2 is
due to the maximum possible value of q_p being 2 when e=0, and that
it doesn't affect the properties of the transform (still equal area).
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