[Proj] Algorithms & Plate Carrée

[Noel Zinn (cc)]

Thanks, Irwin.  That helps, but I am still confused by this statement:

> how can one correct for the distortion due to Plate Carrée?

Where does Plate Carrée figure into this?  Not from Google Earth where the 
poles can be displayed, not possible in Plate Carrée.  I'd guess that the 
"projection" you get in Google Earth is an ellipsoidal orthographic, the 
formulas for which can be found here:

http://www.hydrometronics.com/downloads/Ellipsoidal%20Orthographic%20Projection.pdf

The inverse offered in the link is iterative.  Charles Karney has a closed 
inverse that I can provide.

So, setting aside registration and atmospheric distortion, the problem is 
defined as the difference in area between a UTM "square" and an ellipsoidal 
orthographic "square" with the same geographical vertices.  That seems 
solvable, but is it what you mean?

Noel

Noel Zinn, Principal, Hydrometronics LLC
+1-832-539-1472 (office), +1-281-221-0051 (cell)
noel.zinn at hydrometronics.com (email)
http://www.hydrometronics.com (website)

-----Original Message----- 
From: Irwin Scollar
Sent: Monday, July 23, 2012 8:58 AM
To: proj at lists.maptools.org
Subject: [Proj] Algorithms & Plate Carrée

Noel Zinn wrote:

"Your question can be interpreted in many ways
and it's not clear to me what you really mean. "

I didn't express myself clearly.  Sorry.

For example, given a 1 kilometer square area in
Google Earth, and the same 1 kilometer square
area on a precision digital map made with ground
or aerial survey in UTM-WGS84, there will be an
error when measuring coordinates in GoogleEarth
imagery compared with those on the map for
visible features in both. This error which will
vary over the area because the projections are
not identical in addition to the absolute error
at a given known point as cited by Noel, plus the
optical and atmospheric distortion errors in the GE imagery.

Assuming that one or more points in the Google
Earth image have known coordinates in UTM
obtained either from maps as above or with
differential ground GPS measurement from known
points nearby,  and that optical, perspective and
atmospheric distortions can be neglected (?), how
can one correct for the distortion due to Plate Carrée?

Might this be the same as calculating something
like an inverse of a Tissot Indicatrix for the small area?

Irwin

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