[Proj] +towgs84 approximation error

Noel Zinn (cc) ndzinn at comcast.net
Wed Mar 22 16:59:25 EST 2017


If you want to abandon the small-angle approximation and use sines and 
cosines, you must then define an order for the three rotation matrices 
(about X, about Y, and about Z).  Different matrix orders give different 
answers.  What's your preferred order and why?


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: Jochem
Sent: Wednesday, March 22, 2017 4:41 PM
To: proj at lists.maptools.org
Subject: [Proj] +towgs84 approximation error


I joined the mailing list because I noticed that the PROJ.4 library uses
approximate formulas for the 7 parameter coordinate transformation defined
by +towgs84 (technical details: The elements of the rotation matrix are the
rotation angles instead of the product of sines and cosines of the angles).
For really small rotation angles this gives the same result, but not for
larger rotations.

For my current application I want to transform a map in QGIS with 1 mm
accuracy. However, the approximation causes an error of 4 cm. Since PROJ.4
normally gives results within 0.1 mm accuracy, I did not expect such

What can I do to help to fix this?

Regards, Jochem

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