[Proj] truble to translate coordinates from WGS84 to EPSG:31287

[Mikael Rittri]

Noel,

I didn't use the least squares method to derive my direct projection.
(I didn't have any survey data.)  Instead, my goal was to emulate the 
result of the 7-parameter datum shift.  So I basically fiddled the
parameters, using very few test points. 

> A pertinent question would be, does "direct projection" 
> fit the data better than a 7-parameter transformation? 

My feeling is that when you modify projection parameters 
very slightly, the effects on the projected grid can 
be described as parallel translation, scaling and rotation
- to a first approximation.  Therefore, one should 
expect that direct projection can give equally good 
accuracy as a 7-parameter transform. Not much better,
but not much worse. 

In the paper by Engberg and Lilje, they could usually 
emulate a 7-parameter transform with a few decimeters 
error.  I think this suggests that the two methods 
are (nearly) equally powerful. 
 
For some projection types, though, like Mercator, 
one cannot implement any rotation by fiddling with a 
parameter.  (Perhaps one could replace a Mercator by
a Lambert Conformal Conic with a standard parallel
very near the equator.)  

In the MGI / Austria Lambert example, I found that 
it was easy to fiddle with the projection parameters, 
since one (or two) parameters controls either rotation, 
scaling or parallel translation.

 * the choice of central longitude controls the rotation of the grid;
 * the choice of standard parallels controls the scaling of the grid;
 * the choice of false easting and northing controls the parallel translation.

So I could improve rotation, scaling, and translation independently. 
That is, I didn't have to backtrack.  (I think it is easier with a 
conic projection, since changing the central longitude causes a 
rotation of the grid and nothing else.  With a Transverse Mercator, 
a small change of the central longitude causes mainly a rotation, 
but also some very small other distortions.) 

Mikael Rittri
Carmenta AB
Sweden
http://www.carmenta.com

-----Original Message-----
From: proj-bounces at lists.maptools.org [mailto:proj-bounces at lists.maptools.org] On Behalf Of Noel Zinn (cc)
Sent: den 3 november 2010 14:31
To: PROJ.4 and general Projections Discussions
Subject: Re: [Proj] truble to translate coordinates from WGS84 to EPSG:31287

Mikael,

If you merely "fiddle" the projection parameters (CM, lat0, scale, false coordinates, parallels maybe, etc.), the "direct projection" method might be regarded as a "dirty hack".  But the paper you cited two years ago:

http://www.fig.net/pub/fig2006/papers/ps05_03/ps05_03_04_engberg_lilje_0670.pdf

presents a methodical process for determining the parameters optimally (i.e. 
by least-squares constraint applied to the the survey data).  Seems rigorous and innovative to me.  And if the projection used is conformal, then the "direction projection" method is by definition conformal, too (i.e. 
preserves the angles of intersecting lines).  The 7-parameter transformation is also conformal, but multiple regression equations (MRE) and grid methods (NADCON, NTv2) are not.  A pertinent question would be, does "direct projection" fit the data better than a 7-parameter transformation?

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)

--------------------------------------------------
From: "Mikael Rittri" <Mikael.Rittri at carmenta.com>
Sent: Monday, November 01, 2010 9:06 AM
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org>
Subject: Re: [Proj] truble to translate coordinates from WGS84 to EPSG:31287

> Hello Markus,

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