[Proj] What about datum shift via direct projection?

[ndzinn at comcast.net]

Mikael, 



  

Thanks for these references on direct projection.   Weird, yes, in the sense of unusual, but clever and useful for the reasons stated by the authors.   



  

Regarding the least-squares adjustment for the new CM, scale on CM and false coordinates, linearization of the TM algorithm by Taylor expansion must be exceptionally ugly, but this can be simply accomplished numerically to achieve the same results. 



  

Regarding your questions: 

·          It's clever. 

·          Apparently used in Australia by Featherstone (cited by the authors). 

·          No geographic ambiguity implied in my opinion.   You'll notice the ellipsoid has also changed along with the new parameters already mentioned, an obvious requirement to reduce the residuals of the adjustment.   

·          What the authors have conjured is a TM on WGS84 that emulates a TM on Bessel (RT90) point by point within acceptable error limits.   But this is just an approximation, as is a 7-parameter similarity transformation for that matter.   The only definitive transformation is that achieved by a readjustment of available survey data (lots of trilateration in Sweden apparently) with a new ellipsoidal model.   Only that will achieve the least sum of residuals squared.   Geographicals in 3D are closer to reality than anything we do in the plane.   



  

Again, thanks, 

Noel 




----- Original Message ----- 
From: "Mikael Rittri" <Mikael.Rittri at carmenta.com> 
To: "PROJ.4 and general Projections Discussions" <proj at lists.maptools.org> 
Sent: Thursday, December 11, 2008 9:43:08 AM GMT -06:00 US/Canada Central 
Subject: [Proj] What about datum shift via direct projection? 


Gerald wrote: 
> While there seems to be lull in the hot debate about separation of 
> church and state ... er ... datum and projection, 
> [...] 
> Thus, why is it so necessary to bind the two operations so tightly as done 
> in the proj.4 distribution? I cannot find a precedence for this concept. 

This post is not specifically about the PROJ.4 design (so I changed 
the Subject line), but it is about how much datums and projections 
can and should be separated.   

There is method for datum shift that uses a direct projection.   

As an example, the old Swedish Grid is traditionally defined 
on the Swedish RT90 datum (ellipsoid: Bessel 1841) and using a 
Transverse Mercator projection with 
   central meridian: 15° 48' 29.8" E 
   scale factor:     1 
   false easting:    1500000 m 
   false northing:   0 m 
( http://www.lantmateriet.se/templates/LMV_Page.aspx?id=4766&lang=EN ) 

With this definition, one would need some datum shift method 
to transform between RT90 lon/lat and WGS84 lon/lat. 

However, a simpler method, now recommended by the Swedish Land Survey 
instead of a 7-parameter shift, is to start from the WGS84 datum, and than 
tweak the projection parameters a little: just use a Transverse Mercator 
with 
   central meridian: 15° 48' 22.624306" E   
   scale factor:     1.00000561024 
   false easting:    1500064.274 m 
   false northing:   -667.711 m 
( http://www.lantmateriet.se/templates/LMV_Page.aspx?id=5197&lang=EN ) 

A paper describing this technique is 
http://www.fig.net/pub/fig2006/papers/ps05_03/ps05_03_04_engberg_lilje_0670.pdf . 

So, I have some rather vague questions to the readers of this list: 
- What do you think of this technique? 
- Is anyone else using it? 
- Doesn't the technique imply that a projected coordinate system 
  may have an ambiguous geographic coordinate system?  For the Swedish Grid, 
  I can think of the geographic coordinate system as RT90 lon/lat, if I use 
  the traditional projection parameters. Or I can think of it as WGS84 lon/lat, 
  if I use the direct projection instead. 
- If the correct answer to the previous question is "No, you fool", then what? 
  If I wanted to express the Swedish Grid, datum-shifted by the direct projection, 
  in Well-Know Text, then I would be forced to say that the geographic coordinate 
  system is WGS84 lon/lat. But then the resulting CRS cannot be Swedish Grid, 
  because Swedish Grid has traditionally RT90 lon/lat as its geographic coordinate 
  system. 

I think direct projections for datum shifts are efficient and easy to 
use, and normally as accurate as a 7-parameter shift.  But when I try 
to fit this method into the traditional framework that separates datum 
shifts and projections, and which insists that each projected CRS 
has a unique geographic coordinate system, I run into problems. 

Are these problems caused by inflexibility in the traditional framework? 
Or is the method of direct projection just weird? 
Or am I missing some good way to reconcile them? 
   
Best regards, 

-- 
Mikael Rittri 
Carmenta AB 
Box 11354 
SE-404 28 Göteborg 
Visitors: Sankt Eriksgatan 5 
SWEDEN 
mikael.rittri at carmenta.com 
www.carmenta.com 
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