[Proj] What about datum shift via direct projection?

[Noel Zinn]

My understanding of rubber sheeting is admittedly lacking, Gerald, but I
didn't know that it delivers the feature (fairly precise datum shifting)
that direct projection (per the reference) does.  

For those that have not followed the links, direct projection replaces the
following process,

LL(global)<>ECEF(global)<(7-parameter)>ECEF(local)<>LL(local)<>EN(proj),

with this, 

LL(global)<>EN(proj),

by a least-squares solution of the critical projection parameters (four in
the case of TM, and, additionally, the two ellipsoid parameters change from
local to global) over as many control points as you care to include.  There
is no change of projection.  Though possible, it will significantly
deteriorate the results (residuals on the control points) due to different
distortion footprints. The whole point is to plug the local control point EN
into the same projection with different parameters (and ellipsoid) and get
global (not local) LL.  

This whole exercise is handled mathematically without any visual reference
(the "sheet").  In fact, if you accept the 7-parameter geocentric ECEF datum
shift, the adjustment can be done with random numbers over the area of
interest (Sweden in this case).  But better if it be done with control
points whose survey data were originally adjusted on the local ellipsoid and
readjusted on the global ellipsoid, in order to reduce the residuals as much
as possible.  

I may be wrong, but I think this is more than rubber sheeting delivers.
Does MAPGEN do this?  With the centimetric residuals cited in the reference?
Over the size of a Swedish TM gon zone?

Nevertheless, I share your reservation.

Regards,
Noel

-----Original Message-----
From: proj-bounces at lists.maptools.org
[mailto:proj-bounces at lists.maptools.org] On Behalf Of Gerald I. Evenden
Sent: Monday, December 15, 2008 7:47 PM
To: proj at lists.maptools.org
Subject: Re: [Proj] What about datum shift via direct projection?

On Monday 15 December 2008 3:53:24 pm ndzinn at comcast.net wrote:
> 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.

>etc, etc.

I frankly do not see what is so clever about it.  You can rubber sheet any
2D 
surface onto another---even Mickey Mouse's face.

I did basically the same thing with MAPGEN.  MAPGEN had no idea what 
projection was involve as the "projection" operation in MAPGEN was carried 
out with a polynomial approximation of the projection.  Works fairly well
for 
large scale maps and is generally faster than cranking zillions of point 
though a full precision TM projection.

The only problem is that one still needs all the parts to generate the 
approximating rubber sheet.  And an added problem: keeping an audit trail
for 
others to know what you did.  Also, do others have your magic rubber sheet 
evaluator or inverse operation capability?

Sorry, I have reservations about all this.

-- 
The whole religious complexion of the modern world is due
to the absence from Jerusalem of a lunatic asylum.
-- Havelock Ellis (1859-1939) British psychologist
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