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<p>Hello Chris<br>
</p>
<p>Le 09/01/15 18:46, Chris Crook a écrit :</p>
<blockquote
cite="mid:666FB8D75E95AE42965A0E76A5E5337E14DE0520B7@prdlsmmsg01.ad.linz.govt.nz"
type="cite">
<pre wrap="">The ambiguity I was hinting at was not just to do with converting from one coordinate system to another. It also relates to converting a data set from one coordinate system to another, and then to a third versus converting directly from the first to the third, or for that matter from one to another and then back again.</pre>
</blockquote>
<p align="justify">Indeed a <tt>CRS_A</tt> → <tt>WGS84</tt> → <tt>CRS_B</tt>
<u><i>transformation</i></u> may not produce the same results than
a <tt>CRS_A</tt> → <tt>CRS_B</tt> transformation. But this may
actually be an issue of the pivot system. Coordinate <u><i>transformations</i></u>
(not to be confused with coordinate <u><i>conversions</i></u> in
ISO 19111 terminology) are valid only in some domain of validity,
and have a limited accuracy (not related to the computer floating
point precision). So the <tt>CRS_A</tt> → <tt>WGS84</tt>
transformation may be valid only in some area with an accuracy "<tt>error_A</tt>",
and the <tt>WGS84</tt> → <tt>CRS_B</tt> transformation may be
valid only in some other area with accuracy "<tt><tt>error_</tt>B</tt>".
Naively (I may be wrong) I would presume that the <tt>CRS_A</tt>
→ <tt>WGS84</tt> → <tt>CRS_B</tt> transformation would be valid
only in the intersection of the <tt>CRS_A</tt> → <tt>WGS84</tt>
and <tt>WGS84</tt> → <tt>CRS_B</tt> domains of validity with a
precision not better than <tt>max(</tt><tt><tt>error_</tt>A, </tt><tt><tt>error_</tt>B)</tt>,
or maybe <tt><tt>error_</tt>A + </tt><tt><tt>error_</tt>B</tt>.
This may not be the same domain of validity and precision than a
direct <tt>CRS_A</tt> → <tt>CRS_B</tt> transformation.</p>
<p>
</p>
<p align="justify">On the reversibility, the EPSG database usually
stores a (<i>sourceCRS</i>, <i>targetCRS</i>) pairs only in one
way, for example <tt>CRS_A</tt> → <tt>CRS_B</tt> but not <tt>CRS_B</tt>
→ <tt>CRS_A</tt>. Instead they explain in their documentation how
to reverse the operation. For a <i>Molodensky</i> transformation
we just need to reverse the sign of parameter values. For map
projections this is more complicated, but there is no ambiguity.
So I don't think that the consistency concern applies to the
conversions or transformations back to the original CRS.<br>
</p>
<p align="justify"><br>
</p>
<blockquote
cite="mid:666FB8D75E95AE42965A0E76A5E5337E14DE0520B7@prdlsmmsg01.ad.linz.govt.nz"
type="cite">
<pre wrap="">Depending on how the late binding tables are constructed there would be no assurance that these transformations would give consistent results. Indeed, I suspect that if mathematically if both these were enforced then that would be equivalent to using an arbitrary pivot coordinate system (...snip...)</pre>
</blockquote>
<p align="justify">I think they would be mathematically equivalent
(ignoring numerical errors) for coordinate <i>conversions</i>,
but I would be very surprised if they were equivalent for
coordinate <i>transformations</i> (i.e. a coordinate operation
involving a datum shift) because of the stochastic nature of the
process. This is the discussion in my previous paragraphs.<br>
</p>
<p align="justify">But in addition to all the above, I don't see how
coordinate transformations through a pivot could address the
problem mentioned in my previous email, regarding the
transformation steps not being the method specified by
authoritative mapping agencies...<br>
</p>
<p align="justify"><br>
</p>
<blockquote
cite="mid:666FB8D75E95AE42965A0E76A5E5337E14DE0520B7@prdlsmmsg01.ad.linz.govt.nz"
type="cite">
<pre wrap="">Of course there is a philosophical question as to whether coordinate transformations should give unique or consistent results.
</pre>
</blockquote>
<p align="justify">I'm not sure what "uniqueness" means in the
context of coordinate transformations (not conversions). As
mentioned in my previous email, there is many possible
transformation methods between two CRS. Even if you give me
explicit Bursa-Wolf parameters (the numbers in the - now
deprecated - <tt>TOWGS84</tt> element), assuming the rotation
parameters are zero, there is at least 3 different ways to use
those parameters: <i>Geocentric translation</i>, <i>Molodensky</i>
and <i>Abridged Molodensky</i>. Each way will give slightly
different results, and there is absolutely nothing in the <tt>TOWGS84</tt>
element or elsewhere in the <tt>WKT</tt> telling us which method
to use. The method to use if often specified by the national
mapping agency for a particular country, so just saying "I
unconditionally use the most accurate method" is not necessarily
appropriate from an interoperability point of view...<br>
</p>
<p><br>
</p>
<p>Regards,<br>
</p>
<p> Martin<br>
</p>
<p><br>
</p>
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