[MetaCRS] Fwd: Re: [Proj] Time dependent coordinate transformations

[Chris Crook]

Hi Martin

Your comments below address what I was much less precisely referring to as a "philosophical" question of whether a coordinate transformation (involving a datum shift) should be uniquely defined and invertible.

While I agree that these transformations do involve some error in their definition what I'm mainly  interested, in this discussion thread, is how they are defined and implemented within GIS systems.  In these systems most spatial definitions are not stochastically defined and most users may expect well defined transformations, eg from national datums to global datums.   This certainly can be provided by late binding, but it is not guaranteed by late binding alone - it also requires constraints on the conversions database (including the one you specify, for reversing a transformation).

None the less I agree that there are issues in trying to define these transformation uniquely.  Even between global systems there are multiple published versions of transformations (eg ITRF96-ITRF2008) and no "right" answer.

Cheers
Chris

From: Martin Desruisseaux [mailto:martin.desruisseaux at geomatys.fr]
Sent: Saturday, 10 January 2015 8:46 a.m.
To: Chris Crook; metacrs at lists.osgeo.org
Subject: Re: [MetaCRS] Fwd: Re: [Proj] Time dependent coordinate transformations


Hello Chris

Le 09/01/15 18:46, Chris Crook a écrit :

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.

Indeed a CRS_A → WGS84 → CRS_B transformation may not produce the same results than a CRS_A → CRS_B transformation. But this may actually be an issue of the pivot system. Coordinate transformations (not to be confused with coordinate conversions 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 CRS_A → WGS84 transformation may be valid only in some area with an accuracy "error_A", and the WGS84 → CRS_B transformation may be valid only in some other area with accuracy "error_B". Naively (I may be wrong) I would presume that the CRS_A → WGS84 → CRS_B transformation would be valid only in the intersection of the CRS_A → WGS84 and WGS84 → CRS_B domains of validity with a precision not better than max(error_A, error_B), or maybe error_A + error_B. This may not be the same domain of validity and precision than a direct CRS_A → CRS_B transformation.

On the reversibility, the EPSG database usually stores a (sourceCRS, targetCRS) pairs only in one way, for example CRS_A → CRS_B but not CRS_B → CRS_A. Instead they explain in their documentation how to reverse the operation. For a Molodensky 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.



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...)

I think they would be mathematically equivalent (ignoring numerical errors) for coordinate conversions, but I would be very surprised if they were equivalent for coordinate transformations (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.

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...



Of course there is a philosophical question as to whether coordinate transformations should give unique or consistent results.

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 - TOWGS84 element), assuming the rotation parameters are zero, there is at least 3 different ways to use those parameters: Geocentric translation, Molodensky and Abridged Molodensky. Each way will give slightly different results, and there is absolutely nothing in the TOWGS84 element or elsewhere in the WKT 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...



Regards,

    Martin



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