# Talk:Helmert transformation

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## Wrong formula?

The current equation shows (1+s) on the diagonal.

According to these two web pages

http://www.og.dti.gov.uk/regulation/guidance/co_systems/co_sys_12.htm
http://www.linz.govt.nz/core/surveysystem/geodeticinfo/conversions/datums/transformation-equations/index.html

the values on the diagonal should be 1, and the whole matrix should be multiplied by 1+s (or rather, by 1+s*10^-6, which seems a more sensible way to :express it given that the scale factor is given as a ppm value).

Can anyone confirm which version of the formula is correct? (I would update the article myself, but I currently can't get either version of the formula to work for me) Wardog (talk) 09:35, 13 March 2008 (UTC)

The reference I have been using is
http://www.ordnancesurvey.co.uk/oswebsite/gps/information/coordinatesystemsinfo/guidecontents/guide6.html
which appears to use the same equation, as the Wiki page. It then issues this warning (which I don't know the relevance of, without some serious thinking) Quote:
Beware that two opposite conventions are in use regarding the rotation parameters of the Helmert transformation. Equation (3) uses the right-hand-rule rotation convention: with the positive end of an axis pointing towards you, a positive rotation about that axis is anticlockwise. A way to remember this is: if your right-hand thumb in hitch-hiking pose is the positive end of an axis, the curl of the fingers indicates positive rotation. Some published transformations use the opposite convention. In this case, reverse the signs of the three rotation parameters before applying equation (3). For safety, always include a test point with coordinates in systems A and B when stating a transformation.
As an aside it looks as if the NZ site and the OS site are using the CMS template for their site with different graphics, and color(sic) attributes.
Thank for the references- I can do with a refresher course on ED50.

ClemRutter (talk) 10:19, 13 March 2008 (UTC)

After I first commented on the discrepency, but before you added to the discussion I managed to test both versions of the formulae, and found they gave the same results (to within 10^-6 metres). Although the original looked a bit neater, I changed the equation in the article to the one on the LINZ page, simply because I could put an actual reference to the source. I suppose it could be reverted if you'd prefer the earlier version, and want to add the reference for it.
I also realised that my earlier problems with getting either to work was due to not converting seconds to radians. I put a big bold note about this at the start of the parameters table, just to make it obvious (there was a note about using radians in the intro, but it was not very obvious). Wardog (talk) 10:39, 13 March 2008 (UTC)
You must have been surprised that anyone replied to your post!

I do think the former was clearer, but it is a our duty to report it as it is. So I was thinking a sentence that started with This simple transformation is expressed in two ways that are mathematically equivalent. Then display both: or failing that place the other in a footnote. The reference I gave is already on the page. I have been struggling with a tool http://www.rutter.uklinux.net/ostowiki.html that can be be used to geotag pages, and found that most of the code used on Wikipedia fails to work correctly. When Time permits I want to do more on this so we can switch easily between OSGB WGS and ED50, and at the moment this article is not providing enough data. I am inspired to hve a look at the German page and see what is going on there ClemRutter (talk) 12:23, 13 March 2008 (UTC)

The LINZ formula being quoted needs explanation. The rotation parameters, being radians, or at least convertible to radians, are arguments of sine and cosine, not matrix coefficients directly. As it happens, they express small rotations where sin x ~ x and cos x ~ 1 to first order. In addition, the statement that signs need only be reversed to reverse the transformation is also in need of justification. Here 1/(1+S) ~ 1-S for small S and, in addition the C translation vector is being assumed unchanged by applying the inverse rotation. This last is, to say the least, suspect as datum coordinates are explicitly not being assumed unchanged. 50.152.242.160 (talk) 05:34, 26 December 2013 (UTC)