# [Proj] Left- or right-handed rotation convention: which is which?

mikael.rittri at telia.com mikael.rittri at telia.com
Sat Sep 30 12:21:12 EDT 2006

```Hello,
I am confused.
At my work, I have tried to document the rotation convention used by
our software for seven-parameter datum shifts.  Since it was originally
based on publications from the Swedish Land Survey, it uses the
rotation convention of USA/Sweden/Luxembourg/Australia, as opposed to
the opposite European/IAG/ISO19111 convention.

Following http://www.ordnancesurvey.co.
uk/oswebsite/gps/information/coordinatesystemsinfo/guidecontents/guide6.
html, I have called the USA-etc. rotation convention the left-handed
one.  The British Ordnance Survey writes, about the European
convention,

"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."

But now, I have noticed that the Grids and Datums columns of Cliff
Mugnier (http://www.asprs.org/resources/grids), at least the columns on
Finland and the Netherlands, say that it is the American convention
that is right-handed, and the European one is left-handed.

Well, I suppose that everyone wants to be right, and no one wants to
be left!  But are there any simple, unambiguous names for these two
conventions?  Would the following be correct:
American convention = "coordinate frame rotation";
European convention = "position vector transformation".

Is the "Bursa-Wolf" transformation exactly the same as the European
convention, whereas a "Helmert" transformation is a more general term,
and can refer to either rotation convention (and, indeed, this kind of
transformation in n-dimensional Euclidean space, for any n)?