# 6 degree of freedom helmert transformation

I'm looking to do datum conversions for points with six degrees of freedom, that is, they are described by a heading, pitch, and roll in addition to their position information.

I know how to convert the orientation vector from a local NED or geodetic frame to the ECEF frame (using the method in this paper), but I don't know how to handle the orientation change when I use helmert transforms to convert between the different datums in ECEF space (i.e. WGS84 to NAD83).

So my question is, how can I perform a 6-DOF helmert transform, which preserves orientation information across the datum transformation? Is orientation affected by the transformation at all?

• I am unable to understand what you are asking, because your language of "heading, pitch, and roll" is so different from a datum transformation that the only possible connection seems purely (and abstractly) mathematical. If we make that abstract connection, though, the question is trivial: simply set the scale factor of the Helmert transformation to unity. What, then, do you really want to accomplish? What are your inputs, what are your intended outputs, how should they be related, and what exactly do you mean by "preserves orientation information"? – whuber Apr 15 '16 at 16:35
• @whuber So typically when you do a datum transformation you think of a point on the ground, which only has 3 dimensions of information. In my case I have moving bodies (e.g. a plane) that have a position, but also an orientation. I want to represent them in a different datum, but I think that in addition to having a slightly different position in the new datum, they will also have a slightly different orientation, and I don't know how to calculate the difference. – Nicolas Holthaus Apr 15 '16 at 16:49
• I think of a datum transformation entirely differently: not as a point on the ground, but as a translation, rotation, and rescaling of an ellipsoid used as a reference model for all positional coordinates. Such a geometric transformation of the ellipsoid induces a transformation of all derived quantities, including orientations, vectors, covectors, and tensors in general. In light of this, what is it you are actually trying to accomplish? – whuber Apr 15 '16 at 17:01
• I think I see what you're getting at, but why would you need to change the geoCRS (datum) before you derive data from the plane's orientation. That is, Derive XYZ or lat-lon-h (or H) using the plane's orientation and collected data, then convert to another geoCRS. – mkennedy Apr 15 '16 at 17:08