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## Re: quaternions

 From: Konrad Hinsen Subject: Re: quaternions Date: Wed, 18 Dec 2019 20:17:40 +0100

```Hi Felix and Pierre,

> What I find a bit weird about the name "quaternion" is that it refers to
> the data type, just as "vector" or "complex number", and not to the
> property it describes. Admittedly, I don't know about any other use of
> quaternions than for representing rotations, at least in MD.

Same for me. But you are right, it is a bit strange.

> By the way, "rotation" would be a nice name too.

Yes and no: it is at the same time correct and confusing, because
"rotation" has different but related meanings.

For a mathematician, the story is simple: quaternions are a
representation of the rotation group. And a rotation is a kind of
transformation in 3D space. But in simulations, the quaternions
actually describe orientations of molecules, in terms of rotations
to a fixed reference configuration, whereas the term "rotation"
usually refers to motion, i.e. the *change* of orientation.

In short: it's a mess. But given that we care mostly about simulation
jargon, I'd prefer "orientation" to "rotation". The question then is
if we might want to admit another representation than quaternions for
orientations. If yes, we'd have to put "quaternion" somehow into the
name as well.

>> What you refer to as axis is the unit vector pointing along the
>> "long" axis of the ellipsoid, right? If so, I can think of "axis",
>> "u", "unit_vector", or even "orientation" actually.

"Axis" is ambiguous. What you describe is properly called the axis
of highest inertia, or the first principal axis. There's lots of other
axes one could be interested in.

"Orientation" is worse, of course ;-) The word has other meanings, and
the one you want to describe is only a part of the orientation.

> Practical question: is it required (in H5MD) that the quaternions/axis
> vectors are normalised? Should it be stated?

For quaternions, normalization is a requirement: only normalized
quaternions form a representation of the rotation group. So I'd say yes,
it should be a requirement, and therefore it should be stated.

For axis vectors, I have no opinion - I have never used them in
simulations.

Regards,
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