Why is the result of quaternion rotation an matrix multiplication not the same

Hi guys,

Consider the following:

 R = [1,0,0;0,0,-1;0,1,0];
 y = [0;1;0];

 R*y
 quatrotate(rotm2quat(R),[0,1,0])

The results are (in the same order):

 (0; 0; 1)
 (0, 0, -1)

Why is the result not the same?

I can force it to give the same result if I do

quatrotate(quatinv(rotm2quat(R)),y)

which yields

 (0, 0, 1)

Thanks for the help!

[James Tursa]

See this link for a discussion of the MATLAB quaternion convention:

https://www.mathworks.com/matlabcentral/answers/465053-rotation-order-of-quatrotate

Answer 1

[Jan]

See https://www.mathworks.com/matlabcentral/answers/155400-why-does-quatrotate-produce-negative-rotations : It is the difference between rotating the coordinates or the reference frame.

[Daniel Schneider]

I understand this difference. However, wherefrom do I know if quatrotate rotates the vector or the reference frame?

This

    R = [1,0,0;0,0,-1;0,1,0];

I would say is a rotation rotating a vector 90 degrees around x. When I do

   q = rotm2quat(R)

I would expect q together with quatrotate to be the same. Why not or where in the documentation (rotm2quat or quatrotate) do I find that R will be converted into a transformation rotating the reference frame (coordinate system transformation)?

[Jan]

@Daniel: This is not mentioned in the documentation. I'm working with coordinate transformation for 35 years now and I've seen many codes, which implement the rotations without mentioning in the docs, if the object or the reference frame is accessed. This is horrible if you get a set of Euler angles for a multi-body-system and the author is convinced, that his definition is the only possible way. Corresponding discussions tend to end in flamewars.

Please ask Mathworks to enhance the documentation to clarify this important detail.

[Daniel Schneider]

OK Thanks. That was helpful!

So conclusively:

Let R be a rotation matrix rotating a vector in a fixed frame.

q = rotm2quat( R ).

quatrotate(q,v) will rotate the frame relative to a "fixed" vector v (equivalent to q^-1vq). In order to achieve

   r = Rv

either do

   qvq^-1

or

   quatrotate(quatinv(q),v)

This is not (yet) documented in the MATLAB documentation (at least as we know).

[James Tursa]

Jan: "Corresponding discussions tend to end in flamewars."

My experience also ...