ag.rotate should rotate around selection center of mass/geometry

[kain88-de]

Expected behaviour

If I do ag.rotate(R) I would expect that I can rotate the protein I selected around it's center of mass/geometry. I would propose we add a kwarg origin for this. This point determines the origin or the rotation and we default to the center of geometry (or lab for backwards compatibility)

def rotate(self, R, origin='cog'):
    if origin=='cog':
        point = self.center_of_geometry()
    elif origin=='com':
        point = self.center_of_mass()
    elif origin=='lab':
        point = np.zeros(3)

    self.translate(-point)
    # do rotation
    self.translate(point)

Actual behaviour

The center of the rotation is the center of the coordinate system. This means instead of just an internal rotation I can rotate protein in my lab system to another place.

Currently version of MDAnalysis:

(run python -c "import MDAnalysis as mda; print(mda.__version__)")
0.16.0dev

[kain88-de]

We could also allow to give an arbitrary origin to this name selection

[richardjgowers]

@kain88-de there is also currently rotateby which looks like it does something like what you want?

[kain88-de]

But it doesn't accept a rotation/transformation matrix. Besides I spend today hours until I remembered this fact about rotate. Then that rotate and rotateby behave differently isn't good since one accepts a matrix and the other an axis and angle, plus origin of rotation, even though the docs say they do exactly the same thing.

[kain88-de]

I noticed today (after around one hour of debugging) that this change broke alignto and AlignTraj when we align an a selection instead of the whole protein. The problem is that align.rotation_matrix returns a matrix that assume the rotation is done around a point centered at (0,0,0) in the lab-system. Which was the old behavior when rotate is used. Since this is a very subtle change which can break existing user code in non obvious ways, I would revert this change and have rotate use (0,0,0) as a center for the rotation again. This means that rotate and rotateby have slightly different default behavior but I rather live with that for historical reasons then break lots of code that is used.

I will also include a new alignment test that shows the failure this change introduced.