[Chimera-users] Origin of transformation matrices

[Elaine Meng]

Hi Daniel,
The sum total of my understanding here is in the “measure rotation” description:
<http://www.rbvi.ucsf.edu/chimera/docs/UsersGuide/midas/measure.html#rotation>

The matrix describes a rotation and a translation in the coordinate system of the first model in the command.  I believe this is in xyz coordinates, not grid units.  You can see grid indices corresponding to XYZ (0,0,0) in the Volume Viewer by using menu: Features… Coordinates to show that section:
<http://www.rbvi.ucsf.edu/chimera/docs/ContributedSoftware/volumeviewer/volumeviewer.html#coordinates>

Alternatively (going back to  the“measure rotation” description) the transformation is described as an axis, rotation around that axis (not center of rotation, but I believe the axis is all you need, pinned in space by a point on that axis which is also given) and shift parallel to that axis.

Our expert in this area is away currently, so although he may be able to shed more light on this and whether there is a problem with your calculations, it may be a while, sorry.
I hope this helps,
Elaine
-----
Elaine C. Meng, Ph.D.                       
UCSF Chimera(X) team
Department of Pharmaceutical Chemistry
University of California, San Francisco

> On Apr 9, 2019, at 4:17 PM, Daniel Asarnow <asarnow at msg.ucsf.edu> wrote:
> 
> Hi,
> What's the origin for the rotation/translation output by measure rotation or fit-in-map results? If the origin index is 0, is the transformation calculated around (0, 0, 0)?
> 
> I'm extending my software for transforming single-particle EM alignment parameters to accept a transformation matrix copy-pasted from Chimera and am having a slight difficulty. For most EM maps, the origin MRC header is not set, and the origin appears to be (0,0,0). Thus, if R and V are the rotation and translation from Chimera, the formula R * O + V - O where O is the real origin (boxsize / 2, boxsize / 2, boxsize / 2) should give the correct translation. However, it's exactly one pixel short.
> 
> Best,
> -da
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