[Chimera-users] Origin of transformation matrices

[Tom Goddard]

Hi Daniel,

  The measure rotation command and fit in map output reports a transformation matrix that is a rotation and a translation that maps the coordinates of one model to the coordinates of another model, xyz -> R*xyz + T where R is the 3x3 rotation matrix and T is the translation vector.  These are listed as a 3x4 matrix with the first 3 columns being the rotation and the 4th column being the translation.

  The "origin" of density map is the position in the volume coordinate system where x,y,z = 0,0,0.  This is often *not* (boxsize/2, boxsize/2, boxsize/2).  For instance, for a box size of 100,100,100 the origin may be at grid point 49,49,49 instead of 50,50,50.  The exact center of the volume is at grid point 49.5,49.5,49.5 in this case where grid indices start at 0, ie 0-99.

  An MRC file has no header value that says whether the origin is set.  In other words, in the MRC file, the origin is always set, even if it is 0,0,0.  In fact there are two origins specified in the MRC header.  Chimera usually uses the xorigin, yorigin, zorigin values

	http://www2.mrc-lmb.cam.ac.uk/research/locally-developed-software/image-processing-software/#image <http://www2.mrc-lmb.cam.ac.uk/research/locally-developed-software/image-processing-software/#image>

for cryoEM maps, but for CCP4 files which is nearly an identical format but used mostly for x-ray crystallography it will instead use the nxstart, nystart, nzstart header values.  Whether a file is MRC or CCP4 is given by word 53 of the header.

  The origin being used by Chimera is reported in the Volume Viewer, menu Features / Coordinates, called Origin Index and is grid index units (not Angstroms) with grid indices starting at 0.

	Tom


> On Apr 9, 2019, at 4:17 PM, Daniel Asarnow 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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