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<div dir="ltr">Hi Nat,<div><br></div><div>it should be something like this:</div><div>1. Symmetry operation on fractional coordinates: Yfrac = S*Xfrac</div><div><span style="font-size: 12pt;">2. 'Fractionalisation' operation: Xfrac = G^t*Xcart</span></div><div>3. 'Orthoganalisation' of the result: Ycart = G*Yfrac</div><div>4. All together: Ycart = G*S*Xfrac = G*S*G^t*Xcart</div><div><br></div><div><span style="font-size: 12pt;">where S is a symmetry operator G is the orthogonalisation matrix and G^t is it's transpose. So you can pre-compute G*S*G^t,</span></div><div><br></div><div>Cheers,</div><div><br></div><div>o.</div><div><br></div><div><div><hr id="stopSpelling">From: nechols@lbl.gov<br>Date: Sun, 17 Aug 2014 15:36:00 -0700<br>To: cctbxbb@phenix-online.org<br>Subject: [cctbxbb] real-space symmetry operators<br><br><div dir="ltr">Hi all--<div><br></div><div>I'm trying to figure out how to orthogonalize symmetry operators given a unit cell, which doesn't seem to be something we have code for. These appear in PDB files in the REMARK 290 section but I haven't been able to find any other software that generates them, and the relationship between the symops and the real-space equivalents is unclear. I assume this is conceptually similar to orthogonalizing fractional coordinates, but unit_cell.orthogonalize() does not quite do what I wanted. In the PDB, for P63 it has this (excerpted):</div>
<div><br></div><div>REMARK 290 2555 -Y,X-Y,Z<br></div><div>...</div><div><div>REMARK 290 SMTRY1 2 -0.500000 -0.866025 0.000000 0.00000</div><div>REMARK 290 SMTRY2 2 0.866025 -0.500000 0.000000 0.00000</div>
<div>REMARK 290 SMTRY3 2 0.000000 0.000000 1.000000 0.00000</div></div><div><br></div><div>which looks like it should be relatively straightforward, but I'm not very good with matrices. Does anyone know the correct math for this? The corresponding rt_mx object from sgtbx looks like this:</div>
<div><br></div><div>r=(0.0, -1.0, 0.0, 1.0, -1.0, 0.0, 0.0, 0.0, 1.0) t=(0.0, 0.0, 0.0)<br></div><div><br></div><div>(Yes, I realize that there are much easier ways to apply symmetry operators to coordinates, but I want to limit the number of matrix multiplications involved when starting from Cartesian coordinates.)</div>
<div><br></div><div>thanks,</div><div>Nat</div></div>
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