A computationally elegant and probably faster approach is to use
quaternions, proposed by MacKay in Acta Cryst. A40 165-166. For a recent
description of this method see
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2958452/
George
On 12/27/2012 09:09 PM, Dale Tronrud wrote:
> If you just want the mathematics and are willing to roll your own
> code, you can use the method of Wolfgang Kabsch. I see this has been
> enshrined in a Wikipedia page at
>
> http://en.wikipedia.org/wiki/Kabsch_algorithm
>
> This is what I've used when I've wanted to superimpose points where
> the mapping between the points is defined. If the points in your
> tetramer aren't pathological, like lying in a common plane, you
> shouldn't have to worry about SVD and can just perform the matrix
> inversion.
>
> Dale Tronrud
>
>
> On 12/27/12 11:16, Waugh, David (NIH/NCI) [E] wrote:
>> Greetings,
>>
>> I have what seems like a relatively simple problem to solve, but have not been able to do so using the software tools I know about. I have two sets of 4 points in 3D space (atoms in PDB files). They represent equivalent positions in two tetrameric proteins. I would like to align these points in one PyMol or Coot file. I don’t want a NEW set of points representing the LSQ average of the two sets, which is what I get in Coot’s SuperPose. Instead I am looking for a way to “superimpose” one atom from each set and then rotate one set for the best fit. I’m not an intuitive expert on symmetry, but I think there is probably only one best solution to this problem, right? I also need the atomic distances to be on the same scale in the two sets of points.
>>
>> Thanks for any help!
>>
>> Dave Waugh
>>
>> --
>> David S. Waugh, Ph.D.
>> Macromolecular Crystallography Laboratory
>> Center for Cancer Research
>> National Cancer Institute
>> Bldg. 538, Room 209A
>> Frederick, MD 21702-1201
>> +1 (301) 846-1842
>> [log in to unmask]
>> http://mcl1.ncifcrf.gov/waugh.html
>> --
--
Prof. George M. Sheldrick FRS
Dept. Structural Chemistry,
University of Goettingen,
Tammannstr. 4,
D37077 Goettingen, Germany
Tel. +49-551-39-3021 or -3068
Fax. +49-551-39-22582
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