Hi
In you post you say you want to fit a small number of points. Note
that the
original algorithm of Kabsch has a number of maths pathalogical conditions
where points have symmetry or lie in a plane/line - this is common for
a small number of points (fitting residues or your example).
The maths for an update to this algorithm can be found here
Oldfield St'Fun'Gen (2002) 510-528 (appendix C) where cross terms
are used to generate the eigen vectors. This algorithm is very stable
for fitting a small number of points and might be more suitable for
what you are trying to do.
If you want I can email you the code in C or maybe Java, though it
has rather a lot of other weighting schemes/masking used in the above
paper.
Regards
Tom
> Lsqkabsch should do the trick.
> Herman
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
> Dale Tronrud
> Sent: Thursday, December 27, 2012 9:10 PM
> To: [log in to unmask]
> Subject: Re: [ccp4bb] 3D alignment of points (atoms)
>
>
> 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
>> --
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