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:CCP4BB@JISCMAIL.AC.UK] On Behalf Of
Dale Tronrud
Sent: Thursday, December 27, 2012 9:10 PM
To: CCP4BB@JISCMAIL.AC.UK
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
wau...@mail.nih.gov
http://mcl1.ncifcrf.gov/waugh.html
--
