I don't think Eulerian angles are defined for a non-orthogonal axis system? ?
They are defined relative to perpendicular axes X Y Z e.g. Rotate coordinates by gamma about Z, beta about Y', alpha about Z". Eleanor On 5 September 2014 16:27, Chen Zhao <[email protected]> wrote: > Thank you Eleanor for your reply. I am actually considering how to > describe a pseudo-NCS with an arbitrary rotational and translational > relationship. I don't have to do this but I am just curious. It is more > straightforward if I say how the two molecules are related by a rotation > around unit cell axis than around orthogonal coordinate axis, which does > not have an absolute physical meaning. > > The command line output after coot superpose prints out the rotational and > translational matrices for both the orthogonal and fractional coordinate > system. > > For using coordconv, my concern is that if I deal with a low-symmetry unit > cell, which is not orthogonal by itself, the Euler angles for the > fractional coordinate system and the orthogonal coordinate system should be > different. If I just feed some numbers into coordconv, will it consider > them as orthogonal coordinates? > > Thank you, > Chen > > On Fri, Sep 5, 2014 at 6:24 AM, Eleanor Dodson <[email protected]> > wrote: > >> Rotation matrices are rarely specified in a fractional coordinate >> system? The criteria for checking such a matrix is "Is the determinant 1?" >> and this only holds for orthogonal matrices. >> >> >> >> I guess the way I would do this though. >> >> You presumably have two sets of fractional coordinates, before and after >> rotation? >> >> There is a ccp4 program - coordconv which will read the fractional >> coordinates and generate pdb format with the convention ncode = 1 (You may >> need to fudge the fractional format I suppose..) >> >> You can then use superpose to match the two sets of coordinates and the >> output will tell you the Eulerian angles used for the rotation! >> >> Lots of ways to kill cats! >> Eleanor >> >> >> >> >> >> On 4 September 2014 21:21, Phil Jeffrey <[email protected]> wrote: >> >>> The orthogonal/fractional matrix is outlined here: >>> http://www.iucr.org/__data/assets/pdf_file/0009/7011/19_ >>> 06_cowtan_coordinate_frames.pdf >>> >>> Sorry to say I apparently ditched my old Fortran o2f and f2o programs to >>> do that. >>> >>> Bear in mind, however, that orthogonal has no fixed orientation with >>> respect to fractional - for most space groups "ncode 1" is often used but >>> for primitive monoclinic "ncode 3" is sometimes used, and I think the >>> matrix shown in Kevin Cowtan's document above corresponds to "ncode 1". >>> >>> Phil Jeffrey >>> Princeton >>> >>> >>> On 9/4/14 3:55 PM, Chen Zhao wrote: >>> >>>> I am sorry, just to clarify, the fractional coordinate matrix I referred >>>> to is a rotational matrix in the fractional coordinate system. >>>> >>>> >>>> On Thu, Sep 4, 2014 at 3:52 PM, Chen Zhao <[email protected] >>>> <mailto:[email protected]>> wrote: >>>> >>>> Hi all, >>>> >>>> I am just curious whether there are some tools extracting the Euler >>>> angles from a fractional coordinate matrix. I have no luck searching >>>> it online. >>>> >>>> Alternatively, I found the analytical solution for the Euler angles >>>> from an orthogonal coordinate matrix. So in the worst case, my >>>> problem reduces to calculating the transformation matrix between the >>>> fractional and orthogonal coordinate system. I feel a little bit at >>>> a loss because it is 6 years since I last studied linear algebra. >>>> How can I calculate this for a specific unit cell? >>>> >>>> Thanks a lot in advance! >>>> >>>> Sincerely, >>>> Chen >>>> >>>> >>>> >> >
