I am sorry for my carelessness on the definition of Euler angles. I am just thinking of an Euler angle equivalent. Sorry for the confusion I have made.
On Fri, Sep 5, 2014 at 3:34 PM, Eleanor Dodson <[email protected]> wrote: > 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 >>>>> >>>>> >>>>> >>> >> >
