[phenixbb] Equations of transformation

[Paul Emsley]

On 25/05/11 19:41, Hena Dutta wrote:
>
> Dear Members,
>
>
> I want to know the mathematical relations between 2 sets of 
> co-ordinates, one before and one after the rotation. I used COOT to 
> rotate the side chain (containing atoms N1, C2, N3,  C4, C5, C6, N6, 
> N7 and C8) of Adenine by 180 degree about the glycosidic bond 
> (C1’-N9). How the initial co-ordinates (Xi, Yi, Zi) and final 
> co-ordinates (Xf, Yf, Zf) are mathematically related? I shall be very 
> grateful if someone can tell me the equations.
>
>

I got it from the matrix from the Amore documentation.

Coord_orth
rotate_round_vector(direction, // vector of the bond about which we are 
rotating
                                 position,  // of the moving atom
                                 origin_shift, // typically the position 
of the B atom (e.g. N9)
                                 angle) {

     unit_vec = direction.unit();

    l = unit_vec[0];
    m = unit_vec[1];
    n = unit_vec[2];

    ll = l*l;
    mm = m*m;
    nn = n*n;
    cosk = cos(angle);
    sink = sin(angle);
    I_cosk = 1.0 - cosk;

    // The Rotation matrix angle w about vector with direction cosines 
l,m,n.
    //
    // ( l**2+(m**2+n**2)cos k     lm(1-cos k)-nsin k        nl(1-cos 
k)+msin k   )
    // ( lm(1-cos k)+nsin k        m**2+(l**2+n**2)cos k     mn(1-cos 
k)-lsin k   )
    // ( nl(1-cos k)-msin k        mn(1-cos k)+lsin k        
n*2+(l**2+m**2)cos k )
    //
    //  Thanks for that pointer EJD :).



   Paul.