# [phenixbb] Equations of transformation

Paul Emsley paul.emsley at bioch.ox.ac.uk
Wed May 25 12:11:21 PDT 2011

```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;
m = unit_vec;
n = unit_vec;

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.

```