Re: [phenixbb] Equations of transformation

Hi, we discussed this recently on phenixbb. Here is the copy: phenix.pdbtools model.pdb rotate_about_axis.axis="chain A and resseq 1:123 and (name CA or name CB)" rotate_about_axis.atom_selection="chain A and resseq 1" rotate_about_axis.angle=35 where rotate_about_axis.axis defines the rotation axis (must be two points in space); rotate_about_axis.atom_selection defines the atoms that will be rotated about the axis; rotate_about_axis.angle defines rotation angle in degrees. Instead of specifying atom selection string in rotate_about_axis.axis, you can give it coordinates of two points: phenix.pdbtools model.pdb rotate_about_axis.axis="1.234 2.345 4.567 -2.321 3.765 0.001" rotate_about_axis.atom_selection="chain A and resseq 1:123" rotate_about_axis.angle=35 If interested in the math details - see the code in phenix.pdbtools that does it. Pavel. On 5/25/11 12:24 PM, Nathaniel Echols wrote:

FYI, for anyone inclined to write their own programs, there is a similar Python function for this in CCTBX:

from mmtbx.refinement.fit_rotamers import rotate_point_around_axis xyz_new = rotate_point_around_axis(axis_start, axis_end, xyz, angle_degrees)

I'm not posting the code here because Paul's version is clearer, but it's in $PHENIX/cctbx_project/mmtbx/refinement/fit_rotamers.py. (It wouldn't surprise me if this duplicates a more general function in one of the lower-level math modules, but I'm not sure where to look.)

-Nat

On Wed, May 25, 2011 at 12:11 PM, Paul Emsley mailto:[email protected]> wrote:

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.

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