You can use quaternions to rotate about an arbitrary axis in 3-dimensions. The quatrotate is capable of performing a rotation of all of your atoms in the unit cell by a quaternion (you will have to specify the quaternion using the x, y, z coordinate of the vector to perform the rotation about and the angle to rotate by). If you want to rotate about an axis K = (kx, ky, kz) by angle theta, then your quaternion for "quatrotate" is:
clear; clc;
% Rotate about the (1,4,3) axis by theta = 60 deg:
theta = pi/3; % (rad), angle to rotate by
K = [1, 4, 3]; % [kx,ky,kz], axis to rotate about
k = K./vecnorm(K); % unit vector
r = [1, 1, 1]; % vector to rotate
% Define Quaternion:
q = [cos(theta/2), sin(theta/2).*k];
vOut = quatRotate(q,r); % call quatRotate()
% Example from quatrotate() page:
q = [1 0 1 0];
r = [1 1 1];
vOut = quatRotate(q,r);
% Use Home-Written quatRotate following quatrotate documentation:
% (https://www.mathworks.com/help/aerotbx/ug/quatrotate.html)
function vOut = quatRotate(q,vIn)
q = q./vecnorm(q); % ensure quaternion is unit vector
q0 = q(1); q1 = q(2); q2 = q(3); q3 = q(4); % sort quaternion components
Q = [ (1 - 2*q2^2 - 2*q3^2), ( 2*q1*q2 + 2*q0*q3), ( 2*q1*q3 - 2*q0*q2); ...
( 2*q1*q2 - 2*q0*q3), (1 - 2*q1^2 - 2*q3^2), ( 2*q2*q3 + 2*q0*q1); ...
( 2*q1*q3 - 2*q0*q2), ( 2*q2*q3 - 2*q0*q1), (1 - 2*q1^2 - 2*q2^2) ];
vOut = Q*vIn';
end
You could also use Euler angles, but the quaternion method is compact and numerically more stable.
EDIT: I wrote a simple script that uses "quatRotate" if you don't have the Aerospace Toolbox. You can modify this to take array inputs for "vIn" as necessary.
