Rotate 3-vectors using unit quaternions.

vecp = quatvecmult(q,vec)

Rotates the 3-vector(s) vec using unit quaternion(s) q. The input 3-vector(s), which must be normalized to one, are given as a 3xN array. The unit quaternion(s), which must be normalized to one, are given as a 4xN array. The rotated vector(s) vecp are returned as a 3xN array.

Note that quatvecmult is vectorized and will accept arrays of unit quaternions of size 4xNxMx... and 3-vectors of size 3xNxMx... with an arbitrary number of dimensions, in which case the rotated vectors will be returned as an array of size 3xNxMx... .

Taking an arbitrary 3-vector and quaternion and normalizing the results, we compute the rotated vector

q = [0.1; 0.438; -0.879; 0.699];
q = q./sqrt(sum(q.^2))
vec = [0.3; 0.9; -0.4];
vec = vec./sqrt(sum(vec.^2))

q =
    0.0827
    0.3621
   -0.7267
    0.5779
vec =
    0.2914
    0.8742
   -0.3885

vecp = quatvecmult(q,vec)

vecp =
   -0.8705
    0.2851
   -0.4012

We can convince ourselves that using q to rotate vec is just as valid as using the equivalent rotation matrix to rotate vec.

R = quat2rotmat(q);
R*vec

ans =
   -0.8705
    0.2851
   -0.4012

rotmat2quat, quat2euler, euler2quat, quatinv