quaternion2rotation: Convert Quaternion into a Rotation Matrix
Description
The affine/rotation matrix $R$ is calculated from the quaternion
parameters.
Usage
quaternion2mat44(nim, tol = 1e-7)
quaternion2rotation(b, c, d, tol = 1e-7)
Arguments
nim
is an object of class nifti.
tol
is a very small value used to judge if a number is
essentially zero.
b
is the quaternion $b$ parameter.
c
is the quaternion $c$ parameter.
d
is the quaternion $d$ parameter.
Value
The (proper) $3{\times}3$ rotation matrix or
$4{\times}4$ affine matrix.
Details
The quaternion representation is chosen for its compactness in
representing rotations. The orientation of the $(x,y,z)$ axes
relative to the $(i,j,k)$ axes in 3D space is specified using a
unit quaternion $[a,b,c,d]$, where
$a^2+b^2+c^2+d^2=1$. The
$(b,c,d)$ values are all that is needed, since we require that
$a=[1-(b^2+c^2+d^2)]^{1/2}$ be
non-negative. The $(b,c,d)$ values are stored in the
(quatern_b, quatern_c, quatern_d) fields.
## This R matrix is represented by quaternion [a,b,c,d] = [0,1,0,0]## (which encodes a 180 degree rotation about the x-axis).(R <- quaternion2rotation(1, 0, 0))