Convert Quaternion into a Rotation Matrix — quaternion2rotation • oro.nifti

The affine/rotation matrix $R$ is calculated from the quaternion parameters.

quaternion2rotation(b, c, d, tol = 1e-07)

quaternion2mat44(nim, tol = 1e-07)

Arguments

b	is the quaternion $b$ parameter.
c	is the quaternion $c$ parameter.
d	is the quaternion $d$ parameter.
tol	is a very small value used to judge if a number is essentially zero.
nim	is an object of class `nifti`.

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.

References

NIfTI-1
http://nifti.nimh.nih.gov/

Author

Brandon Whitcher bwhitcher@gmail.com

Examples


## 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))
#>      [,1] [,2] [,3]
#> [1,]    1    0    0
#> [2,]    0   -1    0
#> [3,]    0    0   -1