Convert Quaternion Parameters to a Transformation Matrix

Given a quaternion (b, c, d), a scalar offset (origin), voxel step sizes, and the qfac sign, reconstructs a 4x4 affine matrix representing rotation, scaling, and translation as used in NIfTI-1.

Usage

quaternToMatrix(quat, origin, stepSize, qfac)

Arguments

quat

A numeric vector of length 3 containing the quaternion parameters \((b, c, d)\). The scalar part \(a\) is computed internally.

origin

A numeric vector of length 3 specifying the translation components (often the real-space origin or offset).

stepSize

A numeric vector of length 3 giving the voxel dimensions along each axis (e.g., (dx, dy, dz)).

qfac

Either +1 or -1, indicating the sign from the determinant check in matrixToQuatern.

Value

A 4x4 numeric affine transformation matrix. The top-left 3x3 submatrix encodes rotation and scaling, and the 4th column encodes translation.

Details

This function uses the quaternion formalism common in neuroimaging, adding the offset (translation) into the 4th column, and applying the voxel sizes along each axis. If qfac is -1, the \(z\) scale is negated. The resulting 4x4 matrix is typically used as an affine transform for voxel-to-world coordinate mapping.

References

- NIfTI-1 specification for quaternions: https://nifti.nimh.nih.gov

See also

matrixToQuatern for converting a matrix back to quaternion form.