Convert a Transformation Matrix to a Quaternion Representation

Extracts the rotation and scaling components from a 3x3 (or 4x4) transformation matrix, normalizes them, and computes the corresponding quaternion parameters and a sign factor (`qfac`) indicating whether the determinant is negative.

Usage

matrixToQuatern(mat)

Arguments

mat: A numeric matrix with at least the top-left 3x3 portion containing rotation/scaling. Often a 4x4 affine transform, but only the 3x3 top-left submatrix is used in practice.

Value

A named list with two elements:

quaternion: A numeric vector of length 3, \((b, c, d)\), which—together with \(a\) derived internally—represents the rotation.
qfac: Either +1 or -1, indicating whether the determinant of the rotation submatrix is positive or negative, respectively.

Details

This function first checks and corrects for zero-length axes in the upper-left corner of the matrix, then normalizes each column to extract the pure rotation. If the determinant of the rotation submatrix is negative, the qfac is set to -1, and the third column is negated. Finally, the quaternion parameters (\(a, b, c, d\)) are computed following standard NIfTI-1 conventions for representing the rotation in 3D.

References