matrixToQuatern: Convert a Transformation Matrix to a Quaternion...

In bbuchsbaum/neuroim2: Data Structures for Brain Imaging Data

Convert a Transformation Matrix to a Quaternion Representation

Description

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.

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.

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.

References

- Cox RW. *Analysis of Functional NeuroImages* (AFNI) and NIfTI-1 quaternion conventions. https://afni.nimh.nih.gov

See Also

quaternToMatrix for the inverse operation, converting quaternion parameters back to a transform matrix.

bbuchsbaum/neuroim2 documentation built on Feb. 26, 2025, 3:49 p.m.