Decompose a nalgebra_glm 4x4 transformation matrix into translation, rotation, and scaling (accounts for non-uniform scaling)

decompose.rs

pub fn decompose_matrix(
    matrix: &nalgebra_glm::Mat4,
) -> (nalgebra_glm::Vec3, nalgebra_glm::Quat, nalgebra_glm::Vec3) {
    let translation = nalgebra_glm::Vec3::new(matrix.m14, matrix.m24, matrix.m34);

    let (scale_x, scale_y, scale_z) = (
        nalgebra_glm::length(&nalgebra_glm::Vec3::new(matrix.m11, matrix.m12, matrix.m13)),
        nalgebra_glm::length(&nalgebra_glm::Vec3::new(matrix.m21, matrix.m22, matrix.m23)),
        nalgebra_glm::length(&nalgebra_glm::Vec3::new(matrix.m31, matrix.m32, matrix.m33)),
    );

    let scale = nalgebra_glm::Vec3::new(scale_x, scale_y, scale_z);

    // Normalize the matrix to extract rotation
    let rotation_matrix = nalgebra_glm::mat3(
        matrix.m11 / scale_x,
        matrix.m12 / scale_y,
        matrix.m13 / scale_z,
        matrix.m21 / scale_x,
        matrix.m22 / scale_y,
        matrix.m23 / scale_z,
        matrix.m31 / scale_x,
        matrix.m32 / scale_y,
        matrix.m33 / scale_z,
    );
    
    let rotation = nalgebra_glm::mat3_to_quat(&rotation_matrix);

    (translation, rotation, scale)
}