Get or set a Transform matrix using TRS decompositions

TransformExtensions.cs

using UnityEngine;

public static class TransformExtensions {

    private static void GetTRS(this Matrix4x4 matrix, out Vector3 translation, out Quaternion rotation, out Vector3 scale)
    {
        float det = matrix.GetDeterminant();

        // Scale
        scale.x = matrix.MultiplyVector(new Vector3(1, 0, 0)).magnitude;
        scale.y = matrix.MultiplyVector(new Vector3(0, 1, 0)).magnitude;
        scale.z = matrix.MultiplyVector(new Vector3(0, 0, 1)).magnitude;
        scale = (det < 0) ? -scale : scale;

        // Rotation
        Matrix4x4 rotationMatrix = matrix;
        rotationMatrix.m03 = rotationMatrix.m13 = rotationMatrix.m23 = 0f;
        rotationMatrix = rotationMatrix * new Matrix4x4 { m00 = 1f / scale.x, m11 = 1f / scale.y, m22 = 1f / scale.z, m33 = 1 };
        rotation = Quaternion.LookRotation(rotationMatrix.GetColumn(2), rotationMatrix.GetColumn(1));

        // Position
        translation = matrix.GetColumn(3);
    }

    private static float GetDeterminant(this Matrix4x4 matrix) {
        return matrix.m00 * (matrix.m11 * matrix.m22 - matrix.m12 * matrix.m21) -
                matrix.m10 * (matrix.m01 * matrix.m22 - matrix.m02 * matrix.m21) +
                matrix.m20 * (matrix.m01 * matrix.m12 - matrix.m02 * matrix.m11);
    }

    public static void SetFromLocalMatrix(this Transform transform, Matrix4x4 matrix, bool isLeftHanded, bool isZup, float scaleFactor) {

        matrix.GetTRS(out Vector3 t, out Quaternion r, out Vector3 s);

        // Apply scale factor
        t *= scaleFactor;

        // If matrix is from Z-up system, we convert the TRS to match Unity's Y-up system
        if (isZup) {
            t = new Vector3(t.x, t.z, t.y);
            r = new Quaternion(r.x, r.z, r.y, -r.w);
            s = new Vector3(s.x, s.z, s.y);
        }

        // If matrix is from Left-Handed system, we convert the TRS to match Unity's Right-Handed system
        if (!isLeftHanded) {
            t = new Vector3(-t.x, t.y, t.z);
            r = new Quaternion(-r.x, r.y, r.z, -r.w);
        }

        // Assign local TRS to transform
        transform.localPosition = t;
        transform.localRotation = r;
        transform.localScale = s;
    }

    public static Matrix4x4 GetLocalMatrix(this Transform transform, bool isLeftHanded, bool isZup, float scaleFactor)
    {
        Vector3 t = transform.localPosition;
        Quaternion r = transform.localRotation;
        Vector3 s = transform.localScale;

        t *= scaleFactor;

        // If matrix should is for Z-up system, we convert the TRS from Unity's Y-up system
        if (isZup) {
            t = new Vector3(t.x, t.z, t.y);
            r = new Quaternion(r.x, r.z, r.y, -r.w);
            s = new Vector3(s.x, s.z, s.y);
        }

        // If matrix should is for Left-Handed system, we convert the TRS from Unity's Right-Handed system
        if (!isLeftHanded) {
            t = new Vector3(-t.x, t.y, t.z);
            r = new Quaternion(-r.x, r.y, r.z, -r.w);
        }

        Matrix4x4 matrix = Matrix4x4.identity;
        matrix.SetTRS(t, r, s);

        return matrix;
    }

    public static Matrix4x4 GetWorldMatrix(this Transform transform, bool isLeftHanded, bool isZup, float scaleFactor)
    {
        Vector3 t = transform.position;
        Quaternion r = transform.rotation;
        Vector3 s = transform.lossyScale;

        t *= scaleFactor;

        // If matrix should is for Z-up system, we convert the TRS from Unity's Y-up system
        if (isZup) {
            t = new Vector3(t.x, t.z, t.y);
            r = new Quaternion(r.x, r.z, r.y, -r.w);
            s = new Vector3(s.x, s.z, s.y);
        }

        // If matrix should is for Left-Handed system, we convert the TRS from Unity's Right-Handed system
        if (!isLeftHanded) {
            t = new Vector3(-t.x, t.y, t.z);
            r = new Quaternion(-r.x, r.y, r.z, -r.w);
        }

        Matrix4x4 matrix = Matrix4x4.identity;
        matrix.SetTRS(t, r, s);

        return matrix;
    }
}