AffineTransform.cs

[System.Serializable]
public struct AffineTransform
{
    public Vector3 translation;
    public Quaternion rotation;

    public AffineTransform(Vector3 t, Quaternion r)
    {
        translation = t;
        rotation = r;
    }

    public void Set(Vector3 t, Quaternion r)
    {
        translation = t;
        rotation = r;
    }

    public Vector3 Transform(Vector3 p) =>
        rotation * p + translation;

    public Vector3 InverseTransform(Vector3 p) =>
        Quaternion.Inverse(rotation) * (p - translation);

    public AffineTransform Inverse()
    {
        var invR = Quaternion.Inverse(rotation);
        return new AffineTransform(invR * -translation, invR);
    }

    public AffineTransform InverseMul(AffineTransform transform)
    {
        var invR = Quaternion.Inverse(rotation);
        return new AffineTransform(invR * (transform.translation - translation), invR * transform.rotation);
    }

    public static Vector3 operator *(AffineTransform lhs, Vector3 rhs) =>
        lhs.rotation * rhs + lhs.translation;

    public static AffineTransform operator *(AffineTransform lhs, AffineTransform rhs) =>
        new AffineTransform(lhs.Transform(rhs.translation), lhs.rotation * rhs.rotation);

    public static AffineTransform operator *(Quaternion lhs, AffineTransform rhs) =>
        new AffineTransform(lhs * rhs.translation, lhs * rhs.rotation);

    public static AffineTransform operator *(AffineTransform lhs, Quaternion rhs) =>
        new AffineTransform(lhs.translation, lhs.rotation * rhs);

    public static AffineTransform identity { get; } = new AffineTransform(Vector3.zero, Quaternion.identity);
}