to generate an  expression for 
    \(C(t)\) that is just in terms of \(t\) (and \(P_k\) and \(s_k\),
    both of which are constants for a particular X-spline).
    The idea is to expand the X-spline equations so that, for example ...
    
    $$A0 = h(-t, -s_{k+1})$$

    ... and ...

    $$h(u, q) = u(q + u(2q + u^2(-2q - uq)))$$

    ... becomes ...
    
    $$A0 = (-t)((-s_{k+1}) + (-t)(2(-s_{k+1}) + (-t)^2(-2(-s_{k+1}) - (-t)(-s_{k+1}))))$$
  </p>
    <p>
    The following R code performs the above tr