rises the curve and
    adds a set of <em>shape parameters</em>,
    \(s_k \in [-1, 1]\), which are used to both select and
    influence the blending functions.
    The X-spline curve is calculated piecewise for each 
    (overlapping) set of four control points.  
    The section of the curve between control points \(k+1\) and
    \(k+2\) is calculated as follows:

    $$C(t) = \frac{A_0(t)P_k + A_1(t)P_{k+1} + A_2(t)P_{k+2} + A_3(t)P_{k+3}}{A_0(t) + A_1(t) + A_2(t) + A_3(t)}, t \in [0, 1]$$

    where th