This method makes sense if the four points are (at least approximately) equally spaced along the curve. If they are not equally spaced, the following may be done: Instead of using 1 / 3 and 2 / 3 as...

This method makes sense if the four points are (at least approximately) equally spaced along the curve. If they are not equally spaced, the following may be done: Instead of using 1/3 and 2/3 as the intermediate values, the user may specify values
α,
β
such that
 =
P(α) and
 =
P(β). Generalize Equation (4.44) such that it depends on
α
and
β.