That's a cool page but it's about Bézier curves, while this article is about cubic splines. They are not the same!
The most notable difference is that a Bézier curve is defined in terms of control points that do not (generally) pass through the curve, while a polynomial spline is defined by the points it passes through; there are no additional control points.
The most notable difference is that a Bézier curve is defined in terms of control points that do not (generally) pass through the curve, while a polynomial spline is defined by the points it passes through; there are no additional control points.