Translations:B-Splines/20/en

Having only one control point is often not sufficient. Take the above motivation example. There in option 3 we end the curve tangentially in x-direction. But how can you connect the points (20, 0) and (80, 40) so that the curve ends tangentially in y-direction? To achieve this you need first a right-hand and then a left-hand turn, so a cubic (third order) polynomial. And that means for a Bézier curve that we need (or you can say we gain) a second control point. Animation 3 shows a cubic Bézier curve.