Consider the following task. You have $n$ points $P_0, P_1, \ldots, P_n$ in the plane. Your goal is to draw a smooth curve which begins at $P_0$ and ends at $P_n$, passing through all the points $P_1, P_2, \ldots, P_{n-1}$ in order. Smooth means that the curve has no sharp corners or cusps. How would you do it?

TODO Make a scene with n draggable points, and a button which generates a Bezier curve passing through all the points.

TODO: We already know how to connect two points with a line segment, so we can do a piecewise linear path, but this has kinks.

QUESTION: What does "smooth" mean? At minimum, direction going into and out of each point must be the same. First derivative. IDEA: Put "control" points between each pair of points, and use quadratic Bezier curves to connect them. Define a quadratic Bezier curve.