Graph the Bézier curve with control points P0(4, 1), P1(28, 48), P2(50, 42), and P3(40, 5). Then, on the same screen, graph the line segments P0P1, P1P2, and P2P3. (Exercise 10.1.31 shows how to do this.) Notice that the middle control points P1 and P2 don’t lie on the curve; the curve starts at P0, heads toward P1 and P2 without reaching them, and ends at P3.
Data from Exercise 10.1.31:
(a) Show that the parametric equations
where 0 < t < 1, describe the line segment that joins the points P1(x1, y1) and P(sx2, y2). (b) Find parametric equations to represent the line segment from (22, 7) to (3, 21).