Question

Bézier curves are used in computer-aided design and are named after the French mathematician Pierre Bézier (1910-1999), who worked in the automotive industry. A cubic Bézier curve is deter- parametric equations 1. Choose control points Po(4,1), P1 (28, 48), P2(50, 42), and Ps (40, 5) and draw the corresponding Bézier curve. On the same screen, graph the line segments PoPi, PiP2, and P2Ps using the following parametric equations PoP:4+24t, y-1 +47t PP2 -28+22t, y-48-6t P2P3: x 50- 10t, y-42 - 37t

Answer 1

Given data Cubic Bezier curve is determined by four control points P_0 (x_0, y_0), P_1 (x_1, y_1), P_2 (x_2, y_2) and P_3 (x_3, y_3) Given parametric equations x(t) = x_0 (1 - t)^3 + 3x_1 t (1 - t)^2 + 3x_2 t^2 (1 - t) + x_3 t^3 y(t) = y_0 (1 - t)^3 + 3y_1 t (1 - t)^2 + 3y_2 t^2 (1 - t) + y_3 t^3 Given control points P_0 (4, 1), P_1 (28, 48), P_2 (50, 42) and P_3 (40, 5) Parametric equations P_0 P_1: x = 4 + 24 t, y = 1 + 47 t P_1 P_2: x = 28 + 22 t, y = 48 - 6t P_2 P_3: x = 50 - 10 t, y + 42 - 37 t % Define values for the parameter t = [0: 0.0001: 1]: % Define the Bezier Curves x = P_0 (1) * (t^3) + 3 * P_1 (1) * t * ((1 - t)^2) + 3 P_2 (1) t^2 (1 - t) + P_3 (1) t^3.