Exercice 5: (5 points) Consider the cubic Bzier curve 3 P(t) = {P{B}(t), PER?, te[0,1]. k=0 Viewing P as a parametric curve of degree 4, we can expressed as P(t) = PX"B(t), PER?, 1 [0, 1]. k=0 a) Using the blossom, express the control points px"), k = 0,1,2,3,4, in terms of the initial control points Pk, k = 0,1,2,3. b) Write a program drawing the control polygons obtained by expressing an initial cubic Bzier curve with control points Po = (0,0), P1 = (1,2), P2 = (3,2), Pz = (4,0), as a Bzier curve of higher and higher degrees up to degree 20; that is draw the poly- (N3), p.N-3), PN-3)) for N = 4,5,...,20, where gons (P.N N P(t)= PX-3B (1), PX-3) = R2, t [0, 1]. k=0