Suppose a cubic Bézier polynomial is placed through (uo, vo) and (u3, v3) with guidepoints (u\, v1) and (u2, U2), respectively. Derive the parametric equations for u(t) and v(t) assuming that а. u(0) = uo, и(1) — из, u' (0) = u, - Uo, и'(1) — из — и2 and v'(0) = v1- Vo v'(1)= v3 - v2 v (0) = vo, v(1)= v3, b. Let f(i/3) ui, for i = 0, 1, 2, 3, and g(i/3) = Vi, for i = 0, 1, 2,3. Show that the Bernstein polynomial of degree three in t for f is u(t) and the Bernstein polynomial of degree three in t for g is v(t).