Suppose a cubic Bezier polynomial is placed through (mq, uq) and (M3, U3) with
Chapter 3, Problem 5(choose chapter or problem)
Suppose a cubic Bezier polynomial is placed through (mq, uq) and (M3, U3) with guidepoints (mi, U|) and (112, V2), respectively. a. Derive the parametric equations for 11 (l) and v(t) assuming that M(0) = mq, M(1) = M3, '(0) = 11 ] WQ, M'(1) H3 H2 and u(0) = Uo, u(l) = Us, u'(0) = U] - Uo, u'(l) = U3-U2. b. Let /(//3) = M;, for / = 0, 1, 2, 3, and g(i/3) = u,-, for / = 0, 1, 2, 3. Show that the Bernstein polynomial of degree three in t for /is u(t) and the Bernstein polynomial of degree three in t for g is u(/). (See Exercise 23 of Section 3.1.)
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