1. A Bzier curve is defined by the following equation with four control vertices as shown in the figure P(1) =B0 (1)V + B, (1)V + B2 (1)V + B3 (1)V3. The four blending functions of the control vertices are defined by Bernstein polynomials B(t)=(1-1)=31(1-1), = (3) a-1) * = (-1), =()ra-0 = (3) 2 (1-1) = 31 ={3}*a-1) = r B (1)=(1-1) = 31 (1-1), B(t)= B3(t) = (a) What is the degree of the Bzier curve? (b) Prove that a Bzier curve goes through the first and the last control vertices. (c) Also prove that the tangent vector of the Bzier curve at the start point is parallel to the first segment of its control polygon, and that the tangent vector of the Bzier curve at the end point is parallel to the last segment of its control polygon. (d) Given Vo-[2, 3], V-[3, 6], V2-[8, 8], V-[10, 4] being vertices of the Bzier polygon, determine six points on the Bzier curve at parameter 1 = 0.0, 0.3, 0.4, 0.6, 0.7, 1.0 (the figure below with five marked points is for illustration only). Bezier curve Hints: For (b) and (c), can be done by simple verification. For (d), please also refer to laboratory document for points evaluation on a Bzier curve.