The cubic B-spline curve is a piecewise cubic B-spline curve defined as follows: Given points p₁ = (x₁, y₁), i = 0,1, ···, n, the cubic B-spline for the interval (P₁₂ P₁₁), i = 1,2,,n-1, is B(u)= Eb(u)Pik? k=-1 (1-u)³ 2 where b_₁(u) = b₁(u) = 4/²2 - - 6 u² U 1 b₁(u) = - + 0≤u≤1. + + b₂(u) = 2 2 2 6 " 6 a. b. (2) Argue that moving a control point affects only four curve segments. (3) Show that the cubic B-spline is C²-continuous at the joints, that is, two adjacent segments share the common joint and have the same first order and second order derivatives at the joint. C. ..... (5) Given points po, p1, Pn, the above definition defines B1, B2, Bn-2. How do you add additional points such that the new curve fits the end points and is C²-continuous at new joints? You need to verify that the new curve fits the end points (for one side). = + 3 3