Question

2. (10 points) Find the knot vector for a quartic (k = 5) B-spline created from ten control points.

Answer 1

t (titk-0) Nitlok+). Given that 3, KLU) ki; Ni,k(0: (U-ti) Ninkai Since generat expression for Basic function is k=5 0+1=10 =) 0-9 } inn XCU)-Ž NE 1:0 LU) titk-i-ti U) titk -titl tilostsot) — knot vector voluge tico if ilk ti=i-ktl if Keisn 3 tin-k+2 if i>D (4 ممے 3 NLKUDE if tisuk titi o therwise

Now K= 5, n=9 tilo zis 14) to o OL5 from ti=0 125 @simi looly tzétz= ty: 0 5566 9 t5-5-5+1 = 1 from t6=6-5+1=2 ... 55649 tg=tq=to=t, -t 12 =+13 =tiu=4 Hence, Simillar tq 3, The knot vector 2 41 =(0,0,0,0,0,1,2,3,4,4,4,4,4,4, 4. 4 }