6.2. 4 Example: 3a order B-spline basis functio (Piecewise quadratic case- See Figure 6.2) k=3,Ck-2=C3-2=C1 Ni.3(ti) consists of three piecewise quadratic polynomials y1(u), y2( u) and y3(a). We want to find y(a), y2(u) and y3(a) such that Y,(u. t Figure 6.2: Plot of 3a order B-spline basis function N2.3(t) 3(t)=0 Ni. 3(t: (6.7) Position continuity (6.8 t+1-t )=B(4+3-a)2 (6.9) ti+ v2(u)=A(1-s)2+Bs2+C2s(1-s) (6.11) Note that n(t+1)=y(1+1) y9(t+2)=y(t+2)=B6.2.4 Example: 3 rd order B-spline basis function (Piecewise quadratic case– See Figure 6.2) k = 3, C k−2 = C 3−2 = C 1 Ni,3(ti) consists of three piecewise quadratic polynomials y1(u), y2(u) and y3(u). We want to find y1(u), y2(u) and y3(u) such that Figure 6.2: Plot of 3 rd order B-spline basis function. Ni,3(ti) = N 0 i,3 (ti) = 0. Ni,3(ti+3) = N 0 i,3 (ti+3) = 0. (6.7) Position continuity: y1(u) = A u − ti ti+1 − ti !2 (6.8) y3(u) = B ti+3 − u ti+3 − ti+2 !2 (6.9) y2(u) = A(1 − s) 2 + Bs 2 + C2s(1 − s) (6.10) s = u − ti+1 ti+2 − ti+1 (6.11) Note that y1(ti+1) = y2(ti+1) = A y3(ti+2) = y2(ti+2) = B 5