The equation for the resulting blending surface is ove Bezier B-sp B(,t)=∑∑ Bke Bk.4()N4(t) (9.21) k=0E=0 Bn(,t)=3∑∑(Bk-Bk-1)B3()N4(t) (9.22) E=0k=1 From position and derivative continuity we get B B (9.24) B1t=R(+Q/3 (9.25 B R (2) R2-Q2/3 (9.26) The disadvantage of approximation is the increase in data and the resulting storage re- quirements. The advantage is that the same class of functions is used which makes it easy to include in a geometric modeler and easy to transfer between CAD/CAM systems Special attention needs to be given to the correspondence of parametrization of linkage curves and this may necessitate reparametrization of linkage curves. See Bardis and Pa- trikalakis [1, and Hansmann [7] for more details on these issues Figure 9.3: Blending surface cross-link curvesThe equation for the resulting blending surface is: B(w,t) = X 3 k=0 Xn `=0 Bk,` B´ezier z }| { Bk,4(w) Above B-spline z }| { N`,4(t) (9.21) Bw(w,t) = 3 Xn `=0 X 3 k=1 (Bk,` − Bk−1,`)Bk,3(w)N`,4(t) (9.22) From position and derivative continuity we get: B0,` = R (1) ` (9.23) B3,` = R (2) ` (9.24) B1,` = R (1) ` + Q (1) ` /3 (9.25) B2,` = R (2) ` − Q (2) ` /3 (9.26) The disadvantage of approximation is the increase in data and the resulting storage re￾quirements. The advantage is that the same class of functions is used which makes it easy to include in a geometric modeler and easy to transfer between CAD/CAM systems. Special attention needs to be given to the correspondence of parametrization of linkage curves and this may necessitate reparametrization of linkage curves. See Bardis and Pa￾trikalakis [1], and Hansmann [7] for more details on these issues. t t Figure 9.3: Blending surface cross-link curves. 6