240 COMPUTER AIDED ENGINEERING DESIGN
Equation of the Coon’s patch C (incorporating the correction surface) is given by
rC(u,v) = (1 – u)rC(0, v) + urC(1,v) + (1 – v)rC(u, 0) + vrC(u, 1)
- (1 – u)(1 – v)(1, 0, 0) – u(1 – v)(1.5, 0.5, 0) – v(1–u)(1, 0.5, 1) – uv(1, 0.5, 1)
Plots of patches A,B,C,D and the composite coon’s patch are shown in Figure 7.29.
Figure 7.29 Closed Bézier surfaces
Z
Y X
6 5 4 3 2 1 0 6 4 2
0 –8
–6
–4
–2
0
8
6
4
2
(c)
(a)
Z
Y
X
6 5 4 3 2 1 0 7 6 5 4 3 2 1
(^0) –2 –1
0
1 2
(b)
Z
Y X
8 7 6 5 4 3 2 1 0 6 4 2
(^0) –5
0
5