Computer Aided Engineering Design

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