Computer Aided Engineering Design

236 COMPUTER AIDED ENGINEERING DESIGN

or r 10 II = (0, 3, 0) +^1
3
(3, 3, 9) = (1, 4, 3)

r 11 II = (1, 3, 3) +^1

3

(4, 3, 9) =^7

3

(), 4, 6

r 12 II = (2, 3, 3) +^1

3

(5, 3, 0) =^11

3

(), 4, 3

r 13 II = (3, 3, 0) +^1

3

(6, 3, –18) = (5, 4, –6)

The resulting composite surface is shown in Figure 7.27. To verify the coplanarity condition
suggested in Eq. (7.57), we consider the arrangement of data points around the common polygon.

Figure 7.27 (a) A composite Bézier surface (Example 7.11) with gradient continuity (Case II), (b) vectors
of the control polyhedra at a corner point in the common polygon and (c) vectors of the
control polyhedra at the other corner point

(b) (c) (5, 4, –6)

q 3

q 2

(3, 2, 0)

(3, 3, 0)

q 1

(2, 3, 3)

(a)

(2, 3, 3)

(1, 3, 3)

(1, 4, 3)

p 1

p 2

p 3

(0, 2, 0)

(0, 3, 0)