Graphics Reference
In-Depth Information
Table 9.5. The x, y, z coordinates for different
values of u and v
V
1
2
0
1
1 , 1
2 , 0
0
(0 , 0 , 0)
(2 , 0 , 0)
0 , 1
2 , 1 1 , 1
2 , 1 2 , 1
2 , 1
1
2
u
1 , 1
2 , 2
1
(0 , 0 , 2)
(2 , 0 , 2)
Table 9.5 shows the coordinate values for different values of u and v .Inthis
example, the y -coordinates provide the surface curvature, which could be
enhanced by modifying the y -coordinates of the control points.
9.7.3 Cubic Bezier Surface Patch
As we saw earlier in this chapter, cubic Bezier curves require two end-points,
and two central control points. In the surface patch formulation a 4
×
4 matrix
is required as follows:
13
31
P 00
P 01
P 02
P 03
·
·
3
630
P 10
P 11
P 12
P 13
P uv =[ u 3 u 2 u 1]
·
3300
1000
P 20
P 21
P 22
P 23
P 30
P 31
P 32
P 33
·
v 3
v 2
v
1
13
31
3
630
3300
1000
which can be illustrated by an example.
Given the points:
P 00 =(0 , 0 , 0)
P 01 =(1 , 1 , 0)
P 02 =(2 , 1 , 0)
P 03 =(3 , 0 , 0)
P 10 =(0 , 1 , 1)
P 11 =(1 , 2 , 1)
P 12 =(2 , 2 , 1)
P 13 =(3 , 1 , 1)
P 20 =(0 , 1 , 2)
P 21 =(1 , 2 , 2)
P 22 =(2 , 2 , 2)
P 23 =(3 , 1 , 2)
P 30 =(0 , 0 , 3)
P 31 =(1 , 1 , 3)
P 32 =(2 , 1 , 3)
P 33 =(3 , 0 , 3)
 
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