Graphics Reference
In-Depth Information
Figure 12.20.
Stages of the de Casteljau algorithm.
Finally, the point
3
(
)
=
puv
,
b
=
a
b
+
b
b
+
c
b
.
100
,,
010
,,
001
,,
000
,,
is marked with a square.
Let us work through a concrete example.
12.12.3.1
Example.
Let a triangular Bézier surface p(u,v) of degree two be defined
by the triangular net
=
(
)
b
b
250
241
,,
,,
020
,,
=
(
)
=
(
)
b
343
,,
011
,,
110
,,
=
(
)
=
(
)
=
(
)
b
230
,,
b
331
,,
b
430
,,
002
,,
100
,,
200
,,
The problem is to compute p(1/6,1/3).
Solution.
The barycentric coordinates of (1/6,1/3) with respect to the vertices (1,0),
(0,1), and (0,0) of our triangular domain are (1/6,1/3,1/2). Therefore,
1
=
()
+
()
+
()
b
16
b
13
b
12
b
101
,,
011
,,
00 2
,,
001
,,
=
( (
+
( (
+
( (
)
=
(
)
16 331
,,
13 241
,,
12 230
,,
13 610 312
,
,
1
=
()
+
()
()
b
16
b
13
b
+ 112
b
,,
200
,,
110
,,
101
100
,,
=
( (
+
( (
+
( (
)
=
(
)
16 430
,,
13 343
,,
12 331
,,
19 610332
,
,
