Graphics Reference
In-Depth Information
If we let
n
01
(
)
P
i
=
uu
-
i
j
j
=π
,
j
and
1
1
1
1
Ê
ˆ
Á
Á
Á
Á
Á
Á
Á
Á
˜
˜
˜
˜
˜
˜
˜
˜
P
P
P
P
0
1
2
3
uuu
++
uuu
++
uuu
++
uuu
++
1
2
3
0
2
3
0
1
3
0
1
2
P
P
P
P
0
1
2
3
M
=
uu
+
uu
+
uu
uu
+
uu
+
uu
uu
+
uu
+
uu
uu
+
uu
+
uu
12
23
31
02
23
30
01
1 3
30
01
12
20
P
P
P
P
0
1
2
3
uuu
uuu
uuu
uuu
123
0
023
1
01 3
2
012
3
Ë
¯
P
P
P
P
then it is straightforward to show that p(u) can be written in the following matrix
form:
p
p
p
p
Ê
ˆ
0
Á
Á
Á
˜
˜
˜
()
=
(
)
1
32
1
M
pu
u u u
.
(11.8)
2
Ë
¯
3
Figure 11.3 shows several cubic curves p(u). We have assumed that
uu
u
=+
=+
=+
pp
pp
pp
,
1
0
0
1
u
d
,
and
2
1
1
2
uu
.
3
2
2
3
Note how the spacing of the u
i
affects the shape of the curve. The smaller the value
Figure 11.3.
How spacing affects cubic curves.
