Graphics Reference
In-Depth Information
2
3
−
1
3
−
1
3
r
=
V
[
P, P
2
,P
4
,P
3
]
V
T
=
6
6
1
3
−
1
3
−
1
3
=
1
3
−
1
3
2
3
−
1
3
−
1
3
−
1
3
2
3
−
s
=
V
[
P, P
1
,P
3
,P
4
]
V
T
=
6
6
=
1
3
1
3
2
3
−
1
3
−
1
3
1
3
1
3
−
−
−
1
3
−
1
3
2
3
−
t
=
V
[
P, P
1
,P
2
,P
4
]
V
T
=
6
6
=
1
3
2
3
1
3
1
3
−
−
1
3
−
1
3
−
1
3
−
1
3
1
3
2
3
−
−
u
=
V
[
P, P
1
,P
2
,P
3
]
V
T
=
6
6
2
3
−
1
3
−
1
3
=0
1
3
2
3
−
1
3
−
The barycentric coordinates (
r
,
s
,
t
,
u
) confirm that the point is located at
the centre of triangle ∆
P
1
P
2
P
3
.
Note that the above determinants will create a negative volume if the
vector sequences are reversed.
11.8 Bezier Curves and Patches
In Chapter 9 we examined Bezier curves and surface patches which are based
on Bernstein polynomials:
i
(
t
)=
n
t
i
(1
n
t
)
n−i
B
−
i
We discovered that these polynomials create the quadratic terms
t
)
2
t
2
(1
−
2
t
(1
−
t
)
and the cubic terms
t
)
3
t
)
2
3
t
2
(1
t
3
(1
−
3
t
(1
−
−
t
)
