Graphics Reference
In-Depth Information
Table 6.1.
Values associated with the vectors shown in
Fig. 6.3
x
h
y
h
x
t
y
t
∆
x
∆
y
Vector
2
0
0
0
2
0
2
0
2
0
0
0
2
2
−
2
0
0
0
−
2
0
2
0
−
2
0
0
0
−
2
2
√
2
1
1
0
0
1
1
√
2
−
1
1
0
0
−
1
1
√
2
−
1
−
1
0
0
−
1
−
1
√
2
1
−
1
0
0
1
−
1
Y
P
h
'
y
r
P
t
'
x
'
z
Z
X
Fig. 6.4.
The 3D vector has components ∆
x,
∆
y,
∆
z
, which are the differences be-
tween the head and tail coordinates.
∆
y
=(
y
h
−
y
t
)
(6.4)
∆
z
=(
z
h
−
z
t
)
(6.5)
=
∆
x
2
+∆
y
2
+∆
z
2
||
r
||
(6.6)
As 3D vectors play a very important part in computer animation, all future
examples will be three-dimensional.
6.2.1 Vector Manipulation
As vectors are different from scalars, a set of rules has been developed to
control how the two mathematical entities interact with one another. For
instance, we need to consider vector addition, subtraction and multiplication,
and how a vector can be modified by a scalar. Let's begin with multiplying a
vector by a scalar.
