Graphics Reference
In-Depth Information
where we can substitute from Equation (B.3),
v
y
v
z
v
x
V
v
x
2
v
x
2
v
x
2
=
(
v
z
2
)
2
+(
v
z
2
)
2
+(
v
z
2
)
2
+
v
y
2
+
+
v
y
2
+
+
v
y
2
+
v
y
2
v
x
2
v
z
2
=
v
z
2
+
v
z
2
+
v
x
2
v
y
2
v
x
2
v
y
2
v
x
2
v
y
2
v
z
2
+
+
+
+
+
+
v
x
2
v
y
2
v
z
2
+
+
=
v
x
2
v
y
2
v
z
2
+
+
=
.
.
1
0
Notations.
V
is a position,
V
is the vector, and
V
is the normalized vector.
.
We refer to a vector with magnitude of exactly 1
0 as a normalized vector.
A
normalized vector tells us the direction of the movement.
In general, we can
normalize any nonzero magnitude vector
V
,
=
v
x
v
y
v
z
,
V
by computing
v
x
v
y
v
z
V
=
v
x
V
v
y
V
v
z
V
=
(B.4)
1
V
.
=
V
In general, we say the vector
V
is capable of moving any point in the
V
direction
by a distance of
V
units. For example, vector
V
w
,
V
w
=
500
,
has a magnitude of
√
5
2
0
2
0
2
V
w
=
+
+
√
25
=
=
.
5
We can normalize
V
w
by computing
V
w
1
V
w
=
V
w
5
V
w
0
V
w
0
V
w
=
5
=
100
.
So, we say the vector
V
w
is capable of moving any point in the
V
w
=
100
direction by a distance of five units.
=
5
0
5
0
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