Graphics Reference
In-Depth Information
where
u
=
t
+
v
−
p
If
v
is a unit vector
v
, then
ˆ
=ˆ
v
·
p
−
t
(3.63)
u
=
t
+
v
ˆ
−
p
(3.64)
and
q
=
p
+
u
(3.65)
Let's find
u
in Fig. 3.30.
Y
t
X
v
T
p
Z
u
P
Figure 3.30.
It just so happens that the values of
p
and
t
give rise to a simple solution.
Nevertheless, we will apply Eqs. (3.63) and (3.64) to demonstrate their validity.
Let
1
√
2
i
v
ˆ
=
+
k
=
+
t
i
k
p
=
i
−
j
+
k
Then
=
1
√
2
i
+
·
−
+
−
−
=
1
√
2
i
+
·
−
=
k
i
j
k
i
k
k
j
0
=
0
Using Eq. (3.64) gives
u
=
i
+
k
−
i
+
j
−
k
=
j
Therefore, the line equation is
q
=
p
+
j
, which is correct.
