Graphics Reference
In-Depth Information
Substituting Eq. (3.20) in Eq. (3.21) gives
p
=
1
−
t
+
n
ˆ
·
t
n
ˆ
(3.22)
which is the vector equation of the line. However, there is one drawback with this equation.
Notice that the point T must not lie on the perpendicular from the origin; if it does, then vector
v
would be a null vector and everything collapses!
To illustrate Eq. (3.22), let
1
√
2
i
n
ˆ
=
+
j
and T
=
30, as shown in Fig. 3.14.
Y
λ
=
2
λ
=
1
n
λ
=
0
T
X
Figure 3.14.
=
When
0,
p
=
3
i
and P
=
30
When
=
1,
1
√
2
i
3
i
1
3
2
i
p
=
+
j
·
√
2
i
+
j
=
+
j
and
P
=
1515
When
=
2,
2
1
3
i
1
p
=−
3
i
+
√
2
i
+
j
·
√
2
i
+
j
=−
3
i
+
3
i
+
j
=
3
j
and
P
=
03
