Graphics Reference
In-Depth Information
v
, let's consider the case when the line
is represented by two points in space. If the two points are P
1
x
1
y
1
and P
2
x
2
y
2
,wecan
state that
As we may not always have an explicit description of
ˆ
v
=
x
2
−
x
1
i
+
y
2
−
y
1
j
from which we can compute
v
.
v
v
is then equal to
and T can be P
1
.
We can now write Eq. (3.1) as follows:
ˆ
v
p
=
p
1
+
v
ˆ
(3.2)
where
p
1
is the position vector for P
1
. This scenario is shown in Fig. 3.3.
Y
P
1
v
P
2
p
1
P
p
O
X
Figure 3.3.
In the current R
2
context, Eq. (3.2) reveals
x
=
x
1
+
v
ˆ
y
=
y
1
+
v
ˆ
which expands to
x
=
x
1
+
x
2
−
x
1
v
=
y
1
+
y
2
−
y
y
1
v
and
1
x
1
+
x
=
−
x
2
(3.3)
v
v
1
y
1
+
y
=
−
y
2
(3.4)
v
v
