Graphics Reference
In-Depth Information
The coordinates of P are
x
P
=
x
R
+
y
P
=
y
R
+
x
a
y
a
The lines are parallel if
a
=
b
(6.4)
where is a scalar, and are identical when
=
1.
We write Eq. (6.4) as follows:
x
a
=
x
b
y
a
=
y
b
Cross multiplying gives
x
a
y
b
=
x
b
y
a
or
x
b
y
a
−
x
a
y
b
=
0
(6.5)
Note that Eq. (6.5) is the denominator in Eqs. (6.2) and (6.3), and if it equals zero, it means
that the lines do not intersect.
Let's test the above equations with the example shown in Fig. 6.2.
Y
S
1
a
P
b
R
1
X
Figure 6.2.
The line equations are
p
=
r
+
a
p
=
s
+
b
where
R
=
00
a
=
i
+
j
S
=
01
b
=
i
−
j
