Graphics Reference
In-Depth Information
If P is any point on the plane with position vector
p
=
x
i
+
y
j
+
z
k
then
n
·
p
=
d
(4.6)
As
p
and
q
share a common projection on
n
,
n
·
p
=
n
·
q
(4.7)
Substituting Eq. (4.6) in Eq. (4.7) gives
n
·
q
=
d
ax
Q
+
by
Q
+
cz
Q
=
d
(4.8)
Substituting Eq. (4.8) in Eq. (4.6) gives
ax
+
by
+
cz
=
ax
Q
+
by
Q
+
cz
Q
(4.9)
Y
1
n
1
X
1
Z
Figure 4.6.
To test Eq. (4.9), consider the scenario shown in Fig. 4.6. The line's direction vector
n
is given by
n
=
i
+
j
+
k
and the point on the plane is Q100. Therefore, the plane's equation is
ax
+
by
+
cz
=
1
