Graphics Reference
In-Depth Information
and
y
a
z
a
y
b
z
b
z
a
x
a
z
b
x
b
x
a
y
a
x
b
y
b
a
=
b
=
c
=
Therefore, the plane equation is
ax
+
by
+
cz
=
d
To find d, we chose one of the two points on the plane, say M, and we can state
ax
M
+
by
M
+
cz
M
=
d
Therefore,
ax
+
by
+
cz
=
ax
M
+
by
M
+
cz
M
(4.10)
Y
M
1
b
1
N
X
a
1
Z
Figure 4.8.
We can test Eq. (4.10) using the same example in the previous section, as shown in Fig. 4.8.
The line's direction vector
a
is given by
a
=
i
−
k
and the two points M and N are
M 010 and N 100
Therefore,
0
−
1
−
11
01
10
1
a
=
b
=
c
=
−
10
−
1
a
=−
1 b
=−
1 c
=−
1
