Graphics Reference
In-Depth Information
For example, Fig. 4.11 shows two planes whose plane equations are given by
y
=
0
and
x
+
y
=
1
Therefore, the two normal vectors are
n
1
=
j
and
n
2
=
i
+
j
Therefore,
cos
−
1
√
2
2
cos
−
1
j
·
i
+
j
45
=
×
√
2
=
=
1
4.9 The angle between a line and a plane
The angle between a line and a plane is virtually identical to that used to find the angle between
two planes. All that is required is the line's direction vector and plane's normal vector. The dot
product of the two vectors will then reveal their separating angle.
Y
n
P
T
v
t
p
Z
X
Figure 4.12.
For example, Fig. 4.12 shows a line and a plane where the line is defined as
p
=
t
+
v
and the plane equation by
ax
+
by
+
cz
=
d
