Graphics Reference
In-Depth Information
Y
1
n
1
a
n
2
1
1
Z
X
Fig. 10.40.
α
is the angle between the two planes.
and
α
=cos
−
1
n
1
·
n
2
n
1
n
2
Figure 10.40 shows two planes with normal vectors
n
1
and
n
2
.
The plane equations are
x
+
y
+
z
−
1=0
and
z
=0
therefore
n
1
=
i
+
j
+
k
and
n
2
=
k
therefore
=
√
3and
n
1
n
2
=1
and
α
=cos
−
1
1
=54
.
74
◦
√
3
10.8.3 Angle between a Line and a Plane
The angle between a line and a plane is calculated using a similar technique
used for calculating the angle between two planes. If the line equation employs
a direction vector, the angle is determined by taking the dot product of this
vector and the plane's normal. Figure 10.41 shows such a scenario where
n
is
the plane's surface normal and
v
is the line's direction vector.
If the plane equation is
ax
+
by
+
cz
+
d
=0
