Graphics Reference
In-Depth Information
and
−
211
001
−
110
x
=
−
=1
−
1
1
21
001
0
−
−
10
y
=
−
=1
−
1
11
2
00 0
01
−
−
1
z
=
−
=0
−
1
which means that the intersection point is (1, 1, 0), which is correct.
10.8.2 Angle between Two Planes
Calculating the angle between two planes is relatively easy and can be found
by taking the dot product of the planes' normals. Figure 10.39 shows two
planes with
α
representing the angle between the two surface normals
n
1
and
n
2
.
Let the plane equations be
ax
1
+
by
1
+
cz
1
+
d
1
=0
ax
2
+
by
2
+
cz
2
+
d
2
=0
therefore the surface normals are
n
1
=
a
1
i
+
b
1
j
+
c
1
k
n
2
=
a
2
i
+
b
2
j
+
c
2
k
Taking the dot product of
n
1
and
n
2
:
n
1
·
n
2
=
n
1
n
2
cos(
α
)
Y
n
2
a
n
1
Z
X
Fig. 10.39.
The angle between two planes is the angle between their surface normals.
