Graphics Reference
In-Depth Information
4.8 The angle between two planes
The angle between two planes is readily computed using the dot product of the two surface
normals. For example, given two Cartesian plane equations
ax 1 +
by 1 +
cz 1 =
d 1
and
ax 2 +
by 2 +
cz 2 =
d 2
the normal vectors are
n 1 =
a 1 i
+
b 1 j
+
c 1 k
and
n 2 =
a 2 i
+
b 2 j
+
c 2 k
Therefore,
n 1 ·
n 2 =
n 1
n 2
cos
and
cos 1 n 1 ·
n 2
=
n 1
n 2
If
n 1 =
n 2 =
1
then
cos 1 n 1 ·
=
n 2
Y
n 2
n 1
Z
X
Figure 4.11.
 
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