Graphics Reference
In-Depth Information
Y
T
P
v
t
a
n
p
Z
X
Fig. 10.41.
α
is the angle between the plane's surface normal and the line's direction
vector.
then its surface normal is
n
=
a
i
+
b
j
+
c
k
If the line's direction vector is
v
and
T
(
x
T
,y
T
,z
T
) is a point on the line, then
any point on the line is given by the position vector
p
:
p
=
t
+
λ
v
therefore we can write
n
·
v
=
n
v
cos(
α
)
and
α
=cos
−
1
n
·
v
n
v
When the line is parallel to the plane
n
v
=0.
As an example, consider the scenario illustrated in Figure 10.42 where the
plane equation is
·
x
+
y
+
z
−
1=0
therefore the surface normal is given by
n
:
n
=
i
+
j
+
k
Y
n
1
a
1
1
Z
X
Fig. 10.42.
The required angle is between
a
and
b
.
