Graphics Reference
In-Depth Information
ε
=
(
a
·
b
)(
a
·
t
)
−
b
·
t
(10.81)
1
−
(
a
·
b
)
2
P
's position vector
p
is also the plane's normal vector. Then
x
P
=
x
T
+
λx
a
+
εx
b
y
P
=
y
T
+
λy
a
+
εy
b
z
P
=
z
T
+
λz
a
+
εz
b
The normal vector is
p
=
x
P
i
+
y
P
j
+
z
P
k
and because
p
is the perpendicular distance from the plane to the origin
we can state
x
P
y
P
z
P
x
+
y
+
z
=
p
p
p
p
or in the general form of the plane equation:
Ax
+
By
+
Cz
+
D
=0
where
x
P
y
P
z
P
A
=
B
=
C
=
D
=
−
p
p
p
p
Figure 10.33 illustrates a plane inclined 45
◦
to the
y
-and
z
-axes and parallel
to the
x
-axis.
The vectors for the parametric equation are
a
=
j
−
k
b
=
i
t
=
k
Y
1
l
a
P
p
O
t
1
e
b
Z
X
Fig. 10.33.
The vectors
a
and
b
are parallel to the plane and the point (0
,
0
,
1) is on
the plane.