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.
 
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