Graphics Reference
In-Depth Information
The plane's surface normal is
n
=
a
i
+
b
j
+
c
k
Therefore,
n
·
v
=
n
·
v
cos
and
cos
−
1
n
·
v
=
n
·
v
If
n
=
v
=
1
then
cos
−
1
n
=
·
v
when the line is parallel with the plane
n
·
v
=
0
4.10 The position and distance of the nearest point on a plane to a point
This problem is concerned with the relationship between a point and a plane; in particular, the
problem of finding the position and distance of a point on a plane that is the nearest to some
specific point. For example, Fig. 4.13 shows a polygon representing a ground plane and a point
P in space. The problem is to find the location and distance of a point on the plane that is
nearest to P. Hopefully, it is obvious that the nearest point on the plane is perpendicular to P,
which means that the dot product plays some role in the solution. Let's examine how vector
analysis reveals a solution.
P
Y
r
p
n
q
Q
X
Z
Figure 4.13.
