Graphics Reference
In-Depth Information
Y
n
Q
r
P
Z
X
Fig. 12.15.
A sphere touching a plane.
therefore
n
=
j
and
p
=
i
+
j
+
k
therefore
λ
=
−
(1
−
2) = 1
which equals the sphere's radius and therefore the sphere and plane touch.
The touch point is
x
Q
=1+1
×
0=1
y
Q
=1+1
×
1=2
z
Q
=1+1
×
0=1
P
(1,2,1) which is correct.
12.13 Summary
Unfortunately, problem solving is not always obvious, and it is possible to
waste hours of analysis simply because the objective of the solution has not
been well formulated. Hopefully, though, the reader has discovered some of
the strategies used in solving the above geometric problems, and will be able
to implement them in other scenarios. At the end of the day, practice makes
perfect.
