Graphics Reference
In-Depth Information
4.11 The reflection of a point in a plane
When dealing with mirrors, we need to know how to compute the virtual position of an object's
reflection. Once we know how to compute a single point, most objects can be processed. Central
to the solution of this problem is the fact that the virtual reflection is the same distance behind
the mirror as the object is in front of the mirror. Furthermore, a line connecting a real point
to its virtual reflection is orthogonal to the mirror (see Fig. 4.15).
Y
n
P
T
λ
n
Q
λ
n
t
q
p
Z
X
Figure 4.15.
Let the mirror's plane equation be
+
+
=
ax
by
cz
d
then the vector normal is
=
+
+
n
a
i
b
j
c
k
Let T be a point on the mirror such that
−
TP is parallel to
n
. Let T's position vector be
=
+
+
t
x
i
y
j
z
k
Therefore,
·
=
+
+
=
n
t
ax
by
cz
d
(4.16)
Now
=
+
p
t
n
(4.17)
where is a scalar.
Using
n
, take the dot product of Eq. (4.17):
n
·
p
=
n
·
t
+
n
·
n
(4.18)
