Graphics Reference
In-Depth Information
The distance of Q is
PQ
=
n
If
n
=
1
then
PQ
=
Let's test Eq. (4.15) with an example.
Y
1
Q
P
1
X
1
Z
Figure 4.14.
Figure 4.14 shows a triangle whose plane equation is
x
+
y
+
z
=
1
Therefore,
n
=
i
+
j
+
k
and
d
=
1
We will find the nearest point on the triangle to the origin by making P
=
000.
Therefore,
n
·
p
−
d
i
+
j
+
k
·
0
i
+
0
j
+
0
k
−
1
1
3
=
=
√
3
√
3
=−
2
n
and
i
1
3
=
−
=
+
+
−
−
+
+
q
p
n
0
i
0
j
0
k
j
k
1
3
i
1
3
j
1
3
k
q
=
+
+
Therefore, the nearest point to P is
3
3
3
.
