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which equals R and a touch condition occurs.
The negative value of informs us that the line connecting the sphere's centre C to the point
P on the plane is against the direction of
n
.
Using Eq. (6.35), we can compute the touch point P:
ˆ
6
7
i
7
k
3
7
j
2
p
=
c
+
n
ˆ
=
i
+
j
+
2
k
−
+
+
and
1
7
4
7
12
P
=
7
Using Eq. (6.33), we can confirm whether this point is inside the triangle:
1
7
00
7
20
12
7
03
4
pp
2
p
3
p
1
p
2
p
3
=
6
7
6
=
1
7
r
=
=
100
020
003
1
1
7
0
4
7
0
0
p
1
pp
3
p
1
p
2
p
3
=
12
7
12
7
6
=
0
3
2
7
s
=
=
10 0
020
00 3
10
7
02
7
00
1
7
p
1
p
2
p
p
1
p
2
p
3
=
24
7
6
=
4
7
t
=
=
100
020
003
Note that r
1 and they are all positive and less than 1, which means that the point
7
7
1
7
is inside the triangle, which means that the sphere touches the triangle within its
boundary.
+
s
+
t
=
