Graphics Reference
In-Depth Information
and
c
=
i
+
j
Let's substitute the lines in the original equations:
L
1
:
s
=
−
i
+
j
.
v
)
2
2
+
r
2
=0
(
s
−
s
−
2+1=
−
1
the negative discriminant confirms a miss condition.
L
2
:
s
=
−
i
+
j
.
v
)
2
2
+
r
2
=1
(
s
−
s
−
2+1=0
the zero discriminant confirms a touch condition, therefore
λ
=1thetouch
point is
P
2
(2
,
1
,
0) which is correct.
L
3
:
s
=
−
i
+
j
.
v
)
2
2
+
r
2
=2
(
s
−
s
−
2+1=1
the positive discriminant confirms an intersect condition, therefore
1=1+
√
2 r
√
2
2
√
2
±
λ
=
−
1
The interse
ct
ion points are given by the two values of
λ
:
if
λ
=1+
√
2
x
P
=2+
1+
√
2
=1
1
√
2
1
√
2
−
−
y
P
=0+
1+
√
2
1
√
2
=1+
1
√
2
z
P
=0
if
λ
=
√
2
−
1
1
=1+
x
P
=1+
√
2
1
√
2
1
√
2
−
−
y
P
=0+
√
2
1
1
√
2
=1
1
√
2
−
−
z
P
=0
The intersection points are
P
3
1
√
2
,
0
and
P
3
1+
√
2
,
0
1
1
1
1
−
√
2
,
1+
√
2
,
1
−
which are correct.