Graphics Reference
In-Depth Information
Miss condition
2
x
v
y
v
x
t
y
t
r
2
−
< 0
Tangential condition
2
x
v
y
v
x
t
y
t
r
2
−
=
0
Intersect condition
2
x
v
y
v
x
t
y
t
r
2
−
> 0
Let's test all three conditions using the three lines and circle shown in Fig. 6.4.
Y
λ
v
2
L
2
P
T
2
λ
v
3
λ
v
1
C
c
r
L
3
L
1
T
3
T
1
X
Figure 6.4.
Figure 6.4 shows a circle with radius r
1 centered at C 11 and three lines: L
1
L
2
, and L
3
that miss, touch, and intersect the circle, respectively.
The lines are
=
p
1
=
t
1
+
v
1
p
2
=
t
2
+
v
2
p
3
=
t
3
+
v
3
where
t
1
=
3
i
v
1
=
j
t
2
=
2
j
v
2
=
i
1
√
2
i
1
√
2
j
t
3
=
0
v
3
=
+
