Game Development Reference
In-Depth Information
()
A ray
PSV intersects an infinite cylinder of radius r representing the
edge with endpoints
t
=+
t
E and
E at the parameter value
2
bb c
−−
t
=
,
a
where
(
)
2
VA
2
aV
=−
2
A
(
)(
)
SAVA
0
b
=⋅
SV
0
2
A
(
)
2
SA
2
2
0
c
=−−
S
r
0
2
A
AEE
SSE
=−
=−
2
1
1 .
0
The intersection occurs between the edge's endpoints if
()
]
2
0
<
[
PEA .
t
<
A
1
Sliding
If an object traveling from the point P to P collides with a surface at the point
Q , then the point P to which it should slide is given by
(
)
]
PP
=−
[
PQNN ,
−⋅
3
2
2
where N is the unit normal vector at the point Q .
Collision of Two Spheres
A sphere of radius r moving from the point P at time
=
to the point P at time
t
0
=
1
collides with another sphere of radius r moving from the point
Q to the
t
point
Q at time
(
)
(
)
(
)
−⋅
AB
AB
2
BA
2
2
− +
r r
2
P
Q
t
=
,
B
2
where
AP Q
BPP QQ .
=−
=−− −
1
1
(
)
(
)
2
1
2
1
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