Game Development Reference

In-Depth Information

x2

p=q

x1

p=q=x1

x2

Figure 11.4.
Resolved stick collisions.

by

x
1
=
x
1
+
c
1
λ
d
,

x
2
=
x
2
+
c
2
λ
d
,

x
3
=
x
3
+
c
3
λ
d
,

x
4
=
x
4
+
c
4
λ
d
.

The new position of the tetrahedron's penetration point
p
∗
=
c
1
x
1

+
c
2
x
2

+

c
3
x
3
+
c
4
x
4
will coincide with
q
. For details on the derivation of the above

equations, see [Jakobsen 01]. The above equations can also be used to embed the

tetrahedron inside another shape, which is then used for collision purposes. In

this case,
p
will be a point on the surface of this shape (See
Figure 11.5
)
.

Figure 11.5.
Tetrahedron (triangle) embedded in arbitrary object geometry touching the

world geometry.

In the above case, the rigid body collided with an immovable world, but the

method generalizes to handle collisions of several (movable) rigid bodies. The

collisions are processed for one pair of bodies at a time. Instead of moving only

p
, in this case, both
p
and
q
should be moved towards one another.