Game Development Reference

In-Depth Information

p
i

n

p
i

n

p
i

μ

α

p
i
+

p
i

−

Figure 8.5.

Impulses at contact points (with friction).

Here
μ
can be negative, depending on the initial rope-slide direction; Fig-

ure 8.5 assumes that the rope slides from right to left. This yields

sin
α

μ
cos
α

sin
α
+
μ
cos
α
.

−

P
i

=P
i

(8.5)

Thus, for each vertex we get the “outgoing” impulse from the “incoming”

one. Expressing P
i
and P
i
through P
i
and substituting the results into Equa-

tion (8.4), we get the vector impulse applied by each body to the corresponding

rope vertex (the impulse applied by the rope to each body will be its opposite):

P
i

P
i
=((
d
i−
1
−

d
i
)sin
α
+(
d
i−
1
+
d
i
)
μ
cos
α
)

sin
α
+
μ
cos
α
.

Now we can use the same approach as before, which is to apply a test impulse

to the contact sequence, measure the velocity response, and then do the same

during the solving with a real impulse (of course, the impulse will no longer stay

constant from vertex to vertex—it will be changed according to Equation (8.5)

after each one).