Game Development Reference
In-Depth Information
Given a constant wave speed c , the time step t must satisfy
2
2
2
μ μ cd
++
32
0
<<
t
.
8
cd
2
2
Internal Forces for a Cloth Particle
A particle of mass m at a point P connected to another particle at the point Q ex-
periences the forces
QP
(
)
F
=
k
QP
d
QP
spring
spring
and
(
)
dd
QP
F
=
k
,
damper
damper
dt
dt
where d is the rest length of the spring connecting them.
External Forces for a Cloth Particle
A particle of mass m having a velocity V experiences the force
(
)
F
=+
mk
g
WV
−⋅
N ,
extern
wind
where g is the acceleration of gravity, W is the velocity of the wind, and N is the
surface normal at the particle's location.
Exercises for Chapter 15
1.
Suppose that the fluid surface displacement of each vertex in a triangle mesh
is evaluated 20 times per second. If the distance between neighboring verti-
ces is 0.1 m and the viscous damping constant is
, what is the maxi-
mum wave speed for which Equation (15.25) is numerically stable?
1 μ
=
1
2.
Suppose that the distance between neighboring vertices of a fluid surface
mesh is 0.1 m and the viscous damping constant is
1 μ
1
, as in the previ-
ous exercise. What is the maximum time interval between consecutive eval-
uations that allows a stable wave speed of 2m s?
=