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?

=

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